THE THEORY OF PRICE

tlaird edition

George J. Stigler

The University of Chicago

The Macmillan Company, New York

Collier-Macmillan Limited, London

(-} 13 ~~I

\ c .~2. -~ '~ "

© Copyright, George J. Stigler, 1966

All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical including photocopying, recording or by ' any information storage and retrieval system, without permission in writing from the Publisher.

Fifth Printing, 1968

Earlier editions copyright 1942 1946 1952 by The Macmillan Company. ' '

Library of Congress catalog card number: 66-19406

THE MACMILLAN COMPANY COLLIER-MACMILLAN CANAD~.E0£~~RONTO, ONTARIO

Printed in the United States of A . mer1ca

Prefaee

Not only a man's ideas, but also his ways of ex­pressing them, have a strong persistence over time, so it is possible for the statisticians to determine disputed authorship (as in the case of the Federalist Papers) by the pattern of words and the structure of sentences. I have rewritten the present edition almost completely, but I have no doubt that it is the same book, and by only a slightly different author. Its distinguishing feature continues to be its concentration upon the traditional central core of economic theory-the theory of value. I thank Sam Peltzman for helpful suggestions, Julius Schlotthaue1· and Richard West for doing much of the graphical work, and Claire Friedland for her assistance at every turn.

G. J . S.

v

£ontents

CHAPTER ONE

Introduction to Economic Analysis CHAPTER TWO

The Tasks of an Economic System CHAPTER THREE

Consumer Behavior

CHAPTER FOUR

The Theory of Utility

CHAPTER FIVE

Pricing with Fixed Supplies CHAPTER SIX

Costs and Production CHAPTER SEVEN

Production : Diminishing Returns CHAPTER EIGHT

Production: Returns to Scale CHAPTER NINE

Additional Topics in Production and Costs CHAPTER TEN

The General Theory of Competitive Prices CHAPTER ELEVEN

The Theory of Monopoly

vii

1

11

21

46

85

104

121

146

162

176

195

viii CHAPTER TWBLVE

Oligopoly and Barriers to Entry CHAPTER THIRTEEN

Cartels and Mergers CHAPTER FOURTEEN

The Demand for Productive Services

CHAPTER FIFTEEN

Rents and Quasi-Rents CHAPTER SIXTEEN

Wage Theory CHAPTER SEVENTEEN

Capital and Interest CHAPTER EIGHTEEN

The Size Distribution of Income

APPE~DIX A

Fundamental Quantitative Relationships

APPENDIX D

Mathematical Notes

Index

247 Tlte Theory of Price

257

275

288

313

337

349

chapter one

Introduction to Eeonomie Analysis

A THEORY

Suppose a person wishes to buy a new automobile, and has de­cided upon the make, the body style, and the accessories that he desires. If now, in an excess of diligence, the buyer higgled with every dealer in a large city, he would encounter a considerable array of prices. In one such experiment in Chicago, thirty dealers offered prices for an identical automobile ranging from $2,350 to $2,515, with an average price of $2,436. Obviously the buyer would purchase at the lowest price, if the services of dealers were identical.

But this buyer was atypical and foolish. That he was atypical is a statement of fact, easier to believe than to prove. That. he was foolish is an economic-statistical proposition: if shopping for low prices is not a sheer pleasure, the buyer will soon find that the probable savings from searching further do not compensate for the cost. To visit only thirty dealers requires at least two or three days; if we had chosen a hardware staple the number of dealers would have been in the hundreds and a full canvass would have required several weeks.

So the costs of semiexhaustive search (what of the suburbs?) would be high. The returns would show "diminishing returns"-the lowest price the buyer found would fall more slowly as he expanded the number of dealers canvassed. This is the statistical proposition, which need not be proved here, and is in any case plausible: as one canvasses additional dealers, the lowest price he finds will on average fall but each additional dealer is more likely to quote a higher price than the lowest price already encountered.

1

2 Introduction to Economic .A. . . 1'lalytit

This is simple common sense, which the econorrust translates i the language: lltQ

To maximize !1is utility, the buyer searches for additional prices . the expected savmg from the purchase equals the cost of yjsiting on lln!iJ dealer. Then he stops searching, and buys from the dealer who e Illote the lowest price he has encountered. QUotes

That this rule maximizes utility may be shown, the economi t by considering its failure. If the canvass of an additiona~ · says, wi!l save more_ (on average) than the ?o~t of the canvass, the ~~ller gatns by making the search. Contrariwise, if the cost of a Yer exceeds the prospective gain, the buyer would gain by s seah~ch 1 h . earc tn ess. And ere the trouble begms-for the noneconomist. g

For, first of all, where did maximizing utility come fr ? h. )· · h · om The answer, w tc 1 IS t at It came from experience with sim'l

I 'II . . I ar prob ems, w1 not satisfy a noneconomist. He will say that people t :

ca1Iy do not maximize anything-that the consumer : 1 YPI· d · t d b d · IS azy or omma e y a vertlsers or poor at arithmetic And inde d th

h · e ere are consumers w o not only suffer from these disabilities b t d · ht f d WI u are also ownng con use . 1y attribute to them the cold-bl d d 1 · cal approach of a well-built modern computer? oo e ' ogt-

Second, what precisely is the cost of canvassing one m II All one h d to d · d · · ore se er?

. a . o Is rive over to another dealer and talk to him for_ a few m~nutes. How can a monetary value be placed upon the achtwns-whJCh are pleasant for some people and distasteful tse ot ers? o

Finally, do~s not the economist merely say, in language that is rather pretentious (when he does not use formidable math f I symbols)' that the buyer will visit as many dealers as he vi::~~: more, no less? The rule does not say whether he visits one seller. or every

Th_is is a. wh~lly typical economic theory and a wholly typ' I reactiOn to It. Smce economics is stili tau 1 . Ica have replies to these cr·r .

1. · g_1t, we economtsts must

are they? The basi . I JCisms :v ll~h w~ thmk are adequate. What complaint (that the \~:~~Y, wh~ch Is dtrected chiefly to the third is that that the tl . d y metely says people do what they do)

1eo1 Y oes more than th · · t ' how consumers (and markets) ' II b ~s: l enabl~s us to predict proposition: WI e ave. Constder again the

A Theory 3

To maximize his utili ty, the buyer searches for additional prices until the expected saving from the purchase equals the cost of yjsiting one more dealer. Then he stops searching, and buys from the dealer who quotes the lowest price he has encountered.

The cost of searching out one more price varies-it will be more with higgling than without, for example. But it will vary much Jess among commodities than the gain from a 1 per cent saving in price varies among commodities. On an automobile, 1 per cent is perhaps $25; on a washing machine 1 per cent is perhaps $2. So any person, the theory predicts, will search more for low prices when buying an automobile than when buying a washing machine. A person who enjoys shopping may visit 10 automobile dealers and three appliance stores; one who does not may visit three automobile dealers and one appliance store-but in each case the consumer will search longer before buying the automobile. This is a testable implication, and if the facts contradict the prediction, the theory underlying the proposition is wrong.

Again, since buyers will search more for low prices on commodi­ties which take more of their income, any seller who quotes a price that is high relative to other sellers' prices will sell little-most buyers will search on to find a lower price. So the theory predicts that the range of prices of washing machines quoted in a city's retail outlets will vary more (relative to their average) than the prices of automobiles. This too is testable-and much less obvious than the first prediction.

Suppose we make the tests and find that the predictions of the theory are right. Then clearly the other two objections which were raised also lose their force. The consumer has indeed been acting "rationally"- which is another way of saying that he has been max­imizing utility. (The reasons for introducing utility will be discussed in Chapter 4. ) No doubt some silly people have even paid the higher price after canvassing two sellers, but the dominant tendency must have been to search to a degree governed by costs and expected returns, and act sensibly on the information, or the tests would not have been passed. The consumer must have been able to attach a workable meaning to costs, or the predictions would have been contradicted: the dispersion among sellers on prices of commodities like washing machines would have been as small as for automobiles.

4 Introduction to Economic Analy~

Let us now actually test the theory. The standard statisticalrn . . tl m . t f . t' ea.

sure of relat.ive dispersiOn IS 1e coe c1en o vana wn: the st dard deviation of a group of observations divided by the ave an. . . b t I rage of the observations. One Illustrative u rea set of data for th

second test may be given: e

COMMODITY

Automobile Automatic Washing Machine

AVERAGE PRICE

$2,436.00 223.45

COEFFICIENT OF VARIA 'l'ION

1.72% 3.42

One other objection to this theory, of the many that can be . d d . I b . con.

trrve . , now eserves notice. t m~y e said, ~hat the facts were already known and all the economist has done Is make out a f explanation for them. The answers are various. This objectioa:cfs not factually correct: the theory was contrived first and the f then sought: But it is_ not necessary for the reader ( economis:c~ non-economist) to dec1de whether I am telling the truth 1 Th

I • 1 . · e real

rep y 1s t 1at there are mfinitely many sets of data that b d

. . can e use to test the pred1ctwns. The reader can go out in his cit d collect prices of au_tomobiles and washing machines or (sine~ :~s general theory apphes to all homogeneous goods) prices of refr' t d . I . tger-

a ors an parmg (nJves. There are many other testable predictions of the theo~y . So a competent scientist need not, and should not accept theones (whether economic or physical) on fai th. '

And anyw~y, . although a fancy theory is not so good as a simple ?ne (more thmgs can go wrong with the fancy one)' a fancy theor ts better. than none. Let the reader try to contrive an alternativ~ e_xplanatwn of the f~ct that prices of washing machines vary rela­tively more than pnces of automobiles. He may come up with a ~ul~ such as : the more expensive the commodity, the less its price •anes, that seems to fi t our facts- in fact it makes the sam d' t' B t · · • e pre IC-. Ion.. u qmte astde from the fact that it has no logical basis lt Will be wrong: the price of sugar varies much less than that o_f tea, although sugar costs less per pound. Thjs is not a contrad· -tJOn of our theory, which in a fuller version says that the aggreg~~e amount spent on a commodity governs the amount of search 2

' The data are from two articles b All F . <O,ctober 1958_ and January 1960). Y en · Jung, Jo urnal of Business

And also, m this fuller version t Jls should be added. See my "The E e ~s over what ti~e period the purchases cal Economy (J une 1961). conomJCS of InformatiOn," Journal of Politi-

D

Science as Fiction 5

sCIENCE AS FICTION

A useful general mle, which is all that a scientific theory is, has two properties. First, it ought to be more or less true. Second, it ought to apply to a fairly large number of possible events. Most of the anguish that people have with scientific theories arises be­cause these two conditions are moderately incompatible.

It is easy to make up empirically ''alid rules: for example, the Dow-Jones average always falls on .January 25, 1960. It is even easier for a trained person to make up broad rules: for example, business declines always begin in odd-numbered years.

3 The combi­

nation of the two characteristics is more difficult to achieve. Indeed the combination is, on a strict view, impossible. Every

event, every situation to which a theory can be applied, must differ in a thousand respects from every other. Consider our proposition that consumers canvass more sellers for a lower price when their expenditures on the commodity are larger. Does this apply literally to an invalid, or to a man who wishes to buy something the morning after a 30-in. snowfall? Does it apply literally to the man who gets things 11wholesale" from his brother­in-Jaw, or to the young man and young lady who urgently seek the services of a justice of the peace? Or does it apply equally to the millionaire and the pauper seeking a cup of coffee or to the same man whether buying a meal on his own or on an expense

account? Or to postage stamps? Clearly a general theory must ignore a thousand detailed vari-

ations or it cannot possibly be general. Yet only general theories are useful. In fact general theories are the only useful theories even if they are to be used only once. Suppose, to use a reprehensible example, I embezzle a fortune with which I shall (1 ) engage in a bold speculation and (2) prosper and reimburse the bank or (3) spend my declining years in custody. I wish a theory of capital gains, whether from horse racing or roulette or futures in soybeans. If the "theory" I act on says only that soybean futures rise next week, there is no possible way to test its reliability in advance. But if the theory says that a particular inventory level relative to sales leads to a price rise, I can test it against a dozen previous

instances and get some idea of its reliability. 3 Such as 1837, 1873, 1907, 1929, 1937, and 1960.

6 bttroduction to Economic Analy~

For the scientist seeking to construct or improve a theory tb· fact that theories cannot be "realistic" in the sense of being de~ .

18

d f . crtp.

tive, is a source of endless charm an. . rustratwn. It inevitabJ poses the question: what common tra.1t m the phenomena sho { be incorporated in th~ theory? ?houl.d we, to revert to the sea~~ for low prices, emphasize the natwnahty of consumers, their poss sion of automobiles, t heir years of formal education or- as es. did-the amount they spend on t he commodity? We

The user of a theory has a simpler task: his is not to reas why, his is but to sigh and try. If the right element in the diver~n situations has been isolated, t~e t heory will work: ~t will yield pre~ dictions better than those wh1ch can be reached w1th any alterna. tive theory.

Suppose the alternative theory is very poor: it may be, for exam. pie, that the amount of search for lower prices is a random event normally distributed, and that it yields predictions which bav~ hardly any relevance to the facts?~ The answer is t hat it takes a theory to beat a theory: if there is a theory that is right 51 per cen_t of the time, ~t will be used until a better one comes along. (Theones that are rtght only 50 per cent of the time are less economical than coin-flipping.)

vVben we assume that consumers, acting with mathematical con­sistency, maximize utility, therefore, it is not proper to complain that men are much more complicated and diverse t han that. So they are, but if t his assumption yields a theory of behavior which agrees tolerably well with the facts, it must be used until a better theory comes along.

Economic theories are infinitely diverse in their predictive power. Entirely too many have zero predictive power-they are st-atements of tautologies. T hus, the statement that to maximize profits one should operate a firm where marginal revenue equals marginal cost is a mere mathematical theorem. Some theories have negative power: they predict the opposite of what happens (and then become useful in the hands of a sophisticated user). Thus t he statement of a chancellor of the exchequer that the nation will never devalue the currency is a traditional prelude to devaluation. At the other

.. Such simple o.l~ernntives--nnother is that whatever happened last time Will happen next (!me- are caiJed "naive" models, a terminology due to Mil­ton Fnedman.

a

Some Apologies 7

extreme, the simple rule that people buy more of a thing at a lower than at a higher price is (properly used) a completely universal truth. The essence of scientific progress is to edge up this ladder from ignorance to knowledge, and it is complicated by the fact that the ladder keeps getting longer!

SOME APOLOGIES

The goal of the economist is not merely to train a new generation in his arcane mystery: it is to understand this economic world in which we live and the other ones which a million reformers of every description are -imploring and haranguing us to adopt. This is an important and honorable goal.

It is not an easy goal, however, nor one which is now or ever will be fully achieved. A modern economic system is of extraordi­nary complexity. Imagine a three dimensional jig-saw puzzle, con­sisting of roughly 100 million parts. Some parts touch against, let us say, 1,000 other parts. (That is, each family deals with thnt many employers, banks, retail stores, domestic servants, nnd so on.) Other parts touch, let us be conservative, 50,000 other parts. (Firms that sell to retailers and buy from other firms and hire laborers, and so on.) It would be enough of n task to fit these 100 million pieces together, but the real difficulties have yet to be mentioned. The pieces change shape quite often-a family has twins, a firm does the next best thing and invents a new product. The economist has the interesting task of predicting (in the aggregate) each of these movements. Meanwhile a busy set of people--congressmen, members of regulatory bodies, central bankers, nnd the like--are changing the rules on who the jig-snw pieces will be and bow they are shaped. And of course there nrc other jig-saw puzzles of com­parable complexity, and these other puzzles (foreign economies) are connected at literally a million points with our puzzle.

This analogy is imperfect in many ways-for e.xnmple, it suggests t he fitting together of units of economic life when in fact it is the working together of parts (some sort of gigantic set of gears) that would be more appropriate. Its biggest deficiency is that it does not portray the fact that a change in the relation between two pieces ·will affect other pieces which touch neither of them: thus a change in wage rates in the steel industry will affect (through

8 Introduction to Economic An l Qy~

a variety of economic relationships) the output of crude petrole Yet even with its deficiencies it may convey some sense of the c Utn. • te Otn, plexity of a modern economiC sys m.. . .

The economist nnd his brethern m the social sciences hav '. . . ' e a second level of d1fficulty not shared by the physiCal sciences. 0 main elements of analysis are people, and people who are influen ur by the practices and policies we analyze. Imagine the problemscect

3 chemist if he_ had to de~! with mol~cules ~f ~xyg?n, each of whi:~

was somewhat mterestcd 10 whether It was JOmed m chemical bo d to hydrogen. Some would hurry him a long; others would cry shri~ for a federal program to drill wells for water instead; and sever~ would blandly assure him that they were molecules of argon. A d this chemist, who in analogy would also be a chemical element, cou~d n~ver be absolutely certam tha~ he w~s treating .other elements fairly. Several elements would lnre the1r own chemists to prote t t~eir interests. We ~co~omists h~~e al_ways had the advantages ancd d1sadvant~ges of this !Ively par~ICipatwn by our "units of analysis."

It re~mres no speCial apologies, therefore, that many important econom1c ph~nomena cannot. be explained, or explained only imper­fectly. In ~Ills respect all sciences are alike. That some important a.nd pervas1ve phenome~a can be understood is sufficient justifica­tiOn for the set of theones and techniques which comprise moder

. I . n economic ana ysis.

T o a much greater degree than the other social sciences, economics has developed a formal an? abstract and coherent-corpus of theory. The standards of both logical precision and empirical evidence are steadily ri~ing. Splendid as this trend is, it makes life no easier for the wnter of a t extbook. Adam Smith, the founder of the sci­ence! could (in his Wealth of Nation.~) write in these words about ~he Jmmense increase in output achieved through division of labor

m Western societies :

~f we examine, I say, all these things, and consider what a variety of labour 1:,~mploycd about each_ of them, we shall be sensible that without the ~::;.-;tsta~~e. and co-operatiOn of many thousands, the very meanest person 10 a etvthze~ co~try could not be provided, even according to, what we very falsely tmagme, the easy and simple manner in which he is commonly :~commoda~d. Compared, indeed, with the more extravagant luxury of e c ~reat, hts ~ccomrnodation must no doubt appear extremely simple and asy, and yet It may be true, perhaps, that the accommodation of a Euro-

9 Some Apologies penn prince does not always so much exceed that of an industrious and frugal peasant, as the accommodation of the latter exceeds that of many an African king, the absolute master of ihc lives and liberties of ten thou-

sand naked savages.

A modern economist who hopes to maintain the respect of his col-

leagues will rewrite this:

The difference between the mean income of Habsburg males (1871-1917), not cotmting uniforms, and the mean income (after taxes) of fanners owning an equity of at least 10 per cent in a farm with no more than 12 hectares (11 in Bavaria), excluding dairy farmers, in I90i-15 was $1,800 (in 1914 dollars). The income of African tribal lenders, using the mean of Pa.aschc and Laspeyres indexes (which diverge enormously) fell short of that of the farmers (in 1904-10) by $2,400 (but only S1,400 if we use Kuznets' estimate of the value of a second wife) in 1914 prices. The difference between the means of $1,800 and $2,400 is significant at the 3 per cent level. Incidentally, a tribal leader had an average of 10,000 (±721) members of the tribe in 1908, and they were clothed only by an average of 6.2 sq. in. of cotton bagging. [14 footnot~s omitted.]

I will not say, and you would not believe, that t his change is an unmixed blessing. It is an advance from the scientific viewpoint, however, and the example itself will serve to show this. My own version is pure fiction, but as soon as one starts to think of numbers it is obvious that Smith's statement was wrong. The income of a peasant family in Europe in 1776 (when Smith wrote) was surely less than (say) $500 of present-day dolla rs, and that of an African king was surely not less than zero; so Smith is asser ting that princes had incomes less than $1,000. Even nonstatistical evidence sheds

lavish doubt on this.r.

5 The following quotations-from W. H. Bruford, Germany in the Eighteenth Cent1tTV (Cambridge, England: The University Press, 1935)-may serve:

On peasants he quotes several con temporaries : "The fields and the live­stock provided the necessary food and clothing .... Women spun wool into coarse cloth; men tanned their own leather. Wealth only existed in its simplest forms ... . From morning till night [the peasant) must be digging the fields, whether scorched by the sun or numbed by the cold ... . The traveller comes to villages where children run about half-naked and call to every passer-by for alms. Their parents have scarcely a rag on their backs .. .. Their barns are empty and their cottages threaten to collapse in a heap any moment." (pp. US-21) One noble will do : "Ora£ Flemming, for instance, Generalfeldmarschall under Augustus the Strong, tlle soldier and diplomat who secured for his mastet· the throne of Poland, ... had [in 1722] about a hundred domestics

10 Introduction to Economic Analy~

The corresponding illustration of the need for formal analyti 1

methods to ensure reaching correct conclusions will be illustra:~ at many points in subsequent_ cl1apters. Here let us give a centu;~ old statement of a tl1eory that JS still very popular:

For the most par!',. [employers]_ so far accept the principle of "live and Jet Jive" as to be wJ!hng that their labourers should have any wages th will not sensibly encroach on their own profit. In fact, it is of little cons:: quencc to them how high the wages of labour may be, provided the Pri of tl1e produce of labour be proportionably high. But if among rna ce Iibeml employers tl10re be one single niggard, the niggardliness of thn~ single one may suffice to neutralise the liberality of all the rest. If 0 a single employer succeed in screwing down wages below the rate previous~e current, his fellow-employers may have no alternative but to follow su{ or to see themselves undersold in the produce market.•

1 '

The first sentence is merely cruel, the second sentence is wron and i_he th_ird and fo_urth are grossly fallacious. Yet ask a perso~ un tramcd m econormcs what the merits of these views are and he will usuall_r be unable to arrive at any persuasive judg;nent. At a_ later pomt we shall analyse the fallacy with the assistance of fa1rly elementary analytical techniques:

Some frequently-employed quantitative concepts and re1ation­ships in economic analysis are presented in Appendix A; mastery of this material is a wise investment.

of _different gra~es. There were twenty-three 'superiores,' from an Oberhof­meJStc:, secrctanes and t~!o~s ~own, to an equerry responsible for ninety-two horses, and over seventy mJer;ores, from the lh•c pages and a 'Polish gentle­rna~' wh~ played the Bandor and waited at table, the eight musicians and the1r I tal1an leader, .... The count's &'llaries and wages bill came to 13 534 Thalcrs a ~·ear [say ~60,0001. The appoint.mcnts of the count's palaces ,;ere correspondingly magDJficent; l1e lived on a scale that would make the life of,a Hollywood millionaire look tawdry." (pp. 77-78)

W. T. Thornton, On Labour (London: Macmillan, 1868), p. 81.

chapter two

Tl1e Tasks of an Economic System

The list of things that one can "demand" of an economic system is limited only by the human imagination, itself a fairly outrageous thing. Madmen and/ or reformers have insisted that the economy must produce quite impossible things, such as more than the average amount of housing for everyone. Even calm men, well­acquainted with the laws of arithmetic, have assigned tasks which are adequately diverse. Some wish the economy to elevate the tastes of consumers-drawing them away from comic books to­ward conic sections, from gadgets (mechanical devices not worth their price to the speaker) toward symphony orchestras (which pro­duce music worth less than its cost, and hence is a lmost everywhere subsidized) . Others, again, wish the economy to foster political val­ues : such estimable entities as Thomas J efferson and modern Swit­zerland have believed that an independent agricultural class would be the mainstay of a stable democratic system.1

Ambitious views of the role of the economic system are based upon a sound, a lthough often an exaggerated, instinct. An economic system assuredly influences much of what people call "non­economic" aspects of life. For example, the systems of reward for personal efforts will surely influence the kinds of education that the population desires and receives. When one pauses to realize that well over half the waking hours of mankind have been devoted to earning a livelihood- the fraction fell below a half in the United

' Karl Marx carried this approach to the extreme of asserting that an eco­nomic system hnd within it a set of forces which irresistibly transformed all society. His peculiar limitation on t.his view-that only one more transfor­mation would take place (to coromunism)-chunged t.he view from a hypothe­sis into propaganda..

11

• I I

12 The 'Tasks of an EconomicS

. . . Y8te'll!. States only in this century-It JS obvwus that the economi . of life cannot be separated cleanly from the political cuJct Side ' uraJ and other sides of life. '

And equally, almost every widely held view in "nonecono . · 1· f I h U lll!c''

areas leaves its traces on economic 1 e. n t e nited States th output of playing .cards was reduce~ by a h~avy fe~eral excise ~e because card playmg has been considered fnvolous 1f not imrn ' . . oral The output of newspapers on the other hand, IS mcreased b · heavily subsidized postal rates on the ground the newspapers 'i

· f d · t' A st d f · · are necessary to an m orme CI 1zenry. u Y o activities which tax exempt, or of occupations and industries which are given prere entia! treatment under wartime conscription, would reveal a wh e~­range of such opinions and effects.

0

e We shall not discuss the tasks of an economic system in ter

so broad as these. These wider tasks vary greatly from time to ti:: ~n? p_lac.e to place, but one, more .narrowly defined set of tasks 1s mtrms1c to any and every economic system. These intrinsic tasks are fundamentally four: (1) fixing the composition of output· (2) allocation of resources; (3) distribution of the product; and (4) growth.

FIXING TilE COMPOSITION OF OUTPUT

An economic system has at its disposal a set of resources-labor natural resources, and capital. These resources can always be used to prod~ce a variety of products-even a primitive agricultural commumty can choose betw.een more meat or more grain, more food or more lumber, more housmg or more wars. In a modern society, the adv~nces of technology have created an almost unlimited num­?er o~ different ~o~modities and services, and they can be produced m a literally unhm1ted number of propoitions.

The first. t~sk of every economic system is therefore to establish the compositJon.,of _ou~~ut;, A noneconomist often says, of such prob­lems, .that the pr~ontJes must be established, implying that the most ~mportant thmgs be ascertained and produced, then the next ~ost Important. things be produced, and so forth until either the esources are mcapable of producing more or-inconceivable ~~ate-eve1:y?ne is sated. The language of prio~ities has the merit

emphasiZing the fact that values (estimates of importance or

Fixi11g the Composition of Otttput 13

desirability) have to be attached to various outputs, but it has the defect of grossly simplifying the t ask.

If I were to try to construct a scale of priorities of categories of consumer goods to which most of mankind (or at least my dear­est friends) would subscribe, it might begin confidently something

Jike this:

I. Food-to keep alive n. Shelter and clothing (in cold climates)-to keep alive

II I. Medical care-to keep alive IV. Police protection-to keep alive V. Education-to keep teachers alive

and then stop suddenly. Long before I had to face lihe problem of whether an air conditioner was more or less important than at­tractive furniture or an automobile, I "\Yould have to recognize the deep ambiguity in what I had already ·written. Food certainly has a primacy in survival under ordinary conditions, and most men esteem survival, but even the most gluttinous men would prefer some clothing and shelter, on a -10° F day, to a twentieth helping of potato dumplings. And so it goes through the list: medical care sounds very basic and important, but do men really think that a family with funds just sufficient to straighten a boy's teeth or send him to college should always choose the former alternative?

So the fixing of the composition of output amounts to much more than simply giving priority numbers to various categories of goods. It involves the much greater task of deciding how each increment of output should be composed. I n effect one must approach the problem this way : assume that we can produce a totnl of outputs somewhere about $500 billion.2 How should the first billion of out­put be composed, then the second, and so forth to the 500th. The first billion will be dominated by food; the 500th billion will-if we use numbers appropriate to the United States-contain less than $200 million of food.

Who fixed the composition of output? In our society, where men are relatively free to choose their own goods,. and the productive system responds to these choices, it is done by the individual con-

'How diverse kinds of output are added together to obtain a single number is discussed much later.

14 The Tasks of an EconomicS Yatetn

sumer (household). A man indicates, by the price (amoun money) he offers for a good, the importance he attaches to a t of unit of the good. If he offers $15 for a pair of shoes, and ~~~ther a hat, he indicates that he believes a pair of shoes is l .S t" for as important as a hat. Obviously how much he will offer to lllles

for n unit of a commodity (a subject we investigate in Chap~l' 3 and 4) depends, among other things, on how many units of ~ commodity he already possesses. This system is usually descr~~c as one of consumer sovereignty, and if one does not read into t~d phrase the extreme view that the consumer is uninfluenced by tr ~ dition, social opinion, advertising, and the like, it is valid enough~

Our society does not rely exclusively on the preferences of indi­vidual consumers. In some areas the composition of output is fixed by. political decisions: highways, schools, and police protection are examples. In still other areas the political system imposes limite on the choices of individuals, sometimes for reasons of public safety (guns), sometimes for reasons of distrust of the individual's com­petence to make wise decisions (the electrical wiring of houses, the sale of prescription drugs, and so on), sometimes to please impor­tant groups (the prohibition of certain activities on Sunday).

In other societies and other times this sort of political regulation of the composition of output has gone so much farther as to be almost a difference of kind. In a war economy there is much central direction of the composition of output: the production of automo­biles and refrigerators is prohibited, and the outputs of many goods are limited and allocated by rationing. In a dictatorial society the extent of control over the composition of consumers' goods can be highly variable: it will always prohibit some commodities (for ex­ample, books highly critical of the regime) but often influence the composition of others by taxes, output quotas, and the like.

THE ALLOCATION OF RESOURCES

Once a set of values have been placed on various outputs, it is necessary to organize production so that proper proportions of these outputs, and not other goods or wrong amounts of the desired goods, will be produced. This might appear to be a t ask simple enough to be assigned to technicians: why not ascertain the quantities of

The Allocation of Resources 15 each resource necessary to produce a unit of each kind of product, and then allocate enough of each resource to the making of each

product? . . . . . This delegation to techmctans would mdeed be poSSlble, but it

would not be wise. The task of production also depends upon val­ues: there are generally many ways in which to produce a com­nodity: one can vary t he raw materials; use different qualities ~f ]a bot•; use different kinds and amounts of machinery; locate the plant in a thousand ~Jlaces; a~d so forth. The ~ethods of production that an engineer mtght cons1dcr most "effictent" would probably leave large amounts of certain types of resources unemployed-and therefore lead to a smaller output of commodities than could other­wise be achieved. The choice of production methods must take ac­count of the importance of the inputs as well as that of the finished

FOd& . . In addition the t ask of production consist~ of more tha~ s1mply

producing an assigned schedule of goo~s. Outputs of agr1cultural products vary with the weather-how b1g an allowance for safety should be made by having extra stocks? Demands for goods fluctuate

b Use of chance events-for example the replacement demands eca "I d" t d created by tornados and earthquakes are n_ot east y pre tc e ·.

We have tacitly assumed that the desued outputs are htghly stable, aside from chance fluctuations. But what if consumers may change their preferences next month ?-th~n what sho~ld be ~ro­duced? Or suppose the methods of produ.ctJOn are changmg rap1dly

der the impact of advancing technologtcal knowledge-should we ~~ild the plant today or wait n yet\!" for n bctt~r one, or ten ye~rs f a still better one? The impact of uncertamty on production i~rnot a matter of technology alone; it involves costs a~d r~turns.

F" lly production consists of much more than turmng tro~ ?re intom:ut~mobile engines. It consists of retailing and se:vicJ~~ goods-together as large a pa_rt of our econ_o~y as prod~:~o~heir con~ists of supplying opera smgers, and ski mstruct.ors ·r th staffs of orthopedic surgeons. It i~vol~es the sal~s of sec~rl tes, e collection of debts, and the investigatiOn of foreign bma~ket.s. ch the

All the resources cannot be treated as tools. La or IS mfu . · d men have pre erences

most important resource m all economtes, an refer regular hours of as workers as well as consumers. One may p

The Tasks of an Economic Sy·t 16 "e~

k t} mav prefer irregular hours, one urban life anoth wor - ano 1er " . ' er rural' life. If these preference~ are to be taken mto account, the II . t'Jon of resources is complicated further.

a oca d · d ffi · How can we get the task of pr.o uctwn one e . Ciently? Since

duction involves judgments on mnumerable details (should J pro d' . oe or Henry become foreman?), a_nd rests on many pre 1~t10ns of the future it is not easy to contrive a good scale on whiCh to judg the efflciency of a productive system. Yet such a scale is necessary~ men are often lazy ; stupid men are often unaware of this fact · nepotism is a not uncommon problem; and so on. So the task of getting production done efficiently is not an easy one.

In our society, the basic method of organizing production is through the price system. Just as prices register the desires of con. sumers, so they register the desires of workers. If men prefer to "·ork in a small town, wages will be less there and employers will tend to move to small towns. If a given set of technologies leave some resources unemployed, their price>s will fall and it will become cheaper to use production methods tha t use relatively more of these resources. If there is a chance, say 1 in 10, that a crop failure will drive up the price of oranges, some men will hold inven­tories of canned or frozen orange juice in hopes of realizing the higher prices. The incentives and penalties attaching to the direction of productive enterprises take the form chiefly of p1·ofits-both neg­ative and positive-which are calculated to weed out the less effi. cient and increase the area of activity of the more efficient.

Our society does not rely exclusively on private efforts directed by prices to organize production. Quite aside from providing a legal framework (contract, property, methods of settling disputes), there are many social restraints on production processes. Since a monop­oly is free of the restraints imposed by competitors, there are anti­trust laws and public utility regulatory bodies. Some kinds of ' production processes are forbidden and others regulated for reasons of safety. A. simple example is the examination of the health and comp~tence of a irline pilots; the reader may find it interesting to examme why the owner of the plane is not believed to have ade­quate incentive to look after pilots' abilities. Only licensed persons may .enter many trades and occupations in an interesting mosaic that mclu?~s elementary school teachers (but not college teachers) and electnc1ans (but not physicists).

D · tribution of the Product 'fh,e lS

TflE DISTRIBUTION OF THE PRODUCT

17

G r (Te Bernard Shaw, the well-known I rish economist, had 1~ tb:~ far be would complain bitterly at the discussion of how

rea 1

po.::ition of output is determined in a private enterprise the con~ ~;consumer sovereignty" would have raised his volatile ec?~om)t.lle c;:overeignty of rich consumers, he would have said, and 5 ll'lts- ~ . . P . l·lt have quoted hts favonte author: be rmg c

r vork Jadv, for instance, having a nature of exquisite sensibility, A New • " · ffi h I d . . k t' eJecrant rosewood and s1lver co n, up o stere m pm . sa m,

ordelrs .andead o doo-. It is made: and meanwhile a live child is prowling for lei o . .d •

f tnd and hunger-stunted Ill the frozen gutter outs! e. bare oo "" Here is another instance of the benefit of the quantification of

( ni'cs· pal'ables and counter parables/ are a very poor way econm · • ' . t describe the distribution of mcome.) 0 It is a t.rifie too early in our wo1·k to j udge the merits of Shaw's

111I·1.1t.s on the distribution of income, either in 1889 (when the comp · · b · £ ·

age was written) or today. Assuredly the distri uhon o mcome pass . · · . . is a major task of any econmmc system, and almost every major economic reform movement rests on a proposal to change whatever

distribution is in existence. . But, important as the distribution of income is, .t~e Importance

is probably less from its influence ~n t he c~mpos1.t10n .of output than from its importance in production and m ethical JUdgments of an economy. This heretical view rests on the fact--for it is a fact--that as a very crude rule, if one family has twice the income of another, it spends t".:ice as much on every category of consump­tion. This is obviously untrue in detail: the richer family will not double its purchases of sal t and will more than double its travel abroad. But i f the crude rule is not pressed to the finest classifica-

' From Shaw's essay in Fabian Essays (London, 1950), p. 24. • A counter-parable: . . Dr. John Upright, the young physician, devoted every energy of his bemg

to the curing of the illnesses of his patients. No hours were too long, no demand on his skill or sympathies too great, if a man or child could be helped. He received £2,000 net each year, until he di£-d at the ngc of 41 from over-work. Dr. Henry Leisure, on t he t'ootrary, insisted that eyen pa­tientl! with broken legs be brought to his office only on Tuesdays, Thurdays, and Fridays, between 12:30 and 3:30 P.l'vi. He prefe~rcd to tak~ three patients simultaneously, so he could advise while pla,ying br1dge, at wh1ch he cheated. He received £2,000 net each year, until he retired at tbe age of 84.

I

18 The Tasks of an Economic S Yste~n

tion of expenditures, it has ample support. The percentage dist . tion of expenditures of families with high, low, and average inc tibu. in 1950 is given in Table 2-1. The effect of income on expend'otrnes

I d·t· I . I Urc is cxaggemtcd because ot wr con 1 wns a so vary With incorn . s example high income families bad 4 persons on average, low i~~o for families 2.7 persons. Even so the general agreement betwee llle three distributions is very pronounced. n the

T able 2- 1

Percen t age Distribu tion of Cu rrent Expen ditures of Ur ban F a milies o f 2 or .More Persons, 1950

CATEGORY ALL FAMILIES FAMILIES WITH INCOMES OF

$1,000-2,000 $7,500-JO,OQo

Food 29.6 35 .9 26.9 Alcoholic beverages 1. 6 1. 1 2 .0 Tobacco 1.8 2.2 1.4 Housing 11.0 13.8 9. 8 Fuel, light, refrigeration 4 .2 6.7 3 .4 Household operation 4.6 4.2 5.4 Furnishings and equipment 7.0 5.4 6.4 Clothing 11 .6 8.9 13.6 Transportation

Automobile 11.9 6.3 13.6 Other 1.7 1.8 2.0 Medical care Personal care

5.2 5.9 5.3

Recreation 2.2 2.4 2.1

Reading 4 .5 2.4 5.1

Education, formal 0.9 1.0 0.8

Other 0.6 0 .2 1.0 1.5 1.8 1.3

TOTAL 99.9 100 .0 100.1

The relevance of distribution to production on the other ha d :n.y be suggested by the fact that no tlwroughiy egalitarian soci:t; si:: ever bee? able to construct or maintain an efficient and progres­s s cconomJ.c syst~m. It has been universal experience that some 6 tern o.f ~Jfferenbal rewards is necessary to stimulate workers o~mumstJ_c e_c~nomies have even found it expedient to stimulat~

savmgs by mdJvtduals through rewards At n m h 1 t . shall · . . · "" uc a er pomt we tionalesxtamttne thef relatwn.slup of income distribution to the func-

ruc ure o productiOn.

Economic Growth

.ECONOMIC GROWTH

19

J. ]3. ]3ury tells us, in his cx_cellent The Idea of Progress, that throughout most of recordc~ history the idea of continuous and cumulative progress of mankmd, whether in science or in social or

nomic life, was absent, and that only in the sixteenth century e(co d chiefly in Western Europe) did the idea begin to gain au-an

1. .

thority. We who tve m ?n age when t~e idea of economic progress has reached the econ~micaliy most primitive and rigid economies

ust therefore be remmded that the task of providing growth does m . 1· f f . not really belong l? ~ur 1st o unctions intrinsic to economic life, and that most soCieties known to histo1-y have had economically unprogressive economies ..

But intrinsic or not, It has become a major t ask demanded of all economies: they are required (as sovereigns use this word) to provide technological ad~ances, capital accumulations, improved labor forces, and larger mcomes. So strong is this demand, that sometimes a method by which western nations become richer- in­dustrialization-is confused with the growth itself, and inappropri­ate industries that reduce a nation's income are adopted to increase it. And nations with unbroken histories of secular growth, such as the United States and Canada, now strive through a host of public policies to foster what was once a completely decentralized process.

The constituents of growth are basically two: increases in pro­ductive resources, and increases in the efficiency with which they are used. Both types of increase can be directed by a price system. The rewards for increasing the stocks of resources vary wit!~ the type of resource: higher earnings for bet,ter trained labor; divi­dends, interest, and capital gains for capital accumulation; large incomes for the discovery of new natural resources. The rewards for innovations are profits from a head start in a new trade or exclusive control for 17 years of a process by means of a patent (and control for 56 years by an author, through copyright). Such private rewards are supplemented by preferential tax treatment of research expenditures, subsidized exploration for minerals, and so forth.

There are many social problems involved in economic progress. Huge changes (which those unpleasantly affected call disruptions) are imposed on particular economic areas: the labor force on farms

..

20 The Tasks of an EconomicS

. Ystelrt in the United States has fallen by almost half smce 1910· th ber of engineers has increased almost ten-fold in the sa~le e n~lll-

f · f · Pertod

There are large tasks o m ormmg consumers of new Proct . laborers of new e~ploymen.ts, entrep~eneur~ of new technolou~~. The impact of rap1d economic growth IS felt m every part of gJ:s. life; family size, political attitudes, foreign relations.

5°CiaJ

I t is established practice in economics to postpone the a 1 . of the problem of growth until the analysis of the performana Ysts

b nee f

the first three tasks has een completed for an unch . . 0

(st.ationary) economy. The reason is simple: the proble anging growth are vastly more complex and in any event requ~s of un.derstan~ing of the working of a stationary economy. We

1;:u a~ th1s practice, and the final chapters of this book take us t O\lt

threshold of theories of growth. 0

the And now, on to the analysis.

chapter tbree

Consumer Behavior

We wish to explain the behavior of consumers, and one approach to this explanation would be to view the consumer (or household) as an enterprise. This enterprise obtains income from the sale of labor services or from hiring out capital and uses the income to purchase commodit ies and services which will efficiently serve the desires of the household. It would of course be bizarre to look upon the typical family-that complex mixture of love, convenience, and frustration-as a business enterprise. Therefore economists have de­voted much skill and ingenuity to elaborating this approach, and we shall sketch it in the next chapter.

There are other approaches to the study of consumer behavior, but before we choose one it will be wise to ask what questions we wish to answer with our theory of consumer behavior. As econo­mists, our questions are chiefly of two types:

First, will consumers initiate important changes in the economy spontaneously? If so, will these changes be sudden or gradual? If the consumer is an important source of economic change, naturally we should seek to discover the factors that explain changes in con­sumer behavior, whether they be in religion, political life, changing technology, or other "noneconomic" areas.

Second, how will consumers respond to changes in their incomes or in the prices of goods and services? Will their responses be stable and consistent, or volatile and inconsistent?

The answers to these questions are far from complete, but this chapter will summarize the ruling views of economists. One may say that consumers are generally viewed as passive adapters to the

21

22 C onswner B h e au·

economy rather than as a~ents w~o indu~e changes in the be ~Ot of the economy, at least 10 the t1me periOds ordinarily c _ha\T!or Thus even the large decline in average family size (a decl_onsldered. . me wh· is at least partly a response to economic forces), which h tch to large changes in housing and other areas has been a 1 as led

te d h C . ' . · s ow a d

s a y c ange. onsumers are not revolut10naries like b · n

l. . 0 usme~s.

nova tors, on t us v1ew. ne would have more confiden . " tn. position if it were not so widely held that it has never ~: tn this oughly tested. en thor.

In their responses to price and income changes cons · tol bl · b ' umers beha m a era y _reba le and p~edictable way. They invariabl ve o.ne law as umversal as any m social life· they buy 1 f y obey

h · · · · · ' ess 0

a th" w en_ 1ts pnce. rtSes. The1r buymg propensities are a stable f ~ng of pnces and mcome, and we shall discuss these variabl . unction es m turn.I

THE PRICE OF THE COMMODITY

Th_e price of a product is simply the terms on wh. . acqmred. The oldest and most basic rule of demand tthch It ?an be eory Is that

• The modern economist has an aim . . . function in the language of mathemati~~ a~resJstJble urge ~o write this demand

where :z: is th • ' f x = j(p., p., p,, · · · , R), e ra.e o purchase of X . th pri~es of other consumer goods a~ P• IS. e price of X, p., p., .. . are the

~ expression states that if p;ices dan~ .IS the consumer's money income ~h purc~ase _of X is determined and thafc~mes ared fi..~ed, then some rat~

anges m pnces or income respon s m a stable way to

The symbolic statement· ~f the d d f . 1 I t · emnn unct1on se t . . IS a forcible reminder that rves wo purposes: :~:n~~ ~ c_onsuber purchases as

0~~~::~!n~eaft the effects of these deter·

be 2 per cen~~~~nc~~e ~=r~.~: ~~:~ the resul_ti;g ~:~r:a':~t7:r ~~~:8~; the 2. The notation helps us t d' . per cent If mcome is S8 000 may

: ~~:~: ii~ CO!IS~mer purei~as::t~~:~~ ~v~h~~ngs_ that _are• of;en confused: a consumer b~~:c ~:.s due ,to a change in tbegcd;~!nces or _income, IUid changing)-in this casee t~f : because its price has fall d ~unftiOn . _Suppose pose he buys more ( . e emand function is unch den ot ler thmgs not more-here a nel devcn at the same price) bee anhge : Alternat h•ely sup-c h v emand fu f h ause e hkes th ' · ase, e now will b 20 nc !On as appeared If e commodity function becomes uy per cent more at give~ , _to take ~he simplest prices and mcome, the

a new function. X- 1 2'( . ~ p., p., p,, ... I R),

. f the commodity 23 pnce o 'fh8 • t buY less, and usually buy more, of a commodity

1 '"Jll no peoP e rice falls. wbefl its P

1e · urchases of a commodity depend upon other factors

Sillce tl . p price we must specify these other factors, and we Jl as 1 ts ' l . f th l" as we

1 1 constant when t 1e pr1ce o e commoc 1ty changes

111ust bold ttlcdnue only to the price change is to be isolated. The

1 effec if t 1e 1

all hold constant are: {itctors we s 1

. es of other collliilodities.

1 'fhe pnc . OlleY income of the buyer. ? 'fhe Ill f h b ,. t.es or preferences o t e uyer. 3. 'fhe tas

f tl ese other factors will be discussed below.2

Each 0 ;e was stated t hat no one reduces the consumption of a 'fhe ru · f 11 d 1 · f I · · d · d d'ty when its pnce a s, an t us ormu atiOn IS es1gne

co~::e 1account of the fact that some commodities are indivisibl~. ~ family may still ta~t~ ~~1~ one copy ~f the n_ewsp~per '~hen its

. falls. Such indivlSiblhtieS offer no mterestmg dtfficultJes, but pnce 1 1 C . . it should be emphasized t 1at t 1ey are uncommon. ontmuous vari-ation in quantity can be approached even for a lumpy good by

one of several dev ices:

1. By using it only part of the time, say by rental or joint ownership. 2. By buying the item (say a haircut) with varying frequency. 3. By choosing a larger or smaller, or a more or less durable specimen.

Very few goods come in only one size or quality.'

For a market as a whole, demand curves are contjnuous even if every individual's demand curve is discontinuous, providing (as is surely certain) that not every individual varies his purchases at

the same critical price.

'Note that this is only one possible specification of the factors we hold constant. We might hold real income (to be defined later, but roughly an income yielding a constant am oun t of satisfaction) instead of money income constant, to get a different demand curve. Or we might hold the quantities rather than the prices of other commodities constant, to get another demand ~urve. Any well-defined demand curve can be used but the one described

m the .text is much the most common. '~h1s variation in quali ty does not yield a continuous demand curve {or a f given qu3:lity, of cour;;e. One must then talk of (for example) a quantity

0 automob1le, measured (by means of prices) in terms of, say, a specified

two-year old four-door sedan.

24 Consumer Behavi I hi 111 .or How can we convince a sceptic t 1at t s aw of demand'' .

renlly true of all consumers, a ll t imes, ali commodities? Not b~ f w (4 or 4 000) selected examples, surely. Not by a rigo 1 ae , . . ...

1 rolls

theoretical proof, for none e~osts--:Jt 2s a~ em~mca rule. Not bs stating, what is true, that. econonusts bei.Jeve 1t~ for we could ~ wrong. Perhaps as persuasive a proof as IS readily summarized . this: if an economist were to demonstrate its failure in a particulls market at a particular time, he would be assured of immortalitar professionally spcakin~, . and. rapid promotion. Since mo;~ economists would not dislike e1ther reward, we may assume that the total abse~ce of except~ons is not from lack ~f trying to find' them.• And tlus of course hmts at the real proof: mnumerable ex. amples, ranging from the wife who cuts down on s trawberries be. cause they are out of season ( = more expensive) to elaborat~ statistical inves tigations, display this result.

The "demand cmve" is the geometrical expression of the relation. ship between quantity purchased and price, and our law of demand says that demand curves Juwe a negative slope. {i Three demand' curves for the same commodity arc shown in Figur·e 3-1, corre­sponding to each different value of other p rices ( Y is a substitute} and income.

The responsiveness of quantity to price changes is measured by the elasticity of demand-the relative change in quantity divided by the relative change in price (see Appendix A). The elasticity of demand with respect to price is necessarily negative if quantity and price vary inversely. Can we say any more than that it will differ among commodities for any individual? The only general rule is tl1ttt the elasticity of demand will be (numerically) greater, the better the substitutes for the commodity. Suppose we divide a ho­mogeneous commodity, let us say gallons of identical gasoline into two classes: those from pump A and those from pump B. T he elas­t icity of demand for gasoline from pump B will be very high, hold­ing the price of gasoline from pump A constant. On two days, an

• Fo: the history of the one famous attempt, see "Notes on the History of th,e G1ffen Paradox," Journal of Political Economy, 40 (1947). by In terms of the full demand function, the demand "curve" is given

X = f(p. , Pu, p,, . . . , R), where the bar over each price and income means we are holding them constant.

> . of the Commodity

'f'he frtce

1' purchases will be . dividua s Jll PUMP A

Day 1 Price Quantity

30t 10 gallons

PU)fp B

30.1~ 0

Day£ 30~ 29 . 9~ Price . 0 10 g:\llons (at least)

25

Qunnttt.y . · . 't of demand of the individual for gasolme from

The arc eleastJcl y

P B will be pum o- 10

0 + 10 = -300. 30.1 - 29.9 30.1 + 29.9

bstitution is obvious, but how can we measur~ the Here the :~bstitution between non-ident ica l g~ods? There Js nn

goodness of 1 tJ.Cl.t"' of demn.nd winch we shall soon ·e the cross-e as J ' ' •

easy measm. ' . I fined in terms of consumcr·s' behavior and then~-discuss, but It

1~ ~ c d t explnnation of this behavior. There 1s fore offers nohm lep~n" l~nme~sure of substitution: not only is it diffi­no simple "tee no ogJC ...

0

Figu re 3-1

{R=$4,000

0 P. =$4 y

{R=$4,000

O R=$3 y

{R=$ 3,000

0 1?. =$3 y I 1

1 ' ! I

_ _j

Consumer Behav· u ~ cult to compare heterogeneous things (is radio a better substitute for television than for a theatre or a news!)aper?) h_ut substitutahiJ, ity varies with circumstances (a tract-or IS a substitute for a horse to a farmer, less so to a riding academy ).

This is only one of many places where economists have reached a general position without formal evidence, or even a measurable concept usable in a test. It is wid~!~ accepte? th~t coal has good substitutes (oil, natural gas, electnc1ty) but msulm does not, and that the former probably has a more elastic demand for this reason. When the Antitrust D ivision asked that Dupont be compelled to sell some 22 million shares of General Motors stock over a ten-year period, most economists were convinced that the effect upon the price of General Motors shares would be negligible, simply because these shares were such good substitutes for other "blue chips." This sort of intuitive estimate of substitutability will be encountered often in economic literature; the only sound advice to give the stu­dent is to accept these estimates when they are correct.

The Effects of Time

A given change in price will usually lead to a larger change in the quantity consumers buy, the longer the price. change has been in effect. One reason is simply habit-a shorthand expression for the fact that the consumer does not each day remake all his deci­sions on how he will live. Since the making of decisions is often a tolerably costly, experimental affair, this may be eminently rea­sonable conduct, but it delays the full response to price change.

Whenever a commodity is complementary to another commod­ity, moreover, a full ndjustment will be delayed for· the Jess durable good. A reduction in electricity rates could be reacted to instantly, but the fu ll effect will not be achieved until all the appliances with which electricity is used are purchased by the consumer-and it may be years before all consumers have bought electric water heaters or larger ranges, or built houses with lm·ger· windows.0

' The du~al~ility of appliances does not make t.he demand for appliances m_ore clasrrr.: tn lhe Ion~ run. I t i:> true that only a fraction of consumers WJ!I buy a gi v~'n durable good in lllly year, but their purchnscs will (habit ~srdc) ~c adjusted to the new price so lhc long-run demand cun·c is altninccl ~mmedrntcly. (The appearance of new customers, however, will lcMI to n hunch­lllg o! _purchase!> nf~cr n price rcduc:tion.) The delay in the adjustment of electrrcr ty c~nsumplron to price is d ue to the fact that it depends on the stock of apphanccs, not the annual rate of purchnse of appliances.

27 . e of the Commodity 'J'/Ie Prtc 1 . ffect by a simple example. Suppose con-

r l)av illustrate t 11S ed "nd curve (after full adjustment to \\ e I 'J l long-run em" have t le sunlers ' price)' q = 100- p,

. 3 2 The price has been $40, the quantity D · F1gure - · 1 . trated by u

10 S30 and only one-fourth of t 1e con-1llus : e now fa lls to '

0 The puc 6 .

p

40L-------------~ 30

0 0

Figure 3-2

- . able to adjust to this new price in sumers we shall assume, are the fir;t year. The quantity demanded becomes

ql = J.( lOO - 30) + i(l OO - 40) = G2.5. 4 k"

f the consumers (mu ·mg In the next year, let another 50 per cent o,. . the quantity de-75 per cent in n.II) adjust to the new puce, so manded becomes

q2 = "}(lOO - ao) + -}( lOO - 40) = G7.5.

28 Consumer B h e Q~ And in the third year, when all consumeJ'S adj ust to the n

ew Price qa = 100 - 30 = 70. 1

The demand curve for period 1, when only one-fourth of c adjust to the current price, is, for all possible prices onsulllers

qi = t(IOO - Pl) + !(100 - 40) = 70 - PI 4'

shown as D1 , and that for the second year is,

q2 = t(IOO - p2) + t(IOO - 40) = 90 - tp2,

shown as D2.7 It is apparent that these demand curves ar l t . th I h · d · e more e as Ic, e onger t e peno of adJustment,8 and this is surely tb general rule. e

Expectations of future prices will also influence consumers A simple example is the annual (usually January) sales of texti.l or the annual sag of new automobile prices as the model year ne:s, its end. Larger price movements are associated with the introdu~ tion of new goods: ball point pens, for example, were introduced at a price of $12.50 but within two years were available at Jess than a dollar.

0

But nonseasonal price movements are probably unim­portant in most consumer markets, and for two reasons. Most con­sumer expenditures-roughly two-thirds in the United States, and more elsewhere-are for nondurable goods and services, which are usually expensive or inconvenient to store, and yet are consumed

7

The general demand curve in year t with annually changing prices is q, = t(lOO - p,} + !(100 - p,_.) + HlOO - Pt- 2)

... 100 - ~ - ~ - !!.!=!. 4 2 4 '

so t.be current purchases depend upon prices in the two previous periods in this particular example. 8

At a price of $30, the elasticities of demand are: 1. Long run

dq p 30 dp . q - -1 . 70 = - 0.43.

2. First year after the price change

dq. PI 1 30 dpl. q; = -4 . 62.5 -O.l 2.

3. Second year after the price change

dq2 'P: 3 30 dp: • q2 - - 4 . 67.5 = - 0·33·

• See Thomas Whiteside, "The Amphibious Pen," New Yorker (February 17, 1951).

. f the Commodity he Pr-lce o

T . f ·mly through time. In the case of durable goods (house 29

fnirlY unt 01

st important and most durable), price expectations being the mo role and the expectation of continued inflation may larger ' . . . ha"e a e factor in the rise of home ownershtp.10 These pnce }lave been on usually represent extrapolations of recent price xpectations e 1. trends.l

b~Goo~ . Dura d f durable goods is implicitly a demand for thetr deman or .

The . of transportation or food preservation or shelter. . s-for years · t serVICe . . there will be an expected flow of serVIces, o gtven yeaJ ' b f In any . ttaches a monetary value. If we su tract rom . 1 tl e consume! a . d . wluc

1 1

1 f the services the costs of operation an repatrl h. gros.:: va ue o . . , t ts ~ . set of net services m successlVe years, ::;ay Y1, we shall obtam d a final scrap or trade-in value, s. Distant incomes Y2• Ys, · · : ' ant ~ back to the present if we wish the prese~t :alue must be discoun e r' If the appt·opriate interest rate ts 1, the this stream of sen ICes. . of t value of the durable good IS ~~ s

~ + Y2 ')2 + (1 ~ i)a + ... + (1 ~ i) " + (1 + i )" 1 + ~ (1 + ~ I

. n ex ected life of n years.t2 If the net va ue if the ser~ces .have at . t iill'ough time, and there is no scrap value. f the services ts cons an . o Th h. f financial gain from ownershtp

to This is not a simple problem. ~ d:) 11s in borrowing money ut fixed cferc:-ntial income t.ax ~rcatment aS! t tion of inflation (a.nd co~sumers [~~rest rates. But if there lS a g.ene~als!x~~n~) lenders will demand mterest

are usually not the first to expec . ) of the purchasing power of ~oney: rates which compe~sate fo~. the ~i~~~n:r homes will stimulate. owncrshtp on I) Hence the expectatlOn of nsmg /·1 to reflect the same expectatiOn. f to the extent that interest rates al . . ne sim le case may be sugges ~ve .

"The analysis of price expectatiOns Jn; to do ~o again in the next penod. Assume prices have risen and. ar\:SS~:nt period is a functio~ of (l) p:e~~ Then the quantity dema~ded ~~: th~ future price, say P!"• Jsf ~rha~~Yious rice and (2) future price. . l s some proportion o e P . ~a.ted to equal the present pnce, P•d• p u d in a linear demand fun ctiOn.

) Current ema.o • increase, say J\(p, - p.., ·

can then be written as _ + 1

+ c(p, + >.[p, - p,_.J) q, = a + bp, + CPt+l - a oJP•

= a + (b + c[l + >.))p, - c>.p,_~ h'gher future prircs arl' ex­since c is positive-peo.ple buy more [~o~,>.\ )\olbe positive even thou~h b pected to be-it is possible for (b + c ·t.l b di•counted . . fi t venr WI e ~ . IS negative. h t the services of the rs . b .. months sulcr ,. The formula assumes t a . discount period would e SlX one year; a slightly more precise · x months 11 way. the first year's services are on average Sl.

, I

I

30

this becomes

(1 + i)" - 1 y i(l + i)" .

Consumer Beha . tJtor

The present Yalue of the services is larger, the longer they are ceived ( n) and the lower the interest rate (i) .1s re.

This is mere arithmetic, but it is not irrelevant arithmetic. It has been said that obsolescense is induced by manufacturers through annual 1_nodel change~ whose ?nly purpose is to make Pea. ple replace sernceable used 1tems Wlth no more serviceable but ~omewhat more fashionable new ones. Translated into our aritb1ue­tic this means the y~, Ys, and the like, a re now much smaller than Y1 · If the life of the good is still n years, the present value of tb services is substantially reduced, and the quantity demanded of th: durable good will be reduced.14 'Vhether such a policy would in­crease or decrease manufacturers' profits, a question too complex to discuss here, its main effed would be to make transportation more €:\.'pensive for buyers who wish new cars, and cheaper for those who do not.

One must distinguish the stock of a durable good from the flow of its services. A stock is something that exists at an instant: the family o·wns n automobiles on January 1, at 10 A.M. A year later it owns m automobiles. We can say, on the one hand, that it has a demand for the services of (n + m)/2 automobiles on average during the year, and, on the other hand, that it demands (m - n) automobiles plus the number worn out during the year.u

11

The formula is that of the present Yalue of an annuity of y per year for n years. If tl1e service Bow is perpetual (as with land in some uses), the value of the stream is y/i, and l/i ( = 20 if i = 0.05) is called the "vears' purchase'' price of an income stream. ·

If Alternatively, the price of the use of the services of (say) a new car for one year is increased. This price of the services is the price of a car this year p,, minus the discounted price a year hence, '

Pt+I

i+i' which has been reduced by hypothesis.

a If we take a commodity that does not depreciate with use like bonds the desired stock at timet will be II,, and at time (t + I), h, .. ,. Then' the demand for bond purchases during the interva.] will be

q = ht+l- h,, which will depend upon both the price at time t and the expected price at time (t + 1).

1 Goods · Complements and Substitutes 31 f Otter ·

Prices 0 · · 'd b . of durable goods rmses m unavo1 a le form a ques-

xJstence I . . d d The e. .Jossed over : to w Htt t1me perto oes a demand tion we ha:e? g The answer is one to which the young economist

Pertatn · d 1 t • · d · d b th curve 11 ct accustome : t 1e 1me per10 Is governe y e will eventua y :..::. One can construct a demand curve for an article qllestion one as ... tion for a day, although commonly the time unit Of regular conslll:ldp ·easonal and minor random variations. But for tO 'LVOI S • is a year • d tl ere will be a zero demand for purchase by any a durable goo ' •

1t f the time even though the service of the good

)11ef IUOl> 0

. I b t one consu 1 ·ly. a family may dnve a car every < ay u ed regu ar · th k t is consum every five years. By a familiar argument e mar ·e

bllY one once d ·able good will be much more stable than d curve for a ur . deman .. ·d 1'' demand curve through time. the indtVI ua ::;

F OTHER GOODS: PRICES ~'lENTS AND SUBSTITUTES coMPLEr.

. l t d oods are the second determinant of the The prices of reo~de T~le purchases of automobiles will depend

demand for any g l.. (COI11plements) and the price of common 1 ·ce of gaso me h "

upon t te pn b 't t ) nre could in fact, draw t e cross . ,. cs ( su Stl u es . n I • th earner sen IC f t of K purchased as a given o er demand" curve for~ ~~eT~~:~si s~Jdon; done explicitly, but th~ etas­price (say ~~~) var~e . d the cross-elasticity of deman?, ~~ the ticit.y of this curve, calle . ( ot technological) substitutlon.n

. t' a·UI·e of economic n 't f economls s me ::; l relative change in the quanti y o It is formally define~ as t te . rice of Y. X divided by the relatl:'e change m tdhe (~av a company's stock cer-

. n•:Iders two goo s , J ' l If the consume! co - b ) 'dentical the cross-e as-. d dd serial num ers I • ' . .

tificates w1th even an ° ·. ( . . tl infinite) and pos1t1ve. ticity of demand will be Jmmenseb ts.ttrulctesy,the cross-elasticity will

'd tl en.r poor su s I · , l If he cons1 ers 1e~ v ·J • t. in that perfect comp e-be small. But there lS a certam asy·~~me ·~Y have infinite negative ments (right and left shoe~) WI no cross-elasticities.17 d e

. and function, the cross-deman curv u In terms of our notatiOn for the dem with respect to Pv would be R)

X = f(pz, Pv• f>r, ' · • 1 ' t t v riable is being held cons an . d in

where the bar again denot.cs. that_the a(tl left shoe remaining uncbange B t ., A fall in the price of nght "'.hoes rle b th right and left shoes. u

· · demand or 0 price) will lead to a n se m ·

32 Consumer Beha~,'ict

\\Jwther a conu11oditr has good or poor substitutes (or com 1

nwnts ) depends in good part upon how finely the commodit~ ~­specified A particul!lr brand of coffee has a high cross-eta ti.cit~ with respect to other brands- adually. on the order of +5 or + lo enn ";thin a mocth or two.15 Coffee has a much sma ller cross-etas.,

ticit~· with re~-pect to other ~':erag~s. and be,·erages presumabh· baYe a st ill smaller cross-elasticity w1th respect. to other categori~ oi expenditure. '

.\ dem:md curw for a product is specified only if the price- oi clo8e substitutes or complements are held constant, and this demand cum;- merely a·~rt:: that ,·arious quantities of X " -ill be bought at Y3riou, prices of X. if t he prices of other commodities are un­changei'i. In fact. the prices oi close substitutes or complements of .\ will ine,·itably change (at least in the short run I if the pric~ oi X changes appreciably : an~- large change in the price oi fuel oil. for example, will cause consumers to buy more or less oil burn­ers (complemems l and less or more natural gas (subEtitm cs J and hence affect their prices. B ut it is necessary to separate these indi­rect effe-ct~ oi changes in the prices oi substitutes and complement: ; imply because they rlo not a lways change in the ~arne wa,- when the prict> oi iuel oil changes . . \ t one time :1 10-per cent rise. in fut-1 oil price,. may lead to a 5-per rent iall in the price oi oil burne~. at another time to a 9-per cent fall.

This nece5<:it~- for holding con.£tam the price of a closely related product is imponant enough to de,en·e illustration. Let us assume that the demand iunction ior woolen socks is

qv = 30- lOp., + 4p. ,

where the subscript u- denotes wool. and n denotes n•lon. If the price oi woolen socks tp,..l riseoo 0.10 dollar-, on~ le~ pair ( = 10 X 0.101 "; 11 be purchased. if p. is ron- rant. If p. also rises 0.10 dollars. the purchases of woolen socks "ill fall by only 0.6 pair ( 4 Y. 0.10 = 0.4 lessl : ii instead p. falls by 020 dollar~. Qr will fall

ii th" eb._~ti<'ity oi d<>rnnnd ior ~~ i~ K , the cross-ela..qicit\' of d<>mand f?r left EhOC" ''ith re.."f'e<'t to a fall in the pnce of right ~h~· will Le K 2. 5lnce the t>erce?tage fall. in the. price of n p:lir is only hnlf ns larg!' M tbt> pen-enlage fall m the pnce of nght shoes. This cr~lnsticih· ma1· be quite 5ma ll . · ·

.. Lester G. Telser, "T he D('mand for Bmnded Goods ~ E...01imated from Consumer Panel Data," Ret-icJr of E conomic& o••d StatiJJtia (August 1962).

33

I oTTI8 · · I t ' h' nc _ always mo,·es m some stnct rea 10ns 1p to P.e, we

b. 1.8. Vn le~ Pft or i~ our es timate of the effect of a change in Pte y ke an err

:h:lil Jlltl . ke explicit account of p,.. .. nleSS we tu. . 1 tudies take into account at most a very few com-,... [Jlp!I'1C3 S h fi .

\{ost e b- t ·t te'- but tlus may be as muc a re ecuon on • - or su ::. 1 u ~, . I

leJllents flection of the world. Alummum, for e..'<amp e, p d. - as a re . . h d . .~.e stu 1es . . in furniture and kitchenware, wtt . woo m u> _ 'With 1ron . . d · · 'th conlpet~::.. with fiberglass m boats, w1th red lea. m pamt,. ~: bouse sidings, b"l gn"lls not to forget the maJor coropeuuon

automo I e ' ood chroOle on f lectrical conduction. Or, to take a consumer g . , «ith copper or e ";tb moYies radio, phonographs, attending

· · competes ' k d I wle,,SJon b k and for many homewor · an seep. . ·ents oo s, ' ed . . a]

$pOrting e' . ' 11 booerYe that we ba,·e announc no empmc The reader "'

1 0f - .

00_ of related goods c:imilar to the rule that

tb effects o on ::. ~ · ded rule for e . . . ommoditY reduces the quanmy deroan .

. the pnce Ol a c . . I h 3 rise JO to such a rule is to say that c ose tee -

I :>e"t we can come . b th "' 'fhe c O- - . - h t is commodities sen,ng muc e ~ame . I «ubsutute::--t a . . . . d I , hn I .

oolog~ca ~ . b . po"'itiYe cross-elarucmes, an c ose tee o ogt-purposes-mll ~n e - dit. ec: which must be used jointly in toi-

Jeroen~c;.-eommo 1 ~ . l-.-. .. . cal comp . rt' will ha,·e negau,·e cros.s-e ...,LJC1Ues.

'nfl XJble propo Jons- di erably 1 . CJ • d 'fes do not fall in either cia~. and then -)lost_ pam'. ot _com~o n~c~e~an· eYeD to detennine the sign oi the rect 10,·esng.auon ~ · cross-ela::.-ticity .tt

I~CO)IE

The third determinant of consumer purchases is _inco~e . The . . di th i<: purchased at ,-anous Lncomes

quanuty OI a commo ty at d- . st income: it bas no . - be' con"tant I maY be rawn agam-

(pnce~ mg ~ . h II all it an income cun·e. Two generally accepted ~~me. buFt . we s 3~3 : ne illu3trating the situation income curYe" a re gJ\ en m 1gure ' I'' ood) the - · · 1 · (called A ·'norma g ' in which purcha:-cs n~e wH 1 mcome . . h - - fall 8"' l·ncoroe

· · · ~b1ch pure a...~ • second illustrating the situalJon 1D . . . . . h rela-. · ·· d 1 T he income eln£tJClt~ 1:: t e

rises tcalled an " JOfenor goo · 1

. change in income : th·e chang,e in quantity dh-ide~ _by ~he re auYe oo0' and neeati" e this elaHicity is , of coun:e. posm,·e tor normal g ' -

for inferior goods. . . . Richard 5tone. Th~ ,. F . f d d ftnd cr~I.WtcJllf'S. see . . ~ ,. or a collecuon o ema.n ...... . 8 h -ior in tJac l lltll'u .n. UIQ·

.\Jra.n.rcmcnl of Con~ llllCrs' Experada turci 0~~. c_ 01~ Press. tg.;t ) . Cb.s. ~23 .

dom. /9,)()-1933 ( Cnmbndge, Engl.a.nd : T he l nn efflt.

•

"'

.....

34 Consumer B h e au· As a rule, the dollar expenditure on a cornrnodity r th '01-

the quantity of the commodity, is drawn against i~co~ et thab expenditures and physical quantities are proportional if n~. 'l'otal

· f b · 1 · 'd · . Prtces A .... um orm, ut m genera prices pa1 nse With income p . ....t'

· rices · ?ecause better qualities of the ~~mmodity are purchased at hi l'lSe mcomes and because more reta1lmg services are purcha d ( gher stores, delivery service, and so forth). Therefore the in~e better

0 llle elas.

Normal Good

o------------------------------INCOME

Figure 3-3

ticit?' of the quantity of a commodity will usually be smaller than the mc~me elasticity of total expenditures on the commodity.

T.he. mcome of the consumer may be variously defined. In most ~tatist1cal surveys it is taken as the sum of wages, dividends, and Interest, plus an estimated value of the major nonpecuniary services (fo~d grown and consumed on farms, rental value of owned homes) durmg the year. Capital gains are usually omitted: unrealized gains (such as stocks worth more than they cost when purchased) are hard for the statistician to estimate, and realized gains and losses

/I!C0111B 3.5 ·,ewcd ns cnncell ing (what the seller gains the buyer ftcn "

11rc o . tl <' populntion us a whole. Even if this wcre true ~o the (osesl

111 1 ~rith gains and losses could have different ~pcndin~ pat­

householc 8

·:trc al.::o n ho::.t of problems, amusing to eYery one Thrrc • ~ . . terns. . collectors, on what disbursements m·e deductible as occu-·xcept t a:x ~ . . 1 expenses. pnt

1ona ' btle difficulty is encountered when we consider the time A nore su 1

which in come should be reckoned. Suppose a family :od over r I · · •to 000 pell f !lowing sequence o annua mcomes. "' , , $2.000

has t he $; 000 a nd so fo rth. Should it treat its income as fluctuat­SlO,OOO, ' "IO 000 and $2,000, or as averaging $6,000? It is ob-. between "' ' . · · $6 000- ' "4 000 10g 't an view 1ts m come ns averagmg , Sa\mg"', ,·ious thn~ 1

cyears and dissaving $4,000 in unprosperous years. And in prosp~:o~~10uld normally do this: it. would be foolish , and even the f:u~

11

Y t ltcrnate between a tenement and a nice home, to nsiVC o a 1 · h t

expe ' 'Jd to college one year and to a coa mme t e nex . d its chi ren · · 1 ( t sen do not fluctuate this w1dely or cons1stcnt y e..xcep F ilv incomes d fl t

am J seasons of n year) but they do un ergo uc ua-hnps between . . d h t ~er bstantial magnitude. Even m a per1o as .s or as a year, tions of su f t f families shift about substantially: the corrc-h . comes o a se o (f t ~ m efficient of successive annual incomes runs from 0.65 or lah~~ cowith unstable incomes, such as farm operntors) to 0.9 (for fam~l~es h hief earner is a sales or clerical employee)· fanuhes w ose c . f ·1 . (say) five years I b ·I the average mcome of a anu y ovei ·.

Let us a e . I the deviation of its current mcome from its. permanent. mcom:si:; component of income.:' We shall illus­this level as lts tra . t ~ omponents with a numerical example. trat.e the effect of t r.ansl OI y c odity X according to the Suppose each family buys a comm equation,

X = _!_ (Permanent Income) + 10.~! 50 • 1

ockholder may take the corpo~atlon s ,. It is not true. For example, a st . . •ests it) as capital gam, nod income as d ividends, or (if t~e corporahon rem~ . . to this gain there is no offS('ttmg l~ss.

1 discovered by Milton FnNl-

" This terminology, I find, was 1!ldepende~t y (New York : National Bure:tu mnn in A 'l'hemy of the Consumpll01l Fu1!ctton .

of Economic Research, 1957,>. Is of consumption of a commcxh~ ,. There will also be trans• tory compo~en ' th the transitory component

but if they are not correlated. st;o,nga~d '~~e ignored here. income, they do not affect the prmc1p e

~ ~m~~Bh The distribution of 25 families by their permanent in . e atJiOr in Table 3- 1. We calculate random components of in come

18 sho'l\'n

families by flipping a freshly minted coin, adding ~~: for the~ heads or subt_racting $200 for each tails, and terminatin t for e~ch when the com changes face.23 The purchases of X g he tossing

FAMILY NO.

1 2 3 4 5 6 i 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

PERMANENT

IN COllE

$2220 2340 2450 2550 2640 2720 2790 2850 2900 2940 2970 2990 3000 3010 3030 3060 3100 3150 3210 3280 3360 3450 3550 3660 3780

Table 3- 1

TRANSISTOR¥

INCOME

+3200 + 200 - 400 + 600 + 200 - 800 + 800 + 600 - 200 + 200 + 400 - 800 + 800 + 600 +BOO - 400 - 200 - 800 - 600 - 200 + 200 - 200 + 200 + 800 - 200

OBSERVED

IN COllE

$2420 2540 2050 3150 2840 1920 3590 3450 2700 3140 3370 2190 3800 3610 3830 2660 2900 2350 2610 3080 3560 3250 3950 4440 3580

are plot~d

54.4 56 .8 59.0 61.0 62.8 64.4 65.8 67.0 68.0 68.8 69.4 69.8 70.0 70.2 70.6 71.2 72.0 73 .0 74.2 75 .6 77.2 79.0 81.0 83.2 85.6

ag~inst current income in Fi ure pomts would fall if e I f ~ 3-4, and the line on which all

ac l anuly had its . u permanent mcome is also Or, more econom · 11

of random nu b Jca yl we use runs of odd d which has a he~~ser(s. rl~o, expected number ot~ca~ven( num~ers from a table

or a~ s~ on the first toss is s or tatls) for a family

so the average tra "to t + l + t + . . . = 2 081 ry componer t · 1

1

l lS p us (or minus) $400.

3i ~c~~ . . ·cd It is obvious that the slope of the hne which is fitted to displa) ·. tions has less slope than the true relationship.H

ob~en a . f I . the ~ r·,('C" 1)ennanent mcome o t us group is $3 000 and 1·t,

r1'j e :1 ye ' "'I:> 1 , • :) J. l ·rent income is S310i9-thc difference is due to the small . raue cUI 11 . h . l n.' e "' the sample and wou c vams . w1t 1. a larger group. Yet only

51ze 0~ 1. . a.re below the true regressiOn hne to the left of the true 3 fal)llle:.

90

• • •

2,500

• I I • I I I I•

• •

Income Line, Permanent Income

3,000 3,500 INCOME

4,000 4,500

Figure 3-4

mean ($3,000), and only 3 families arc above it to the right of this mean. The average transitory components by current income

are: CURRENT I:-< COME

A.VEUAGE TI1ANS!TORY CO~ll•ON&NT

-S520 - Hi7 + 233 +GOO

Under S2500 2500-3000 3000- 3500 Over 3500

And this sort of pattern is inevitable, because the very fact that a family has a large negative transitory component tends to put

11 The least squares line is 1 X =

144 (Current Income) + 48.7.

i .

I

£ fF

I. :d .

38 Consumer Beha . tnor it in a low current income class, and the very fact that the fa .

1 . t t . . llll 'i has a large posi tive transitory componen pu s 1t m a high cur . . . rent income class. For th1s reason budgetary studtes of a group of fa .

d h . tnJ.

lies at any one time un erstate t e responsiveness of expenditu . res to changes in permanent mcome.

A century ago the first important student of family budget Ernst Engel, proposed the law.: the larger a family's (or a nation•si income, the smaller the fracbon spent upon food. The " law" wa~ deduced from budgets of Belgian workingmen's families, and fo~ a century it has had the good fortune to be mostly true, as a descrip. tion of both rich vs. poor families and rich vs. poor nations. The curves displaying expendi tures on any category of consumption, as a function of family income (what we term an income curve), are often called Engel curves, no doubt because he never drew one.

Engel's law was an empirical generalization, but it had an intu­itive appeal because food is widely viewed as serving a primary need; so once it is met additional income will go mostly for other things. We now have dozens of such empirical rules: most budget studies will reveal income elasticities above unity for domestic ser­vants, restaurant meals, medical care, expenditures on the education of children, and so on, and income elasticities below unity for grain products (and purchased food generally), fuel, newspapers, liquor, and so forth.25

TASTES

The quantity of a commodity demanded at given prices and in­come depends upon the likes and dislikes of the consumer. These tastes, as they are called, are in turn governed by a great host of circumstances: age, sex, and family composition; cultural tradi-

• A collection of such results c!l.n be found in S. J . Prais and H. S. Ho~th~er, The Analysis of Family Budgets (Cambridge, England: The Untverstty Press, 1955). For the early work in this area see my "Earlv History of Empi.rical Studies o( Consumer Behavior," Journal of Political Eco11omy, 62 (1954 ). It should be noted that Engel asserted that F!Y falls as Y in­cre~s, if F ia expenditure on food and Y ia income. This is equivalent to asscrtmg that the income elasticity of food is less than unity: if P = q>(Y),

d(F /Y) F -w-- = y• l ,,., - 1}. so if the expression is negative, 11, < 1.

> 39

'fastes drink wine; Americans duel martinis); religion tions (F.renchroen goes far beyond dietary rules) ; and even educa­(whose tnflucndce f describing tastes quantitatively will be presented . A tnetho o

uon. l ter. in the next c 1ap f problems, including most of those we shall

For a vast . arrayt 0

ary to treat tastes a s fixed. The stability of it ts cus om · h I I

encounter, 1 a priori: tastes depend upon sue s ow Y >nstes could be argduec gt·"phic characteristic:) and cultural tradi-"" . h. gs as emo " . chang!Dg t m 1 ould not be influenced apprectably by most tion. Moreover, tastes s 1 ·st studies I t is hard to see how an em-

. the economt · ff of the act10ns 1 should have any important e eel upon

il for examp e, ff · bargo on o • 1. ther than through the· e ects on pnces the denHmd fot· gaso me o

and incomes. t h assumption of constant tastes are not These defens.es of ld ethey are buttressed by a wholly different

wholly itnplauslble, at d. t ion is made on the basis of an ceo­line of argument. If a pre ICt t to be fixed and if the prediction

. that assumes as es ' . . nomic analysiS . th n the neglect of tastes has been JUStl-

is confirmed by expenenc~~l eeconomic analysis of consumer ~ehav-ned. Hence every success . astes is support for the neglect.-• iol' that neglects changes 1l1 t. ·st sa'-·s that if one collects

cific · the econ01m J • f Let us be more spe . . . . 10 per cent and adjusts or

. t of a pnce n smg . ' 1 d a thousand ms ances . n well over 950 cases the quantity pure lUSC

income changes, that 1 l ld find this statement to be wrong, will decline. H any student s lO.U ? will he please notify the profes~IOn t . t boundary over which the

And now to retract. 'There lS no s rtct d' of tastes have been t and many s u ICS

economist dare not s ep, . I l1and for housing, one natu-made. In a study of the lo.ng tel1~11 c c~ e In a ~tudy of the trend

· t h nges m fnmt Y S121

• th ge rally investlga es c a . f . ns one considers · e a of employment in the medical pro essdlO·t 'urbanization. Pertinent.

f 1 Pulntion an I s ' th and sex structure o t 1e pod 1 ·cr and wherever ey . ·ntroduce w lene• components of tastes a1 e 1

. th t tastes ba ve · rediction, a sho,vtng. · n so too

,. And every failure of an. economiC p ·nvnlidate a predtctton, b~tbl the chnngcd? Not quite. Changtn(t tastes c~n s~me other iroport~t vnna ~one­can a mistaken a~nlysis--the neglect ~msy statistical tcchn!Clue. T~~oks for improper formulatiOn of the the~r~i c much more often than he probable mist looks for these sources of 81 ur~ beeu found to be more changing tastes--simply because they lave than changing tastes.

40 Consumer Beha·• vtor

are helpful, and it is only their enormous variety that keeps them out of the general theory.

Two propositions on tastes are deeply imbedded in economic

thought. The first proposition is that human wants are insatiable-that

there is no real income so large that a family would not like more. (The assertion does not tell us whether the liking for more incorne diminishes as the family becomes richer.) Although this proposition emerged long before the day of statistical analysis, it bas always been essentially an empirical proposition- the richest sovereign seemed ever-willing to augment his wealth. The exceptions which are alleged (it is not evident that any exist) have usually been attributed to "primitive" people.

The insatiability of wants is more than a philosophical observa­tion on human nature-it is an integral part of economic analysis. There is no place in economics where it is asserted that if an indi­vidual buys some of a commodity at a given price, be will not on a';erage buy more if the price is reduced. Nor are there many econo­mists who would explain the failure of a society's income per head to grow on the ground that all wants were satisfied.

The second proposition is that tastes are extremely varied-that one man's meat is another man's poison. And t his proposition lends itself to quantitative measurement. When the purcha~es of families with equal incomes are compared at a given time (so prices are also held fairly constant because all families buy at about the same prices), most of the original differences in purchases among families still remain. Thus, even with so broad a category as all food, the coefficient of variation of family expenditures is more than 30 per cent, and after eliminating income differences, it is still 25 per cent. In other words, among families which spend an average of $1 ,600 on food in a year, roughly one-sixth spend less than $1,200 and one-sixth more than $2,000.27 In the case of more specific commodi­ties, such as white bread and peanut butter and tennis balls, the diversity of family tastes becomes almost astronomical.

The diversity of taste raises some interesting problems in eco­nomic organization. Whenever it is uneconomic (expensive!) to sup­ply a good or services on a small scale (opera, unusual automobile

"'This di,·erlrity is exaggerated by lhe use of current instead of permanent income.

41 emand Functions Marlett D .

8 skrit on bowling) the individual will be unable

les books 10 an nless they are shared by a sufficient number of stY ' h' s wants u . · h h d ·

SatisfY 1 1 , t aste!'! in housmg dtffer more t an t ey o m to 1 P eop e s ~ .

ther peoP e. s production techmques have had much less o '1 and mas . be tomobl es, . t t ion industry. But as a soc1ety comes au the cons rue . f . I cope in . . can afford to pay the h1gher costs o spec1a-5 · its c1t1zens · · t k 1 vealthler' . 11-feration of vanettes a es p ace. ' d and a pro ized goo 8

DEMAND FUNCTIONS rrtARK.ET .

d . me curves so far discussed pertam to an

d an mco . f The deman W hall briefly indicate how to pass rom · 1 household. e s to Ch te individua k t demand functions, but postpone ap r

. . . dual to mar e mdlVld finition of the market. 6 the e

D mand Curves Market e . arket buy at the same price or at

· d. 'duals m a m Since. all m. lVl . 34)' we can construct a market de~an_d

ft.xed dtfferentul.ls (s~e ph . t lly the demand curves of allmdi­curve simply . by addmg 1 o~Izo~ : n in Figure 3-5. Ench of the indi­viduals. A simple examp e lS ~v D D D~) has been drawn to vidual demand curves (D J, 2, ,, 4,

p

1---+-.·--, r.---t-t---, '- - - --,

I L-- --,

L--,_ ""'\.--, I L--., L-,

D4 Dr 05 o, 02 03

0 Figure 3- 5

0

42 Consumer BehaVior

display highly discontinuous responsiveness to price simply to sh that the market function takes on a smoother form. ow

It can be shown that the elasticity of the market demand cur is equal to the weighted average of the elasticities of the individ v~ curves, the weight~ being the relative quantities purchased by e:c~ buyer.28

Market Income Curves

The aggregate income curve of the market for a commodity un­fortunately , bears a very complicated relationship to that of th individuals who constitute the market. The lack of symmetry ~ the demand relationship arises from the fact that prices are usually equal (with allowance for transportation costs) for all individuals whereas incomes are unequal. The effects of an increase in income' therefore, depend upon how income is initially distributed and ho~ the increments of income are distributed.

We may illustrate this complexity by combining the income curves of two families, denoted I, and I2 in Figure 3-6. Only three of the innumerable possible market income curves are drawn:

M 1-the market income curve if the families have equal incomes. It is the sum of / 1 and 12 •

M 2-the market income curve if family 1 always has half the income of family 2.

M3-the market income curve if each family bas an initial income of $3,000 and family 2 gets twice as large an increase in income as family 1.

Yet it is commonly said that "the" income elasticity of demand for a commodity is +2 or -1 or some such value. This may repre­sent an historical estimate, and then it simply says that as income increases were distributed among families during the period in question , on average they led to elasticities of + 2 or -1. But it may represent also another view: the distribution of income among families is fairly stable (for reasons we shall study in Chapter 18), and when all fami ly incomes increase in the same proportion, the elasticity of the market income curve is the weighted average of the individual income elasticities (the weights being the relative expenditures on the c.ommodity in question) .29

.. See mo.themnticnl note 4 in Appendix B. • See mathemat.ico.l note 5 in Appendix B.

Demand Functions Market

zoo

150

uJ a:: :::> t;: 0 z 100 w 0-)<: w

50

0

350

~300 :::> 1-0 z w 0-

~250

12

I r 3

I I

4 5 6 INCOME (Thousands of Dollars)

(a)

43

1j

7

OL,---~6----~8----~,0~--~12~--~14--1 NCO ME (Thousands of Dollars)

(b)

Figure 3-6

1: I

44 Consumer Behavior

RECOMMENDED READINGS

Friedman, M., A Theory of the Contumpti.on Function, New York: National Bureau of Economic Research, 1957.

Prais, S. J ., and H .. S. Ho~tha~ke\ The Ana~ysis of Family Budgeta, Cambridge: Cambnd~c Umvers1ty I rcss, 1955.

Schultz, H., The Theory and Measurement of Demand, Chicago: Uni­versi ty of Chicago Prc..r:.s, 1938, Cbs. 2-6.

Stone, R., The M easureme11t of Con8'ltmers Expenditures and Behavior in the United Ki11gdom. 1920-1938, Cambridge, E ngland: Th<' Uni­versity P ress, 1954, Cbs. 20--23.

Working, E ., "What ~o Statistical 'Demand Curv~s' Sh~w?" Quarterly Journal of Econom1cs, 41 (1927), 212-35. Reprmted m Readings in Price Theory, Chicago: Richard D . I rwin, 1952.

PROBLEMS

1. Make numerical schedules of the demands of two consumers, whose functions arc

Ql = 100 - p

q, = 50- p/2.

T hen add the demand curves horizontally and compare the elasticity of each stJhedulc with that of t he combined schedule, a t p = 50.

2. Budget studies of families made at any one time show that richer families employ more servants than poorer families, and the income elas­ticity calculated from these cross-sectional data is about +2. But over the last half century t he income of the average American family has risen while the number of servants has actually fallen. How can these results be reconciled?

3. The equations of the income curves underlying F igure 3-6 are

/1 = - 5Yt2 + 55Y. +50,

I,= - 6Y22 + 60Y:,

where Y is income in thousands of dollars, and the equations hold over the range from $2 to S9.5 (thousand). Verify the shapes of i\1,, M,, and M. in Figure 3-6.

4. What is the income elasticity of each of the income curves in Problem 3 at nn income of 55 thousand ?

5. Given the demand function which portrays a lagged response of

45 problems . . . f l 7

. changes (it. JS g1ven m oo note , page 28), draw the buyers to p!1CCf r t his year when prices in t he two prececding years were:

d curve o de!ll

60 (a.) Pr-: = 40; Pr-1 = 40

(b) PH = 40; Pr-t = 50

(c) Pr-: = 40; p,_, = 30.

tb obsen·cd expenditure pattern for the 25 families in 6. Cnlcul~rthe ~ ransitory component of income is twiee as large. Thnt

Tnbk 3-l h family's permanent income for each consecutive head is, add ~()() to. eac or subtract $400 for each eonsecutivc tail. L" the ob-1n a co~ tossl.llgl, sticit" larger or smaller than that of the income line

d Jl}COIDC e a J serve ?

11\ figure 34 ·all nsumers have identical demands for a given commodity, 7. ~uppose. c~stances from t he central city. What would happen to

but live van;us d curve reckoned at the cent ral city if transportation the roarket . em:~e product rise? What will happen to the elasticity of costs per umt o . . . ? demand ii the demand function JS hnear .

chapter four

The Theory of Udlity

Utility theory made its way into economics almost a century a when it was still semifashionable psychological doctrine to a got, th t , b h . sser · a man s e avwr could be explained by his desire to achi I d 'd . eve

p easure an av01 . pam. I~ was a natural extension to say that the pl~asure (or utJhty) ~er1ved from a commodity varies with the quant~ty of the commo?1ty, but increases less rapidly than the quant1ty. of_ t.he comm??1ty (law of diminishing marginal utility) . The maxJmJzmg of utJhty provided a basis for a theory of moti­va~d consumer beha~ior, thus complementing the pursuit of profits wh1ch was the basts for a theory of motivated behavior of entrepreneurs. For~ short ~ime the utility theory was taken vety literally: some

e~~om1sts beheved that there were definite numbers of units of ut1hty to be attached to the consumption of given quantities of goods,. numbe1·~ which were in principle measurable. The greatest fiower~ng of th1s theory was achieved in the famous monograph of FranCis Y. Edgeworth entitled Mathematical Psychics (1881). Edgeworth, who was one of England's greatest economists, even dis­cussed su~h pr?blems as whether a woman obtained as much utility from a g1ven mcomc as a man, on which he reached the correct answer.1

The_ increasing criticism of this psychological theory (known as hed~n1sm l. a~d the closer examination of the role of utility in eco­nomic analys1s (particu larly by Vilfredo Pareto), led economists to ab_a~don everything but its substance. The simple measurement of ut1hty, the comparisons of utilities derived by different people,

'See .Mathematical P&vchict, p. 78.

46

47 tiorlal ConBumer

1'h6 [?a .1.t rguments to support public policy proposals-all

f ut1 1 Y a · · h I Wh t · the use 0 11

abandoned m pa rt or m ": o e. a was retamed «ere gradua Yt of what we may term a ratiOnal consumer.

the conceP "'!lS

TIONAL CONSUMER TfiE J~A

cterization of Tastes fhe Cbara mine the nature of the rationality attributed to

Before w~t~xadesirable to develop a graphical method of describ-d. ·duals 1 IS .,. · f · ) L t in .JVI • d'. r"d al's tastes (or preferences or ut1 1ty unctiOn . e

· the ID l\1 u b" h · f th 20 b" tDg th t the individual is offered 1s c 01ce o e com I-

us ~ssur:ef t;o commodities, X and Y, which are listed in Table :1~o~he choices could be determined by an actual offer of sale

Table 4-1

Combinations of Two Commodities, X and Y

Q UANTITY OF X

9 10 11 12

QUANTITY OF Y COMBINATION N UMBER

10 1 6 11 16

11 2 7 12 17

12 3 8 13 18

13 4 9 14 19

14 5 10 15 20

of the various combinations for various sums of money, a method ("revealed preference") which will be discussed later. For the present we simply ask the individual to rank the combinations in the order in which he prefers them for his consumption.

There are several difficulties in actually conducting such an ex­periment with specific commodities. The first is that the individual will normally have some knowledge of the prices the commodities currently command in the market. If X costs $1 and Y costs $5, he will be tempted to calculate the values of the various combina­tions, and rank combinations in the order of their value-on the ground that even if he personally does not care much for Y (say recordings of zither concertos) he can always exchange them for X, wh-ich he does like, in the market. On this approach he would

I I

48 The Theory of Utili ty

cboolle combination 5 in preference to combination 16, even though he much preferred to consume the latter combination. W e must rul out the values (or resale possibilities) by some artifice which corn~ pel him to consume the commodities.

The second difficulty, which is of an entirely different nature is that he may be undecided as between some combinations. R~ may prefer combination 12 (llX and 11 Y) to combination 11 OlX and l OY), but be unable to express a clear preference between com­binations 12 and 8 (the latter has lOX and 12Y). I n fact, if the commodities are divisible we can always construct combinations that ~cern equivalent to the individual. If, for example, he prefers

9X and 14Y to l OX and lOY,

and

lOX and l OY to 9X and ll Y,

we can find a value of Y somewhere between 11 and 14 such that with 9X it is equivalent to l OX and lOY. W e then say that he is h1dif!erent between the combinations.

And this leads us to a third difficulty: what if his rankings change from one day to the next? T his difficulty will be postponed: we shall assume that his preferences are stable.

The combinations of Table 4-1 are displayed as little circles in Figure 4-1, Panel A. In Panels B and C we have drawn different lines through the circles, to display two possible rankings that two different individuals might make. The lines (called indifference curve ) obey one rule: All combinations on a line arc equivalent to the consumer. And our fundamental argument is t hat the con­sumer's preferences can always be characterized by such indiffer­ence curves.

In Panel B, the individual (B) requires several units of Y to compen ate fo r the loss of a unit of X, as between combinations which ~re equivalent. In Panel C, the individual (C) requires only a fraction of a unit of Y to compensate for the loss of a unit of X , as between combinations which are equivalent. Hence we may say that B sets a higher preference (utility) on X relative to Y than C does. '

Only extensive experiments will convince the reader· that any set

,.. fhC

y

14 13

12 II

10

0

. l Consumer ]latto11a

G,.--g 10 II

( 0)

12

y

14

13

12 I I

10

X

y

14 13 12

II 10

G 0 9

G ---- - ----0 9 10 I I 12

(c)

Fig ure 4-1

X

49

10 I I 12 X

( b)

of tastes can be charact-erized by such indifference curves. In the four panels of F igure 4-2 we show

A. A person who considers X u tterly useless: say Y is food and X is tickets to marathon d ances.

B. A person who considers X a positive nuisance: say Y is food and X is garbage.

C. A person who considers X and Y absolutely equivalent: say ~ and Y are objects differing only in color, and this is deemed Irrelevant .

D. A person who considers less than 4 units of X desirable, would never be caught dead with 4 to 6 units (a difficult feat), and would find more than 6 a nuisance.

'

50 y

The Theory of V .. ttltty y

\!..!wr"-

~ ~

X 0 ---0~--------------

(a) (b) X

p. .. >k

y y

~ I

~ t:-/ I I

X 0 4 6 X (c) ( d )

Figure 4-2

In order to simplify the discussion f . d.ff mists make two assumptions: o m 1 erence curves, econo-

~ · i~e consume: ~nds both commodities desirable.z . e commodttles are continuously divisible-m·lk

are prototypes. 1 and sugar

These assumptions place two lim"t . . . The latter ensures ob .

1 h 1 abons on the md1fference curves.

, A . ' Vlous Y, t at they will be continuous curves 3

ny nuisance commodity can b d fin , of garbage, call it garbage removal· .e ~e ~ td to beco'!le desirable: instead

• Strictly speaking co t. . ' 1~6 ea o work, call tt leisure. n t b , n mm~· requues also tl t th a e etween combinations diff . b . . !a e consumer can discrimi-

ermg Y mfinttestmal amounts.

f·onal Consumer 51

fhe no t . . . Iy collect ions of discrete pomts. The former ensures

9nd not s~~:~e a negative slope : if both commodities are desirable,

thnt theY bination has more of X, it must have less of Y or and one ~o~ions would not be equivalent to the consumer. More­the combJDf a_ ner assumption insu res that as between two indiffer-

the on . h. I . over, the consumer prefers the Ig 1er one, because 1t contains curves, h y d X ence · X nd more Y, or as roue an more .

v.s much .ta T he indjfference curves, on the conditions stated, are Conve;rt, Y· · · dd. · · · I · . and negatively slopmg; m a 1t10n It IS a most umver-

onunuous t th · · Th. I · c med that they are convex o e ongm. 1s, et 1t be •allY assu · · l fi · t. · " d · an empirical proposition, not a c e m .Jon-m fact it is nolefi, t18 empirical proposition encountered in this chapter. How can the rs we prove it? 'fhe line of proof first used by economists was in t r·ospective, and . fact was based upon the P.rinciPle ~ diminishing marginal utility. ~he early utility theorists assumed that the utility derived from a commodity depended upon the quantity of that commodity. If we define the marginal utility of a commodity as the increase in total utility divided by the increase in the quantity of the com­modity with which it is associated, t heir proposition was that the marginal utility diminishes as the quantity increases. If U ( n) is the utility derived from n units of a commodity, they asserted that tbemarginal utility of (n+ l) units, U (n+ I )-U{n), was greater than that of (11 + 2) units, or, U(n + 2) - l':l(n + 1) . For surely one sat isfied increasingly less important desires as the quantity of a commodity increased : the first gallon of water (per week) was necessary to survival, the fourth to cleanliness, the fifth for one's wife, t he one-thousandth to a green lawn, and so forth.

If so, indifference curves would be convex. The various combina­tions on an indifference curve y ield equal utility. If we decrease X by t::.. X, and require A Y of Y to compensate for the loss of t::.X, then

(t::.X) (Marginal utility of X) = 6X · MU"'

is the loss of utility from the decline in X, and

(6 Y) (Marginal u tility of Y) = 6 Y · M U v

is the gain · tT f ·r th . . m u 1 1ty rom A Y , and these two must be equal 1

e utthty of the new combination (X + tuY, Y + ~ Y) is to equal

52 . The Theory of ..

that of (.\ .Y). (Notice that tJ..X is negative.) But if Ut1ltty

t:.X. MV~ + t:.Y. MU" = 0,

Suz = - tl Y - M U z . t:.X - MU

11•

Tlus last expression is the slope of an ind' ff called the marginal rate of substitut 'Jon f Ytf erenc~ curve, nnd is · p· o or X· 1t · 'J · m Jgure 4-3. As we continue to decrease X b . ' Is. t lustrated MU., of the remaining quantity gets 1 . Y equal Increments

atger, and the MU f • v o the y

I

0~-------------------X

Figure 4-3

increasing quantity of Y gets smaller: the slope becomes numeri­cally g~e~ter as we move to the left along the indifference curve. And th1s IS what convexity means.

Thi.s proof ruled for a short time in this form, but it had one unsatts.fac~ry asp~~t. Diminishing marginal utility does not imply c.o~vex1ty If the ut1hty of a commodity depends also upon the quan­tities possessed of other commodities. In this event the decr·ease in X may, for example, increase the marginal utility of a given amount of Y , and spoil our argument.{

The second line of proof is based upon observable behavior. If the consumer buys some of each commodity, the indifference curves

• The precise relationship is gi\'en in mathematical note 6 in Appendix B.

53 . l Collstt?ner

fhe f{,o(rOIIO h rigin. (Jt will be shown that with linear be convex to t e

0 rves only one of the commodities would

(llll't. . difference cu ' . f I t • 11csve 111 · d ) We shall return to th1 s proo a er.

or co ' be purchase . !(Cllern\1)

- .J et Line · · · d b' · fhC JJuu8 rves display subJeCtiVe attitudes towar 0 JeCtJVe Indifference ~u W. need to be able to display also the terms

d services. e · d d tl · · d Ods an d d services can be acqmre , an us IS one

go 1 e goo san on which t 1es lled budget line. Suppose we add

sofa so-ca bY mean~ t f purchased, times its price ( Pt) ;

noun o Xt • . ( ) the Ill t f X· purchased, times 1ts pnce P~ ; the amount 0 f ,,: purchased, times its price {p3) ; h amoun o "'a h ]' t) t e d forth to the end of t e IS (an so . . . ( )

t of x purchased, times 1ts priCe Pn · the amoun "

t b the total amount of income the consumer pos-

Th sum mus e h . t e ' f list of commodities is complete t e mcome mus sses for t our . se 'd. me form Thus we may write the budget equatiOn as

be bel tn so · XtPt + X2P2 + . . . + XnPn = Income = R.

Of many of the x's may be zero for any individual.

course · ffi · t t Tw additional remarks on budget constramts are su c1en a

this ;int. The first is that the budget equation says that transac­tions are v~-that there is no th~ft or co~rcion. The second is that the equality of purchases and mcome 1s really a matter of definition: we can always find appropriate "'commodities" to keep the equation in balance. If our time period were a week (it is usually convenient to make it longer) , and the family bought a house, the purchase of the house would be offset by the increase

in debt of the family.5

The budget line in a two-commodity world would become

XP,. + YPv = R. 1f the prices of commodities and the income of the individual are fixed, say at $2, $1, and $30 respectively, this becomes

$2X + $1Y = $30 or

2X + Y = 30,

h~ Orfl • if we wished to avoid introducing stocks into an analysis concerned e~ 'llift · · · ., tiy WI ows, only the cost of the w~;.-ek's shelter would be in the budget . • .,ua on.

--.. > ~ The Theory of Utility smce we may cancel out the common dimens ion of doll . budget line can ob,·iously be drawn on t.he same seal a;~· This h:we employed for indifference curves, and thjs budget e~ at. We

line nnd a uecond, in which Pr = 83 are shown in F i 0

4r Price)

' gure -4. The

r

30

20

10

o~----------~,o~~~2~o----------~3o _________ x

Figure 4-4

~lope of the budget line with respect to the X axis as can be seen when it is written as is -Pr! Pv,

' y = R - p~ X

P71 P11 •

The collection of possibl b' . · · e com mat10ns of X and Y t he consumer can po. "ess IS the set f · · . ·

d y 0 POints In t he tr1angle bound('d by the X un axe~ and the price line If h d . . sumption we shall mak l . e spen s nil hi mcome, an as-it e, le must be on the budget line for below

I J

XP:z: + YPII < R. The consumer usually bu t .

portunt in the mark ts . y~ .a . a con.tant pnce ; he is too unim-occa ionally price d:e .

10 w He? he dea l~ to influence prices. But

n liCII(:dule of mtc fo. ~a7· \~'lth quanltty: a simple example is · 1 e ec rlcJty such as 5¢ per kwh for t he fi rst

The R ational Consttmer 55

100 k"·h and 4¢ per kwh thereafter. In this case (which is left to tbe reader to draw) the budget line will have a kink at X = 100

' being steeper to the left of 100 than it is to the right. And there are more complicated pl'ice systems, such as thnt involved in a flat sum for installation of a u tility se•·vice and another pri ce per unit.6

We shall put such complications aside, a nd analyse the constant price case.

Rational Consumer Behavior

Let us now consider more closely t he behavior of a rat ional con-sumer. T here are t hree characteristics of a rational consumer:

1. His tast.es are consistent, 2. His cost calculations are correct, 3. He makes those decisions which maximize utility.

After t hese characteristics have been explored, some widely held objections to the realism of this t heory will be confronted.

Consistent Tastes. One must distinguish ~harply between n set of tastes that is consis tent and a set of t astes that i admirable. A consistent set of ta tes is one in which the order of pre ference among combinations of goods is well-defined. If combination A (say 7X + 11 Y ) is preferred to B (say 6X + 12Y ) , and B is preferred to C (say 5X + 13Y}, then A is preferred to C.

Consistency exclude. intersecting indifference curves. For con­sider the two intersecting indifference curves in Figure 4-5. On I ,, Q, is equivalent to Q~; on I~, Q, is equiva lent to Qa. Hence the intersection implies that Qz is equivalent to Q3. But Q: contains more of each commodity than QJ, nnd on our a,..s utnplion t hat all commodities a rc desirable, Qz is preferred to Q3. Hence t he indiffer­ence relationship between Q, and Q~ and Q, and Q, is not transitive, the technical name for thi consi ·tency condition.

Consistency, to repent, has only this na rrow meaning of well­ordered preferences . Con~istency docs not mean logica lly harmoni ­ou preference : it might be consistent, in ous· na rrow ense, for an individual to prcfe1· to pay $10 more to fly in a plane whose chance of crashing was one in 10,000 less t hnn the chance of crlLsh-

• Jn thss en"<' the pricP line c·nn be defined only if tl•c ti 111e period o~·cr wt.ich t t.e utility service will he u"Cd is known. If, for cxnmvl~, tile penod of use is mdcfinitcly long, only interest on the cost plut< deprc<·sullon should be charged as an annual cosL.

56 The Theory of Uti[' ing o_n a. chcape1.' fl i g~1t (thus setting n. marginal value of tty on h1s hfe) while sunultaneously playing Russian .

1 SIOO,OQo

. • Iou ettc for Sl ,OOO, thus settmg a $6,000 value on his life 1 Fo . ·

1 once

case, the admiration of a dozen equally shallo,~-min1d 1~ t le latter might be esteemed highly. e observers

Even more, of course, consistency does not im!Jly I' h f t Tl . en lg tenrn

o tas es. 1e consumer could with consistency prcf t ent telephone book rather than Shuke~=:peare or to lister 0 read the

~ ' en to a boiler

y

Figure 4-5

factory rather than to M t Th' . of man's behav· · · czar : IS IS only to say that the analysis

lOr JS not an ethical study. Correct Cost Calculat · Th .

goods a · . tons. e costs of vanous combinations of rc Incorporated 111 the b d t .

dition of rational .· . _u ge equat1on, and our second con-be reckoned corrc ~~ha;1~.r lS

51~~ly the requirement that the cost vious as to be vu~ a~· bu IS condition ~f proper arithmetic is so ob­that not all aritl gt· ' . ~ let us spell Jt out in a few cases to show

1me IC IS Simple.

' With . ~ six-chambered revolver the l probabili ty of death is valued a t si,ooo. probability of winning is 3 and a

The Rational Consumer 57 As a primitive example, a commodity X is sold fo!' S2 at shop A,

fot· $2.10 nt shop B. Then the hudgct equation should rend, 2Xa + 2.1Xo, so far as this item is concerned. If X, is identical with X 1,, in all respects (including the services of the two shops) , Xb will drop out of the consumer's purchases, as we shall show Inter.

At a next level of soph istication, or rather naivete, the consumer can 11buy" n fund of money for Christmas presents by (I) putting money in the bnnk each month, and receiving interest, or (2) join­ing one of the Christmas fund plans whereby he is compelled to cont ribute, and not allowed to make early withdrawals, and receives no interest. The cost of t he fund is (say) 8100 by the second plan, and ~98 (i f the interest averages 4 per cent on an average balance of 850) by the fi rst plan. He will obviously choose the former·. Yet some people choose the latter .

One can of course explain the participation in n Christmas fund by introducing another item of preference: a desire of people to protect themselves against a future lack of will power (or a desire to be charitable toward bankers) . I£ we stopped the ann lysis with this explanation, we would turn utility into a tautology: a reason, we would be say ing, can always be found for whatever we observe a man to do.

In order to preserve the predictive power of the utili ty theory, we must continue our Christmas fund analysis as follows. The fore­gone cost of putting money in a Christmas fund is the interest one could earn by putting the same money in a savings account. If interest rates on !'avings accounts rise, the cost of buying protection against a loss of will power rises and less of it ought to be bought : relat.iYely more saYings will go into savings accounts, relatively less savings into Christmas funds.

As another example of cost analysis, Jet us assume that a monopolist sells both razors nnd blades, and that (what i- unreason­able), possessing a razor Lhe consumer uses each week either one blade or no blades (if he gi\'eS up shaving by razor). Will the con­sumer care how the t wo items are priced, given their total cost? The answer is no. If the razor lasts indefinitely, its cost per week is the interest on the investment, or

58 The Theory of Utility

. . . h . te st rate and p, the price of the razor, and the co~' If t IS t e m re ' . -~

f h . p"r week is this interest cost plus t he pnce of a blade or 0 s avmg c '

ip, + 52 P&,

the consumer will be indifferent {at i = 0.05) whether blades are 1~ and razors 110.40, or blade.s 2~ and razors r.ree. (If the number of blades is variable, the situation IS more comphcated.)

Let us finallv take a more difficult example. A household ren~ a home for $200 a month, and contemplates purchasing it for 120,000. Here the monthly cost of home ownership would be the sum of

1. interest per month on the $20,000, whether paid for in cash or mortgaged 100 per cent ;

2. taxes per month on the house; 3. minus the saving in income taxes because interest payments

and taxes are deductible; 4: repair costs per month ; 5. depreciation of the house; 6. the costs (agents, fees. worry ) of selling the house, if the

family moves in the future; 7. minu.~ the pleasure of independence, or plus the pleasures of

insolence.

These costs will vary with the family's situation- for example item 3 varies with the fami ly's taxable income.

Maximizing Utility. We come now to the part of rat ional be­havior that provides purpose to consumer behavior : the maximizing of util ity. Let us translate this assumption into terms of indifference curves and budget lines before examining it critically.

On our assumption that t he goods are desirable indifference ~\lr:'('S have negatiVE' !;)opes, nnn thp comhina tions I on a higher mdtfferPnce curve a rE> always prE>ferrerl to t hose on a lower indiffer· rnce curve. Hence to maximize utility if: to select from the attain· ~bl~ combinations of goods that. combination which is on the highest tmhfff'r~n cE>. curvE'. T n Figure 4-6. thP combination chosen is Q -eomhmatJOns R nnrl T , for example, are also available hut rep· resent low<'r levels of utility: combination 8 is superior to Q but CO!-it s more than the available income.

The Rational Cons'umer

y

0 Figure 4-6

59

X

The slope of an indifference curve has been de.fine~ as. the m ar­ginal rate of substitution of Y fo~ X . Since a pr1c~ lm~ IS tangent to the highest indifference cmve 1t touches, the prlC.e .!me ftnd t~e indifference cun•e h ave the same slope, so the cond1t10n of maxi­

mum utility may be rewritten, p .8

s" .. = p:· What can the economist respond to a. person (say a psychiatris t)

who insists that he does not maximize utility? It would be easy to persuade him tha t he does not minimize utility: after al~ he is alive, and not drinking cmnkcase oil. It would nlso be poss ible, as we sha ll sec later, to p oint to empirical implications of the as ­sumption, but since these implicat ionA began to be developed only about 40 year·s after the theory waA propol<ed (1871 ) . what led econ·

omil"t !" to accept it? • This equation holds only if the price. line and indifference cu~e are tangent.

Tf a price line touches the highest indtfTercnc~. curve on an. axn:1, so ~nly ~ne commodity is purchll8ed (say Y). the eondttton for maxun um sat18fact1on hecomes.

8 11• < P.!Pw if X ~ 0. ~n!'h ""om er" ~olution11 ahound in "linear programming."

I I

I

I t t. I . . ~ I I ~ ! f

I t''

60 The Theor11 of Ut'l' • • t lly

The main reason was mtrospechon. Everyone has irr t' · f t t t a 10llal foibles: a common one IS to re usc o P~ e~ ra postage on a lette

if one does not have the exact denommabon, thus saving r . one or

two cents, at the co~t of a more e~pens1ve special trip to t post office. Y ct. hy nnd large om nchons are geared to the he

. I t t ' .d 'l goals we seek to achieve. n rospec we ev1 ence Wl l never conv· . . m~a

sceptic, and perhaps the only remarkable thmg about inti'Osp t' on utility mnximizing is that virtually every economist fo:cd10~

. . I . d n tt convmcmg over so ong a peno .

Consumer Beha,•ior

We can now proceed to the derivation of consumer reaction t price and income changes. Let us begin with income.

8 0

Variations in Income. Tbe budget line, which displays the com.

y

Figure 4-7

The Rational Consmner 61

bination of goods which (at given prices) the consumer can afford is

XPz + l'P11 = R = Income.

As income rises, the budget line shifts to the right., but without a change of slope because prices arc being held constant. A whole nrray of budget lines is shown in Figure 4-7, with incomes labeled.0

y

X

Figure 4-8

Each budget line is tangent to an indifference curve, and this is the point of maximum satisfaction for the consumer. These points are joined by the dashed curve, T . If T is positively sloping, more of each commodity is purchnsecl as income rises. If T has a negative slope, as in Figure 4-8, less of one commodity will be bought as income rises (and such commodities are often called inferior) .

• I ncome wilL be proportional to the intercepts on either axis.

62 The Theory of Urt· . , I tty

Clear!" both (or, in the case of more commodtttes, all) com .... d' . J • • ld ... o the

eannot be inferior or the enttrc mcome wou not be spent. s l'arintion in Prifes. The corresponding derivation of the d

I f th . etnand cun·E' reC'Juires only t tat we vary one o e Pl'l('CS, holc!ing ill and the other price constant. Let the Yariable price be p a c.IOille

. . "' ' 0< re. wrtte the hudget lme ns

Y= R-XP". P, p"

As Pr rises, the slope of the price line ( -P,/P11 ) becomes a 1 · b th · I' b arger negattvc num er- e pnce me ecomes steeper. An arrav of . lines arc drawn in Figure 4-9. · Pnce

Again the tnngencies with indiffet·ence curves can be read oft' and are connected by a dashed curve M. As we have drawn th~

y

X Figure 4-9

The Rational Consumer 63

indifference curves, the quantity of X purchased diminishes as its price rises, and this is of course the usual state of affairs. But it is possible to draw the indifference curves so more of X i · bought as the price rises; we do so in Figure 4-10. This result is paradoxical and what is even more paradoxical is that Marshall believed such

Px =2

X

Figure 4-10

a situation once arose. The1·e is some evidence that this "Giffen case'.' (as it is called) never existed, and none at all that it did.•o But 1t could exist, and we shall shortly explain why.

Income and Substitution Effects. The logic of the Giffen case and o.r these exe:cises in geometry, will be clarified if we go back to a simple question: what happens when the price of a commodity

•• See reference, footnote 4, p. 24.

The Theory of Ut'l' M ~~

S tlle consumer has been on the budget line, falls? uppose

O.lX + 0.5Y = 50,

(where P, = 10¢ and Pv ~ ~f) ' buying 200X ~nd 60Y. Thi~ combination is labelled Qo m Ftgure 4-11. If the pnce of X falls to

64 , the budget line becomes,

0 .06X + 0.5 Y = 50,

and a new combination (Q~) is purchased . When the price of X fell by four cent", the consumer obviously

became better off: he could continue to buy 200X and 60Y, and

y

X

Figure ~-11

The Rational Consumer 65

still have $8 ( = 200 X 0.04) left. Suppose, in fact, that simultane­ously with the fall in P,, an $8 income tax were levied upon him. Then the new price line (with Per = 0.06) would shift to the left and go through Qo, because X = 200 and Y = 60 is a point on the price line, 0.06X + 0.5Y = 42. With such a tax, the consumer would have moved to combination Q11 because this would be the point where utility was maximized. And clearly Q, lies to the right of Q0 : the convexity of indifference curves guarantees that a flatter price line will be tangent at a larger quantity of X. Or, in common­sense terms, since X is relatively cheaper, with a fixed 11real" income the consumer will buy relatively more of it than before the price fall. 11 Now let the vacillating tax collector refund the $8. The price line moves to t he right, and the indiYidual returns to Qz. The move from Q, to Q: is therefore called the income effect, and the move from Qo to Q, the substit1'-tion effect.

The substitution effect is always negative: a fall in price always leads to an increase in quantity. But the income effect. can go either way. In the normal case it reinforces the substitution effect: the restoration of the increment of real income due to the price fall leads to an additional increase in the consumption of X. But with inferior goods (such as coarse bread, tenements, and old polo ponies) the income E'ffect is negative. It can even dominate the sub­stitution effect, and then we have the Giffen paradox-which is il­lustrated in Figure 4-12 {an elaboration of Figure 4-10) .1 :

A Utility-based Supply Curve. Whenever an individual possesses a stock or flow of anything (potatoes, labor services) he may be­come a seller ns well as a buyer of it. It is easy to enlarge the utility analysis to deal with this situation.

11 Strictly speaking, Q, lies on a slightly higher ind.ifJerence cun·e than Q. so real income is (by definition) slightly larger at Q, than at Q0 • But if thP price change is small, the difference between measuring the submitution cfft>rL along indiffrrPncP curve T. und between In nnd /, is mathematically negligible (meaning a higher order infinitesimal).

u In the preceding chapter t'Omplements ond substitutes were defined in terms of the cross-elasticity of demiUld. In the theory of utility, different definitions ha,·e been de,·eloped that nre more logical IUld leS8 u~nble. When one thinks of bread and butter as complements, one is thinking of tMtes. and it is therefore more appropriate to define the relationship between goods in terms of the indifference curves, quite independently of prices Md income. And thil' is whnt is done; see, for cxnmple, R. 0. D. Allen. Jllatlrt>malicnl A.nalytis for Economuts (London: Macmillan, 1938), p. 512.

I

I j

r 66

y

Figure 4-12

The Theory of Utility

X

Let us assume that the individual possesses an initial stock Xo of a commodity, and that the quantity he possesses aft-er making any exchanges he wishes is X. Then X- Xo is the quantity demanded if X> Xo. The budget equation becomes

or (X- Xo)P., + YP" = R,

XP., + YP11 = R + X0P.,.

Hence when t~e price of X rises, the budget line becomes steeper as before, for ~ts slope is - Pr/ P11, but now it also is raised by the amount of the mcrease in the value of the initial stock.

»

The Rationa~ Comumer 67

y

0 X

Figure 4-13

The geometrical derivation of the supply or demand curve for X is illustrated in Figure 4-13. At an initial price Pr, with price 1ine AB, the individual is at Q1-as drawn here he wishes to hold less of X than his original stock, and supplies Xo- X,. If the price of X falls by half, the budget line becomes CD,18 and the quantity sup­

plied falls to X o - X 2 ·

There is a double income effect with an initial stock of X. A

u The intercept of the budget line and the X-axis is now given by

X _ R + XoP. R + X - P. • P. o.

The corresponding Y-axis intercept is R XoP. Y•-+ - · P., p~

The Theory of (Tt 'l' M t~

• . 1·ncrea-=:es the real income of a given number of doll"

fall m pnce .. ~ . b f d . ..rs. f 11

. price will reduce the num er o ollars of tnco But a. a 111 • f v . ld Ille

. d f the c:n)e of X. If possesswn o .A yte s a subst"'nt· 1 recen·e rom · ~·· . .. Ia t. f a perc:on'" income, as IS true of a wage earner when 'l7

por 1on o - ~ . . <'-.

1 b (time) the latter effect will be dommant. Hence a fall

1s a or ' · · 1 • . ratec: will (1) lead to an mcrease m e1sure (whose cot m wage ~ . s . f regone wage income), and (2) lead to a decrease m leisure IS 0 . d I . . I

because of the fall in real mcome, ~n e1sure 1s a normal good. If the latter effect. is dominant, there IS a abackward bending" sup­ply curve of labor as a function of wage rates, in which more labor

is supplied at lower wage rates.

Revealed Preference Some economists, disenchanted with the subjective overtones of

utility theory, have resorted to an alternative approach, that of revealed preference. T he philosophy of this school was well-ex­pressed by Bernard Mandeville, a most penetrating man:

I don't call things Pleasures which Men say are best, but such as they seem to be most pleased with; . .. John never cuts any Pudding, but just enough that you can't say he took none; this little Bit, after much chomping and chewing you see goes down with him like chopp'd Hay; after that he falls upon the Beef with a voracious Appetite, and crams himself up to his Throat. Is it not provoking to hear John cry every Day that Pudding is all his Delight, and that he don't value the Beef of a Farthing?"

The essence of the approach is to look at observed behavior, and from it deduce certain properties of tastes. The theory is formally independent of utility, but it is inconceivable that the right things would have been observed without guidance of t he utility theory.

Suppose we can observe a consumer at many equilibria-each with a different set of prices and quantities. At one time he is at ~~o on price line B,o (Figure 4-14). The individual prefers this pos1t10n to any other on or below this budget line, or he would not have chosen it. I n principle (a phrase used to denote the combina­t ion of incredible circumstances and unbelievable ingenuity) we could observe him at a hundred other diffet·ent relative prices. Let

K~~.~:~i~~~le19°24/ )thVe B1 e1es (1714), (Oxford, England: The Clarendon Press,

• ' 0 . ' pp. 151-52.

The Rational Cons11mer 69

us find the budget line (Bn) which lends the consumer to choose combination Qg, a combination necessari ly inferior to QIO. The choice of Q

9 reveals it to be preferable to C\'CI'Y other point on or

below Bn, so all these points are in ferior to 01o· By similar argu­ment Q

10 is preferable to eYcry point on or below line Bs. If the

y

Ba

0 X

Figure 4-14

relative price changes arc made small enough, t his procedure will

t race out all combinations inferior to Q,o. A parallel procedure will trace out all the combinations superior

to Q10

(Figure 4-15). On budget line Bn, if Qll is chosen it is pref­cmble to Q10 and hence to all points on or below Bu; simila rly Q1~ is preferred to Q11 and hence to Qlo· The combinations t.raced out by this procedure will define a curve which converges to that

!':"'-~ . ~: · ' •.

70 The Theory of Utility

y

0~----------------------------------x Figure 4-15

obtained for combinations inferior to Q10, and the common bound­~ry. of the preferred and unpreferred combinations will define the mdlfference curve through Qlo· The two sets of revealed preferences are brought together in Figure 4-16; with sufficient ly small price chan~es the two sets of lines converge to the indifference curve. T~~s approach dispenses with almost every requirement except

chonslstency .of P~eferences of individuals. But since it is obviously eart-breakmg m its d t .

')) t a a reqUirements, an t he properties 1 us rated by revealed f h t'l't pre erence ave of course been inferred from

u 1 1 Y theory I ts chief f f · of utility th . th unc IOn Js, therefore, to reassure critics route · . eo?'

1 at the same results can be reached by another

, m prmc1p e.

The Rational Consumer 71

y

0 X

Figure 4-16

APPLICATIONS OF UTILITY THEORY

T he elements of the theory of utility are before us: for what can it be used? The uses are of two different sorts. On the one hand, it is possible to make predictions concerning the behavior of individuals, and in this role utility theory provides a set of hy­potheses. On the other hand, ut ility is a bridge between observable phenomena and subjective states of satisfaction , and in this role allows inferences to be drawn concerning welfare effects of policies. Both uses deserve illustration.

Utility Theory as a Hypothesis

The theory of the rational consumer has numerous empirical im­plications. The most famous one is the assertion, discussed above, that the demand curve for a commodity must have a negative slope

t

i i ~ a

I , I ,

The Theory of Utility 72 ..

. •111 or positive. But It IS not a very useful I . me effect IS sm. . if t te m~o . nil known dt-mand curves have negat1ve slopes. hypothesis, ~mrc 1 the,.es can be derived, however. Recall our

Many simpler typo ~ d' I • • l ( • 57) of an identical commo 1ty sod at two \'iou ~ examp c p. . d h

P~ · · tl consumer knows the pnces an t c fact of ~rice~, wiTtelrc bt:~gct line 2Xa + 2.1Xb = 10, displays this situn-JdcntJty. te ' · A · t th' · · . 8 · the higher-pnced source. gams Is pnce hne tiOn, where IS . • I f .

d t l . di'fference curves wh1ch hnve t 1e 01 m we raw 1e 1ll '

Xa + Xo = constant,

· it makes no difference whether the consumer has Xo and X6 smc(~ _ 5) and (X6 + 5). To maximize utility, the consumer

or o • • d ' ff obviously buys only Xo, for the htghest m 1 erence curve he can reach is inter8ected on the axis (Figure 4-17) . This is ensy to test, at lenst in principle.

Figure 4-17

Applications of Utility Theory 73

Or consider a wholly different a rea. In addition to a desire for profits, the entrepreneur wishes certain consumption amenit ies in his business (a noble edifice, a handsome offi ce, a delectable ~ecre­tary, certain social types of associates ). All hnve costs, of course, and the corresponding budget line and indifference curves are shown in Figure 4-18. He buys OC of the amenities at a cost of BA (of foregone profits) . In certain a reas (public utilities) the state regu­lates prices to put a maximum on profits, which a re reckoned after

(/')

!= ...... 0 a:: a..

A

0 c AMENITIES

Figure 4-18

0

business expenses which of course include the costs of these ameni­ties. Hence to the limited degree that the regulation is effective the budget line becomes flatter- there are smaller costs to the amenities in terms of foregone profits. The new equilibrium, P', nec­essarily has larger amenitiesY;

"The new budg~t. line is flatt.er because the regulator:'· body objects much leS'3 to amemt1es than to money profits. For an elaboration of the argument and empirical evidence on effects on the racial compooition of the labor _force, see A. Alchian and R. Kessel, "Competition, Monopoly and the Pursu1t of Pecuniary Gain," in A &peclB of Labor EconomiC$ b\· A Conferent'e of the Uni\'ersities-National Bureau Committee for Eco~omic Research (Princeton, N. J .: Princeton University Press, 1962).

The Theory of Util"t 74 t y

. t. c:s is necessary to multiply such predictions f Only mven JVCnev . I . d' "d o

. . th 1e The theory of the ratwna Ill JVJ ual, who seek the utJhty eory. "bl . s to fulfill his goals as efficiently as possJ e, ~ertams to a vast area

duct C\'en if it does not proVIde a complete theory of human con , · 1 f

·t of that conduct. We econom1sts 1ave been remiss 1 o any pal . h . ,. t. f ' bel

. . · developing and testmg t e 1mp wa Ions o the theory · Je\e, m "k I t d' b ' I . b b tests indeed are we h e y o 1scover a etter theory on y y sue , •

of economic conduct.

Welfare Analyses Suppose a wholly alien creature ~ere to ob~erve two ev~nts. First,

one man displayed a card requestmg a charitable contnbution, to which the other man responded by handing over $20. Next, one man displayed a revolver, and the other man responded by handing over S20. Surely he would be unable to distinguish between the two tmnsactions, and if told that the former donor felt the better for his gift, would feel entitled to infer that the latter donor felt likewise.

To read any meaning in terms of satisfaction or welfare into observable events, clearly we must have a bridge between states of welfare and observable events, and this is the chief role played by the utili ty theory. Unlike the alien creature, we do not need an elaborate theory (or rather, possess parts of it intuitively) to distinguish the effects of charity and robbery, but for many prob­lems a much more formal apparatus is necessary.

We shall examine three examples of welfare analysis. The first is the theory of cost-of-living indexes, on which economists have long labored. The second example is a famous piece of the apparatus of welfare economics. The final example, price discrimination, is intended chietJy to display a technique with many applications.

Cost -of-Living Indexes. The phrase, cost of Jiving, connotes the amount the family spends on consumption, but this important cost is termed consumer expenditures. The phrase actually means the cost, over time or between places, of living at a constant level-which means, of course, staying on the same indifference curveY

~' .Spe~ial me~tion should be made of the important modern literature on utility m relation to risk, to which references are made at the end of the chapter.

"To avoid this ambiguity, the official American index is called the Con-

p

Applications of Utility Theory 75

Price indexes developed out of the inflation following the Cali­fornia gold discoveries, and they have not lost their intimate con­nection with inflation. If an average family earned $5,000 in 1960 and $5,500 in 1962, in which year was it "better off"? The answer is that if a (perfect) index of the cost of living rose less than 10 per cent between these years, the family was "better off" in 1962.1•

One basic assumption must be made before we can make any progress toward an index number: tastes must not change. For no meaning can be attached to the same level of satisfaction when satisfactions change. Suppose Smith is a vegetarian in year 1, and meat-eater in year 2. No matter how t he prices of grains and meat move, one cannot measure the cost of living, for there is no quantity of meat which yields the same satisfaction as the previous q_uantity of grain: the man is different at the two dates, and the question has become the insoluble one of finding the money incomes which will yield equal satisfactions to two men. 19

Let us assume that in a given year the average family buys two commodities-the argument of course applies to any number-in quantitjes 0q0 and bqo (where a and b are the names of commodities, and 0 the year) at prices aPo and bPo· Then

,.qo aPo + l>qo 1>Po = oRo,

was the amount spent. The budget line and the observed combina­tion (Q

1) are shown in Figure 4-19. In the next year prices change,

and the foregoing combination would have cost

oqo aPt + bqo 1>P1 = oRt.

If we treat this latter expression as a budget line, it will necessarily go through the combination bought in year 0 ; but it~ slope will be different if the prices of A and B have not changed m the same

proportion.

sumer Price Index. On the practice and problems of price. indexes, .see Gove)­ment Price Statistics (Washington, D. C.: Joint Econom1c Commat~ee, 1~1 ·

'"A perfect index would lake account of ~com~ ta~es and public sen'lces, which both the official index and the present diSCUSSIOn 1gnore.. .

"Of course one can postulate that money incomes that ~til ya~ld the dm: real income to a vegetarian and a meat-eater, o_r to a dt.tch-dtgger al~ .

Thi · · f t do e m some mcome-eQu tzmg prime minister, are equal. s ts m oc n . . 8

of philosophies, but it is an ethical judgment, not a descnphon of state real income.

iiJ

The Theory of Utility

76 . had a money income oRo in year ? . an~ oR • in Year If the famtly 1 t as well off in terms of ut1hty m the latte

1 't must be at eas . . 't r '

1 1 1 the original qurmtltJCs, so 1 was as well otT

ar It coufc JUY • h . d 'ff . ' yc · b bly reach a lug er JD 1 erence curve w1tb R nd it could pro a . I f 11 . o t 8 . . tl commodity whose pnce tas a en relatively (A

by substttutmg 1e

8

A

Figure -l-19

in our diagram), say at point Qz. So we can assert that the cost of liYing rose from year 0 to year 1 at most in the proportion,

oRt _ o(}o oPl + b(}o bPt

oRo - o(jo oPo + b(}o 11Po1

which is generally written

.C = 'X(}oPt, Xqopo

:here t~e summation signs indicate addition over all commodities,

Th~ ~ IS the name (of Etienne Laspeyres) given to this index. IS Js the form of the ind d t . r . . ex usc o measure changes m the cost of

t v~ng m. the United States, with a sample of prices of 400 goods an servtces and a new set of quanti t ies (weights) every decade.

p

Applications of Utility Theory 77

The Laspeyres index measures the change in the cost of living as the family lived in year 0; obviou~ly another index could be made to measure the cost in year 0 of thr way the family lived in year 1. Here in year 1 the family bought quantities .q. and ~q, and prices aP1 and hp., on the hudget line

By exactly the same argument used to reach the I.aspeyres index, we can say that in year 0 the family would be at least this well off if it had spent

because it could have purchased the year 1 quantity in any case, and usually it could reach a higher indifferen<'e curve by buying relatively more of the commodity whose price had fallen relative to the other prict>. In fact the pr<'vious diagram nE>E'ds no change other than to relabel oRo as .R., and oR1 as ,R". So we conclude that the cost of living in year 0 relative to year t ro!le at most in the proportion,

1Ro oQl oPo + bQl &Po 1R1 = oQt oPt + &(}li>PI

"l:.QsPo = I.qlpl.

But normally index numhcr~'< nrc reckoned forward in time, so if ,Ru/ ,R. is the maximum relative change in the cost of living (as in year 1) from year 1 to year 0 , then its reciprocal,

is the minimum relative rise in year 1 relative to year 0 of the cost of living as in year 1. Here the <P represents Hermann Paasche, who, like Laspeyres, was not the first to propose the index named after him. If we should ever encounter a. case where a theory is named fo r the correct man, it will be noted.

The Laspeyres index, as we have said, is a maximum estimate of the change in the cost of living from year 0 to year 1, and the Paasche index is a minimum estimate. Pnfortunntely, they do not pertain to the same level of living: the Laspeyres ind£"x prices the

r

The Theory of Utility 78

th Paasche index prices the year 1 budget. Of year o. budg:~~e ~uantities were consumed both years, the indexes course If t~de t' I but in this ease the only probable cause is that would be 1 en 1ca ,

rices have not changed! . P . bl m in calculating index numbers IS the treatment One baste pro e .

h · the qualities of goods. We cannot properly attnbute of c anges m f 1' · · f · all of the change in price to the c?st o IVlng 1 . an tmpro;ed com-

d·t (a betwr automobile or tmproved surgtcal techmques) is mo

1 Y • f · nl · t h dit' · 1 d On the other hand 1 one pnces o Y ose commo 1es mvo ve . , .

whose qualities do not change, he Wlli find that a .large and e~er · · share of the con~umer's budget must be Omitted. A devtce r1smg ~ . . .

that can often be employed is a farrly straightforward extenston of the basic logic.

Changes in quality are gradual, and they can be at least partially measured by measurable characteristics of the commodity. Automo­bile quality can be measured by weight, horsepower, length, auto­matic vs. nonautomatic transmission, and so on. If these measures are properly chosen the differences in prices of various models in any one year will be well explained by these differences in charac­teristics. We can then say, for example, that 10 horsepower are worth $40, and automatic transmission is worth $180. If next year a gi\'cn model of car sells for $200 more, but has 10 more horse­power and an automatic transmission, its quality-corrected price actually fell $20.20 Economists generally believe-certainly this one does-that the official index has considerably overstated the rise of prices because of the failure to cope with quality changes.

Consumer's Surplus. When a reflective man buys a crowbar to pry open a t reasure chest, he may well remark to himself that if necessary he would have been w!_lli,ng to pay tenfold the price. When a parched man drinks a free beer on a hot day, he is apt to consider it a bargain. Marshall gave the odd name of "consumer's surplus" to these fugitive sentiments.

Let us define this surplus as the amount over and above the price actually paid that a man would be willing to pay for a given amount of a commodity rather than go without it. Then we may illustrate this ~;;urplus by two indifference curves between money income ( = all other goods) and the commodity in question (Figure

,. ~hie, ~cthod il! used in :Zvi GriJichP..a, "Hedonic Price Indexes for Auto­moblle.s, ID Gouernmer.t Pnce Stati3tics (Washington D. C.: Joint Economic Comm1ttee, 1961). '

............ - ------- ' ~ .

Applications of Utility Theory 79

4-20A). The individual would be as well off with an income of OA, and the pri\'ilege of buying OC of the commodity at the indicated prices (given by the slope of AB) , as with an income of OE. Hence AE is a measure of his consumer's surplus. Alternatively, be pays a total of DA for the OC units, and would be willing to pay an

I E

0 c (a)

X

~, .. ~~ )'\11 ,._.. ~ Consumer

~.s. <l Surplus 1-=o=:.:..!:..:..=.::... __ -4... " -w

<...> a:; a...

0 c ( c)

0

Figure 4-20

c (b)

Demond

X

8

X

additional FD. Therefore FD is the additional amount he would pay if he already has OC of the commodity, whereas AE is the additional amount he would pay if he has none of the commodity and the option is offered to him. The two estimates may differ.

Let us follow Marshall a step further in assuming that the mar-

The Theory of Utility 80

. come does not change appreciably if only l tTty of money tn Th .

gina u 11 . . t on commodity X. en every mdifference

a small .amount 18

hspen e shape but be vertically higher or lower wtll have t e sam . h h' . l'f .

curve 'ff urves 21 Armed w1t t 1s strop 1 ymg prop th ther indl I"I'Cnce C • t' f -

an ° struct a simple represents ton o consumer rtv we can now con

e • ' . terms of the demand curve. surplus m . at A b.n , is the maximum amount he would

If a consumer IS ' • h h . . 't f X (Figure 4-20B). Actually, Wit t e mdtcated

pay for one um 0 • • h ld . 1. h pav"- only t.a. The maximum pnce e wou pay for

pnce me. c . ~ fi •t · Th' d 't 1 av1'ng paid .:la for the rst um , ts t..a2. IS second n c:econ um , 1 •

~ . pr'Jce ( Aa ) should be measured along II 1f only t.a was rnax1mum "' 2 • •

paid for the first unit , but since the mdtfference curves are parallel

rtio 11 the same b.a. is obtained on I. The process may be con-ve ca y, - . . t o ed I reach Q. The maximum prices are m fact the actual de-lOU ~.o h . .

d Prices so the demand curve represents t e maxtmum pnces man , . t't' H , which will be paid for the var1ous quan 1 tea. ence consumer a surplus can be displayed as the area under the deman~ curve,. ~nd above the price line (Figure 4-200). Under the special condttton of a constant marginal utility of income, this correspondence is exact (and F'D = AE in panel A), but in general this relationship between consumer surplus and the area under the demand curve is only approximate.22

•

A characteristic application of the consumer surplus techmque is provided by a study of methods of solving the water shortage that New York City faced some years ago.23 One method of con­serving "·ater would haYe been to charge the large number of users who were not metered and paid only a flat sum for water. It there­fore did not pay for those consumers to repair leaks or even to wear out faucets by turning them off, and something like 200 mil­lion gallons a day were so wasted. If these users were metered, this amount of water could be saved, at a cost of (1) about 150

11 Since the slope of an indifference curve is marginal utility of X

- marginal utility or income' if the marginal utility of income is constant, the slo~ of the indifference curvea will vary only with X.

.. Sec J. R. Hicks. "Consumer's Surplus and Index Numbers," Re-uic10 oJ Eco110mic Studiu. 9 (19{2) , 126-37.

• This diseulll!ion is based upon Chapter 10 of J . Hirsh Ieifer, J. C. DeHaven, and J . W. Milliman, Water Srtpply (Chicago : Universitv of Chicnuo Press, ~). . -

Applications of Utility Theory 81

per million gallons per day for the cost of metering, plus (2) the cost of repairing leaks, which we shall ignore, and plus (3) the consumer's surplus lost by refltricting consumption if the marginal cost of water was raised from zero to say 15¢ per cubic feet (the going rate). If the demand curve is taken as linear in this range, the average value of the water saved was 7.5¢ per 100 cubic feet or $100 per million gallons. Hence the total cost of saving water, including consumer surplus lost, was about $150 per million gallons.26

Price Discrimination. As our final example of welfare analysis, we shall examine price discrimination. Price discrimination arises when a commodity is sold at different prices to different people.21

Suppose, for example, that salt is sold to one person for 10 cents per pound, and to another person for 20 cents per pound; all other prices are equal for the two persons. The buyer at the lower price consumes salt until the mnrginnl rate of substitution of a com­posite 11othet· goods" (with a price of Sl.OO per unit) for salt is 1 for 10, whenever the buyer at the higher price has a rate of substitution of 1 for 5. If they were to exchange salt and other goods at some intermediate ratio, say 1 to 7, both would gain. At the margin the buyer at the higher price would gain 40 per cent (j) more salt per unit of other goods given up; the buyer at the lower price would gain 43 per cent more units of other goods per pound of salt given up.28 Price discrimination plays the same role here as a tariff plays in the theory of comparative cost~: it is an obstacle to maximizing utility.

This kind of problem is commonly analyzed geometrically by an artifice that is worth describing. Suppose the two parties have a total of OY,, of other goods ami OX0 of sa lt (Figure 4-21): perpen­cliculars are then projected to 0'. The incliffcrcmce curves of indi­vidual A (who gets salt for 20e ) are drawn with respect to YoOXo, and tl10~e of R- (salt for 10¢) are rotated 180° and drawn with respect to Y00'X0 • Then any point in the rertangle represenU. a distribution of the given quantities of salt and other goods between

"The cit:v fathers, or step-fathers. rhosc instead to build a new dam, at a <·ost of Sl,OOO per mil Eon gallons. ~·A more> prc>ciso definition will be given later, p. 209 . u He now obtains l of a. unit or other goods per pound of salt, where formerly

he received only fo of a. unit, and • - 10 T- ~ -o.43.

82 The Theo,-y of Utility

I for example, at S, A gets OM of salt and B the two individua s:

getsw ·J~Xo.. dJ'scriminat ion the price line of A {drawn with t·espect Jt.fl prlCC · ' . f h ·

to OXo) will have a slope of -!,the raTtJlo o .t. el. pncef Bof ~he salt to that of other goods; it is labeled Pn. 1e pnce me o wtll have

Yo ~----------------------------~0'

• s I I I

0~---M~------------------------------J Xo

Figure 4-21

a slope of -fG-, with respect to O'Y0, it is labeled Pb. If the position with discrimination is one of equilibrium, the two price lines inter­sect at a point (R) such that each is tangent to an appropriate indifference curve. 21

. "'At point R, not only is each consumer maximizing utility but the quantj­tJes demanded of the two goods equal available amounts.

Problems 83

Now consider a point Q where the two individuals' indifference curves are tangent. Each individual would be bett-er off at Q than at R, for each would be on a higher indifference curve (remembering that the B curves are measured from 0') . There are many poin ts such as Q, and we have joined them by a curve CC (called the contract curve). Only points on this curve maximize utility for each man, given the level of uti lity attained by the other, and only with a nondiscriminatory price will the individuals arrive on this curve. Any movement along the contract curve injures one party and bene­fits the other, but movements to the curve can benefit bot.h.21

RECOMMENDED READINGS

Alehian, A., "The Meaning of Utility Measurement," American Economic Review, 42 (1953), 26-50.

Ellsberg, D., "Classic and Current Notions of 'Measurable Utility'," Eco­nomic Journal, 64 (1954), 528-556.

Hicks, J. R., Value and Capital, Oxford: Oxford University Press, 1939, Part I.

Friedman, M., and L. J. Savage, "The Utilit.y Analysis of Choices In­volving Risk," Journal of Political Economy. 56 (1048), 2i9-304 ; rf'­printed in Readings in Price Theory .

Stigler, G. J., "The Development of Utility Theory," Journal of Political Economy, 33 (1950), 369-387; reprinted in Essays ir1 the HistonJ of Economics, Chicago: University of Chicago Press, 1964 .

PROBLEMS

1. Draw the indifference curves which display the following preference system:

(a) Two commodities are useful only in fixed proportions {left and right shoes) . (b) One commodity is fully divisible but the other comes in (or i.s useful only in) integral units (gasoline and tires) . (c) "I like my martinis drier than you do." (d) Consumption of one commodity reduces the enjoyment of t.he othf'r (WCTU tracts and bourbon)

.. The length of the cont.ra<•t curve is given b:v the "initial" ronditions o~ a problem. Here individual A would prefer .di~ri.~in~tion to f~lling below 1~­difference curve A,, and B would prefer diSmmmatwn to falhng (toward 0 > below B,.

The Theory of Utility

84 9

and Paasche indexes: 2. Calculate the r.aspeyre

Quantity of bread Quantity of beef Price of hread Price of beef

YEAR Q YEAR 1

200 100

15¢ 20¢

170 120 12¢ 25¢

mustrate graphically and ex'J)lain. . I t t I Utilities of X andY vary as follows.

3. Supp()S(' t II' o 3

TU,= VX TUII =lOY- y: (Y < 5)

(a) ConstnJct indifference curves between X and Y for a level of satis-faction of 24. _ (b) Suppose the utility of each commodity doubles (to 2 v' X and 2 [tOY - Y']). Construct the indifference curves for a level of satisfaction

of 48. 4. Demonstrate that people are better off with rationing by prices

than with rationing by fixed allotments, given the distribution of income. 5. A consumer challenges you to disprove empirically his assertion that

his indifference curves intersect. If you have an unlimited number of ob­sen·ations on his actual consumption {at all relative prices and incomes), how would you meet the challenge?

6. If the marginal utility of Y is constant, all indifference curves have the st1me slope at a giv<'n X . Prow.

ebapter five

Pricing with Fixed SuppUes

Once the demand curve of a commodity is established, we know the price at which each quantity can be sold. But we have begged two questions in constructing this demand curve: what is the mar­ket, and is it competitive? After we answer these questions we can analyse the pricing of commodities in fixed supply.

T H E MARKET

A market, according to the masters, is the area within which the price of a commodity tends to uniformity, allowance being made for transportation costs.

The price of a commodity "tends to uniformity" for one reason: the buyers at point B refuse to pay more than the price at point A plus transportation, and the buyers at A a.ct similarly. Or the sellers act in this manner. The market area may well differ between buyers and sellers.

As the buyer of an automobile, I will perhaps search only over a circle with a 10-mile radius about my home, so I may readily return to the dealer for services. But this cannot mean that the market area is 314.16 sq. miles, for othc1· buyers are located else­where and their circles of search overlap mine. The market area, so far as buyers are involved, is the sum of the areas within which the mobility of consumers is sufficient to ensure the tendency to uniformity in price, allowance being made for transportation costs. !or automobiles, this m·ea will probably contain a city and its ad­Jacent suburbs; for the services of gardeners it may be a small

85

Pricing with Fixed Supplies 86

for goods purchased by mail order it may be portion of a city i

nation-wide. f n the sellers ' viewpoint will usually be larger The market area rot . . rt

· h b ers' viewpoint. There IS no 1mpo ant tendency than from ~ eM~Y apolis to buy potatoes in Maine. Y et one of f people m mne or · . •nt. t"cal ~tudies of demand revealed that the price

the earhest sw. ts 1 ~· · , · Minneapolis depended upon the nat10n s output of

of potatoes 10 • B d b h b t given this output, was not m uence y w ether the

potat.oes, u , . · ) 1 I I t t (1· 0 Minnesota and W1sconsm was arge or small oca ou pu · ~ ·

An investigation was made to determine the effect of variat ions in the · d t" of Minnesota and Wisconsin taken together on the price of

pro uc 10n . . · · 1 ed · tat in Minneapolis and St. Paul. This mvest1gat10n resu t m the

po oes · · M" t d w· · discovery that variations in the productiOn m mneso a an 1sconsm had no measurable effect on the price of potatoes except to t he extent that the production for the entire United St.ates wa~ affected:

Although the fact is surprising, it is very readily explamed when once recognized. The explanation will be some~hat clear~r if ~he price ~ituation as shown in (an accompanying figure] 1s borne m mmd. Cons1der the extreme case of an excess production in Minnesota exactly equaled by 8 deficiency of production in Maine. In order to take care of the deficiency in the supply for New York City, for example, an unusual quantity is shipped in from New York and Pennsylvania. Large quantities of potatoes having been shipped east instead of west from New York and Pennsyl­vania, their pbce is taken by Michigan potatoes. But since Michigan potatoes are bC'ing shippt>d somewhat farther east than usual, Minnesota potatoes can be sold without competition in what is ordinarily Michigan terri tory. The result is that the Minnesota potatoes sell at practically the same price that would have been obtained if production in both Minnesota and :\1aine bad beE>n normal.'

On the other l1and, sometimes the market area as defined by sellers is smaller than that of buyers: a cotton farmer will have a rela­tively small area in which he will sell his crop; the buyers may deal in every cotton-picking state.

Since the market is defined by the uniformity of price its area ~i~J be at least as large as the larger of the areas of seller~' compe­tition and buyers' competition, or the sum of the areas when they partially overlap.

M'. H. Working, "Factors Determining the Price of Potatoes in St Paul and E mn~apolis," ~cchnical BuJJetin 10, University of Minnesota Agricultural

xpen ment StatiOn (1922), p. 25.

-Competition 87

The size of the market also Yaries with the t ime we allow for price adjustments. A perishable good, once i t reaches a given city. will be sold there even though it turns out that n higher price could haYe been fetched elsewhere-but future shipments will iron out the d isparity. Once an apartment is built, its rental depends upon the housing demand of t he community. But in the long run (mean­ing a period long enough for the supply of houses to be varied sufficiently). apartmentg will not be bui lt where rentals a re unre­munerative, and more will be built where they are remunerative. There is accordingly a tendency for apartments of given quality to have the same rental throughout the country. But this tendency is slow in its workings bl:'cause the stock of apartments changes very slowly, and it is modified hv geographical immobilities of re"ources ( in particular, la nd) which we shall discuss later. B ecause of tht> mobility of t>n trepreneurs and also of consumers. in the long run most market::> are of very large geographical t>Xtent.

A perfect market is one characterized by perfect knowledge on the par t of the t m ders. Or stated differently, in a perfect market no buyer ever pays more than nny seller will accept, and no seller accepts le~s than nny buyer· will pay. These conditions can be met only in a completely centralized market, which is approximated by a few Pxchanges ~uch as the New York Stock Exchange.

COMPETITION

A competitive markE-t is easily defin ed only for a perfect market: it. il' then a market in which tho individual buyer or seller does not influence the price by his purchase!' or sales. Alternately stated, the elasticity of supply facing any buyer is infinite, and the elastic­ity of demand facing any seller is infinite.

A market may obviously be competitive on only one side: a mil­lion buyers can deal with only one seller (monopoly) or a million sellers can cleal with one buyer (monopsony). But for the time we shall defer such situations and deal only with competitive situations.

W e have defined a perfertly rompetitive market: what a re the conditions under which it will normally arise? The condit ions are four:

88 Pricing with Fixed SuppNes

1 d If t11crc i~ not perfect knowledge, there Will 1. Perfect b~otc ~ a_e.nt which transnctions will take place and

be nn nrrny 0

1 pr~c;, cli~plav such an array. There ". •ill then 'often

nhno~t nil rca mnr c ~ ~ · 't t ' t d b' •. -' • 1 . r g nncl to this ('Xtcnt n SJ ua JOn crme Ilnteral be "copr for ngg 111

' ' I · I' ' II t h d . . ,. _ "' But if the !'cope for 1Igg mg IS sma ' e eparture monopol~ nn:,e .. from competition is small. .

I ,1,.1/Jers There must be many buyers or sellers 1f each z. Jarge n • , , · · h · "

. 1 • 0 nr11rcciablc influence upon t e pnce,- nnd they act IS to lrl \ e 11

indcpcnclcnt ly · . 3, Product homogeneity. If the product 1s not l~omogeneous, it

is meaningless to speak of large numbers. H enc_e, 1£ every unit is " t'nllv unic')lle (as in the market for domesbc servants), t here

c~>~en 1 • • 't h' h cnrmot be large numbers. Yet, if the vanous um s are 1g ly sub-Ftitutnblc for one another, the market can approach competition.

4. Divisibih'ty of the product.

Perfect competition is n typical example of a concept of e\'eryday life that has been taken OYer by economist~ and developed into F:omethin~ almost unl·cla tecl to its original form. Originally competi­tion meant. a multiplicity of tmclers, and only thnl. But when it wn~ discovered that 5 traders might coll ude, n vast number seemed neces:-:uy to guarantee that collusion would not he feasible. When it wM ren lized that eYen a thousand sellers and buyers were not enough if cnch pai1· dealt in ignorance of the others, perfect knowl­edge was ndded. The explicit recognition of homogeneity of product came from the fnct that even minor differenrc:: (a sunny disposition or a fancy container) might lead some people to pay a slightly higher price.

Divisibil ity has a similar origin. Edgeworth, whom we have met heforc nne! shnll meet again, was a diabolica lly clever man. H e cont rived the following problem: n thou~and (or a million) masters hire one sen·ant cach- cxnctly the number :wailable-and no ser­vant can work for two masters. Each master wi ll pay $100; each servant will accept S50- what will the wage rate be? That it will be bctweC!n S50 and SlOO, and hence indeterminate, is no cause for nnxicty. But let it be S-50-then a single servant can leave the mar­ket and force the wage up to SIOO-so even perfect knowledge, large numbers, and (let us assume) homogeneity are not enough to de-

'1\~orc precisely, l11c largest burcr or seller 111\IRt provide only n small fra cllon of the quantity demanded or supplied, which involves, i~ audition to huge numbers, no extreme inequality of size.

i Competition 89 prh·e an individual of a large influence over the market price. Hence we assume divisibility, so the departure of one worker leads (say) to about a 30-second lengthening of the working day for other workers, and his power to influence price is dcstroved.3

If the reader bristles at the acceptance of n~sumptions such as perfect knowledge and complete product homogeneity, he is both wrong and right. H e i~ wrong in denying the helpfulness of the use of pure, clean concepts in theoretical analysis : they confer clarity and efficiency on the analysis, without depriving the analysi.~ of empirical relevance. He is right if he believes these extreme as­sumptions are not nece.ssary to t he existence of competition: it is ~ufficient, for example, if each t rader in a market knows a fair num­ber of buyers and sellers, if all traders together have a comprehen­sive knowledge so only one pl'ice rules. The reason fo1· not stating the weakest a~sumptions (necessary conditions) for competition is that they are difficult to formulate, and in fact are not k"''lown pre­cisely. Again, more work for the next generation.

The Demand Curve of the Competitive Firm

Since the competitive firm contributes only a trifling fraction of the tota l market supply, H has n trifling influence on market price.• We may illustrate this influence by considering a market with a unitary demand elasticity (pq = $1 ,000), in which there are already 100 firms. Each supplies 2 units and the price is therefore Sl ,000/200 = $5.00. An additional supplier now appears. If the 100 firms continue to supply 200 units, the new supplier faces the de­mand schedule:

Q UANTITY

0 1 2 3

PRICE

Sl000/200 ~ $5.000 1000/201 = 4.975 1000/202 - 4.950 1000/203 - 4.925

• An eight hour day contains 480 minutes-s.c. (before coffee breaks), so if C'nch of the remaining 999 workers works slightly IC'ss than half a minute for the employer of the ''anished servant, his employer's need will be satisfied. Or, altemntivel~·. each of the thousand masters hires n worker for 30 seconds less.

• The use of "trifling" rather than "absolutely no" is a trifling concession to realism. It would be more precise to use the lat ter phrase, but then some students would believe that the theory is inapplicable where there is eYen a trifling influence, and this is not true.

90 Pricing with Fixed SupPlie

8

t the are elasticity of the new supplier's demand at If we compu e an output of 2, it is roughly

3- 1 4.925 + 4.975 = - ~. 9.9 = -99. m · 4.925 _ 4.975 4 o.os

It . · fact a general rule that under these conditions the elasticity IS, ID , h l . .

of the demand curve of a firm is equal to t e e astJCJty of the mar-ket demand curve times the number of sellers: 5

p

0 0 Figure 5-l

We illus~rate. such individual demand curves for 2, 5, 10, and 50 sellers m Figure 5-1, all on the assumptions that the market demand has unitary elasticity and the output of all firms except one sum to 200. Of course competition connotes fairly numerous selle~s, and the demand curves for 2 and 5 sellers are put in only to d1splay how rapidly the individual demand curves become elas-

• See mathematical note 7 in Appendix B.

--price Determination 91

tic. It would require a very large diagram to make the difference between the demand curves for each of 50 and each of 100 sellers percepti hie. .

These demand curves were dertved on the condition that all firms sell at the same price. But suppose 100 firms had agreed to fix the price at $5, and .one now contemplated his demand curve if he secretly cut the pnce to $4.99 to trustworthy buyers. Assuming that the 99 other firms continued to adhere to $5; the demand func­tion of this price cutter would be

PRICE

$5 . 01 $5 . 00

$4. 99

QUANTITY DEMANDED

1000

0 2

4.99 = 200.4

Now his elasticity of demand is approximately

200.4 - 0 . 4.99 - 5.01 10.00 200.4 + 0 ... 4.99 + 5.01 = - 0.02 = -500.

Of course if he cuts prices secretly and expands sales immensely, the other 99 firms will soon discover their sales are vanishing. But if he is moderate in his sales (perhaps only doubling sales to 4 units) he will reason that the price cutting will not be detected.8

This reasoning will also be followed by at least 5 or 10 of his rivals, and if 10 double their sales to 4, only 160 (200- 40) units will be demanded of the other sellers, each of whom will suffer, with rising animosity, a decline of 11 per cent in sales.1

This arithmetic portrays the history of a thousand price agree­ments. We shall discuss monopoly, which is what this is, at a later point, but it seems appropriate to emphasize here that large num­bers of sellers not only make the formation of collusive agreements difficult, but also encourage each individual seller to violate the agreement.

PRICE DETERMINATION

Commodities in fixed supply, at least for limited time periods, are very numerous : they include the paintings of Rembrandt, the first editions of Shakespeare, and the number of Fords or Chevrolets

• After all, each rival will lose only 2/198 units or 1 per cent of his sale.s. 'Sales of each will be 160/90 = 1.78, a. decrease of 0.22 from 2.

' It .

.. ,,

H'~·------

92

fi ld Tile" include also the number of shares of com111 ve years o . -' on

to k. . n large indu trial eompany, and the number of dwellin s c m . I:r . II th . g units in a eity- at least. for a tune. :1Istor~ca Y c most nnpo1tant example of all ha~> been the stock of an agncultural product between

harvests. Thr same nppamtu!' of supply and demand can be used for all

these market . But the details of the apparatus vary in an impor-

p

s

D

0 0

Figur e 5-2

tant respect with one characteristic of commodities and services: can they be stored? Let us call commodities which cannot be stored peri.shing. It is customary to describe all goods which will not sur­vive either time or repeated use as perishable, but those which may be used only once (like a bullet) are often capable of storage for a long period.

Perishing Com modities

The traditional case of a perishing commodity was fresh fi sh or stnnvbcrries brought to market before preservation by freezing was

~ .. ,.;t

l price Determination 93

.,sible. The stock was nntumlly thrown on th . k ro~npetition) for what it would fetch and we e mtar et (under coT . . , . . • . may ranslate this b havJOr mto a vc1 ti.cal supply curve (8 10 Figur 5_2) Th

e . d t . l b e . e de nd curve IS e crmmec y tastes income and . -rna . . . • • pnces of other Oods as descnbed m prev10us chapters lind the 1·nt t· g • . . . ! ersec Ion of

the two curves (at p,, Qo) IS. the eqUib.bnum price. The quantities would be per day or other period for which the perishing commodity remained salable.

The equilibrium price is the price from which there is no tendency to move, so long .as the underlyi~~ supply and demand conditions do not alt~r. It IS a st~?le. eqUilibrium, in the sense that if the market is !arred. ~ff .eqUihbri.u~, the dominant forces push it back toward this eqUlhbnum. pos1~10n. For example, if a rumor of 8 shortage of the co~mod1ty dnves the price above Po, the fact that the quantity su pphed exceeds the quantity demanded will drive the price down toward equilibrium.

These terms were obviously borrowed from physics-has the econ­omist made sure that they really make any sense in economics? The answer is, let us hope, yes. The stability of equilibrium is indeed the normal state of a ffai rs in a tolerably stable world, and from it we deduce important properties. For example, there is a mysteri­ous dotted line through (po, Qo) in Figure 5-2 which I have not bad the audacity to label a demand curve. If it were, the intersec­tion with the supply curve would still be an equilibrium point but it would be highly unstable: the slightest accidental fall in pric~, for example, would drive price ever lower, because at each lower price the quantity supplied exceeds the quantity demanded. A stable equilibrium, then, implies that an increase in the quantity supplied must lower the price, so it implies (in this case) a negatively sloping demand curve. Stability conditions are n source of information at many points in the subsequent chapters.

I s stability something we can take for granted? EconomisU! have generally argued its acceptance on the intuitive ground that wildly unstable market prices (and quantities traded) are not often ob­served. This is a relevant consensus, although not a conclusive one. There are in fact some cumulative processes in economic life (one has the name of galloping inflation), but we shall follow the general practice of assuming t hat the equilibria are :;table.

Now that fish and strawb~;>rries can be frozen, are there any per­ishing commodities left? A few commodities like Christmas trees

PXH ..

J

94 Pricing with Fixed SupPlies

d t flowers nrc perishing, but the important examples a re in an cu . d . services. The motel rooms for rent on n given ny m a. g_iven area nrc e~~cntinlly fixed in number and under per~ect competitton would be thrown on the market each day nt an estimated full-occupancy price, so long as the price exc~e??d a ny c?sts. of occupancy. T here are two reasons why this fle:;.nbthty of price IS not fully attained although there arc scnsonal variation in rates, h iggling, and so on: The fi rst reason is that some monopoly power may be possessed by the owners, and the second is t hat the costs of searching are high for the tourist and not negligible for the owner . The symphony concert, the train o•· plane on a scheduled run, the services of pro­fessional men at a given time, the supply of longshoremen on a gi,·en day-nrc all instances of essentially perishing services. Some have prices which do not clear the market because of public or private controls.

But tolernble stability of price is not inconsistent with a price that clears the market. If the demand is steady, the day-to-day flurtuations in price will not be large (unless supply fluctuates). And if demand is postponable (storeable), t he same effect can be achieved. Suppose that the supply of cut flowers fl uctuates errati­cally, and that consumers consider flowers tomorrow to be a very good subst.itutc for flowers today. They will then have, on any day, a highly elastic demand for flowers, and the price will be rela tively st able.

The usefulness of even the simple graphical analysis of Figure 5-2 is likely to be underestimated by students who have not ex-peri­enced the ability of men to make mistakes. Consider one of the attacks launched on the " law of supply and demand" by William Thornton just before graphical techniques were int rcduced in England.'

Wl1en a herring or rn::tekeral bo::tt has discharged on the beach, at Hast­ings or Dover, last night's take of fish, t he boatmen, in order t o dispose of t heir cargo, commonly resort to a process C<'llled " Dutch Auction." The fish are divided into lots, each of which is set up at a higher price t han the salesman expects to get for it, and he then gradually lowers his terms,

• The full attack (not this instance) happens to be famous because it Jed, or permitted, John Stuart Mill to abandon the wages-fund doctrine. Mill's position in English economics in 1869 was roughly that of Napoleon in the French Army in 1810, so the abandonment was the source of some comment, cspe<:ially since the criticisms were flimsy. The quotation is from On Labour, pp. 47-48.

P ·ce Determination n 95

t .11 he comes to a price which some bystander is willing t un 1 1 d ! · o pay rather I n not have t w ot, nn to w uch he nccordingh· ngr""" S t HI

1 1 b J ..... s. uppose on Occasion the ot to 1nve cen n hundredweight and the . one . . • pnce agreed

..,0 s I£ on thr snmc occns1on, mstend or the Dutch form f . to ... · ' . o auct1on I Ord inary E nghsh mode had been adopted the result rru'crht h bee ' t 1e · . ' o ave n

d·trerent. The operatiOn would then have commenced by some b t d I b' I 1 . h h ys an er

rnnking a. bid, w 1c 1 ot 1crs m1g t ave successively exceeded, until a sum

p

20S 18S

0

-- --------

Figure 5-3

0

s

0

was arrived at beyond which no one but the act ual bidder could afford or was disposed to go. That sum would not necessarily be 20 s: very possi­bly it might be only 18 s. . .. In the same market, with the same quantity of fish for sale, and with customers in number and in every other respect the same, the same lot of fish might fetch two very different prices.

If we translate Thornton's criticism into a diagram (Figure 5-3), we observe immediatelv that the result is due to the fact that his demand curve has a ve;tical branch. This is absurd in a competitive market demand curve.

. ·: ~-~~----~~--~ .............. ~ ........ --------.-~·

Pricing with Fixed Supplies 96

S ble Goods torea h re important case of storeable goods, shares Let us turn to t e fmohe"t or those first editions. Now the supply

k · heaves o w " of stoc_ 01 s n e; a vertical line, denoting the total absence of curve 1

8_ no lo gh ller-for he has always the alternative of sell­

alternatives for t e se ing t-omorrow, or never.

p

0 T 0

Figure 5-4

In fact the very identity of a seller may be uncertain. Jones may sell his four-year-old car at one price, and buy a second at another. Where this uncertainty arises it can be dealt with by the device of "reversing" the supply curve. Let us arbitrarily divide up traders in a market into "buyer·s," who have none of the commodity, and "sellers." who posses initial stocks of it (which they may wish either to augment or t-o sell). The "buyers' " demand curves will be those already discussed in Chapters 3 and 4. The "seller's" supply curve, as we havt.> shown (p. 65), will be constructed in exactly the same way. These curves are shown in Figure 5-4. The total sto~k is shown

. Deter1nination 97 Pil-ce . . . .

tical line TC. At any pnce OA, a defimte quant1ty 1s ns the d v~r by "buyers," AR. At this price a quantity AB is supplied deman ~ but we can alternately say that sellers wish to hold BC by se~leJ 5' ·ce for this is the portion of the stock which they do t tlns pn ' k T · a ff . for sale. Thus if the total stoc (0 ) IS 150, and sellers

not 01 ;~ (AB) at price OA, they are implicitly demanding 40 units

offer If e add AR and BC, to get AG, we have the total quantity (BC) · d ;'at this price by "buyers" and "sellers." Applying this demand e at all prices, we obtain the aggregate demand curve D,, Proce ure 1 k 1' t th 'l' b · and its intersection with the tota stoc me se s e eqm 1 rmm

Price Po· d h · bl f Th' onstruction does more than eva e t e mmor pro em o .1f8

·eng buyers and sellers. It illuminates a common fallacy. class! Y' . 1 f oAo h . an people have said that 1f a stock sel s or Vt a s are on M . y day that this is not the "true" price because only a modest a gwen · h b h be of shares were traded-If a huge block ad een t rown ~~mther market, the price would have fallen drastically. Indeed it

· ht have but if a huge block had been thrown on the market JDJg I •

th. ould have meant t hat many holders now beheved the stock IS W d '

was a poor investment at the price. In effect a large ecrease m d mand has been implicitly assumed. Since the large block of stock w:s not thrown on the market, the holders thought it was worth at least this much. The fact that one could not buy a large block of the company's outstanding stock at the market priee, similarly, merely means that one cannot double the demand without influenc­ing the price.

The holder of a durable commodity has to take account of two elements of return:

1. The marginal utility (measured in money terms) he derives from holding the commodity. Examples are the pleasure of driving a car or of admiring a painting or of cashing dividend checks paid on a stock.9

• The condition for maximum satisfaction is Marginal Utility of A Marginal Utility of B _

Price of A Price of B This ratio is called the marginal utility of income because it is the am_ot!nt

of utility received per dollar of expenditure at the margin .. If we_ d1nde the marginal utility of (sa.y) a painting by the marginal utlhty of mcome, we obtain the marginal utility of the painting expressed in dollars.

Pricing with Fixed Supplie8 98

h · the prire of the product from now to (say)

2 The <' ange m . · ·h· 1 ay be positive or negabve.

next year," JC' m

I t from holding the commodity then consists of The tota rc um d · · ·

the sum of the ut ilit y (ul and the ~edct~ Ipnc.re~selem pfrtPce l~A_p). f n first edi tion of Ricar o s rtnetp s o o ttical The owner o .

d Taxation (1817) of which there are probably 400 Economy an . ' . . . · tl'e world expects Its pnce to rise because the number

coptes m • • . · B h · and wealth of potential owners are mcreas~g. ut t e pnce cannot

ge rise 80 fast as the interest received on sums of money on avera . . k' to h ld' R ' invested in securities comparable m r1s mess o mg Icardo's Principles. If it did, economists would ~uy the. b~ok and. have the Ieasure of owning it without cost, whtle recetvmg the mcrement ~f value. In equilibrium, in fact, tt + ap, the (marginal) return to the hnlder , must equal the cost of holding the durable good. This cost is composed of the amount that could be earned on the sum elsewher·e, ip (where i is the appropriate interest), p lus any cost of possession of the good (insurance of a painting, and so forth).

It follows that the greater the utility to be derived from holding a commodity, the lower must be its rate of .increase of price. People will not hoard a keg of nails unless its price is expected to rise by i per cent; they will hold the Ricardo if it rises by only lip = ip - u, or l!i.p/ p = i - u/p per cent , where u/p is t he annual utility of possession per dollar invested in the commodity.

Speculation A more interesting and important pricing problem is posed by

the existence of stocks of goods which are periodically pro­duced- agricultural produrts are of course the leading example. The tasks in rationing a fixed supply until t he new crop is harvested are two: to provide supplies throughout the period of fixed supply, so that the entire stock ·will not be consumed early in the year; and to provide a carry-over as insurance against future crop fail­ures, increases in demand, and the like.

The former task is relatively the easier one : the demand for foodstuffs and text.iles is tolerably stable over the period of a year, although there a re some fluc tuations in demand due to fluctuations in consumer income, seasonal changes in tastes, changes in fore ign demands, and so on. If demand (as a schedule or curve) were abso­lutely identical in every month, and no carry-over was needed, the

• price Determination 99

. would rise each mon th by t he costs of holding the stock F pr1ce ' f h ld . . or, if the price '~ere h~m otrmk, nny ot er .this m~nth would have the

. of selhng 1s !l oc now a a giVen pnce p or of h ld' choice . . • ' o Ing it a month and rece1vmg only (p - c), where c is the cost of carry-ina' the good a month . There fore.he would sell now, unt il the current

«:' was depressed , and the prtce next month elevated enough to pn~ . . k ' co,•er the costs of carry mg a stoc for . a month . This gradual rise in price is in effect the method of chargmg consumers for the service of holding the stock . . .

The second task , prov1dmg a stock for emergencies, is less simple.

A. of anY time there a re an immense array of possible events each S h . I

of which will influence t e pnce at any future date. Let our com-modity be wheat, ":ith a current price of $2 a bushel; then the possible events may m clude:

1. A fu ture crop failure, which can be lat·ge or small, leading to prices ranging up fr~m $2 ~o $4, with smaller probabilities of the bigger failures and higher pnces.

2. A future bumper crop, also of variable size, with corresponding future prices from $2 down to Sl.

3. A business depression, leading to a modest decline in price and quantity demanded.

4. A war, leading (perhaps through conscription of farm workers) to a reduction in output and a higher price.

5. A fair prospect of increased or decreased demand for expon.s. 6. A possible shi ft in consumer tastes away from wheat toward

meat.

The only t hing a holder of wheat can be quite cert ain of is that something unu~ual will ha ppen.

The carry-over will be held in warehouses, but who will own it and take the risks of profits or losses ? The natural answer is: a group of people who specialize in predicting future demands and supplies . This group, called specu lato1·s, develops skill in collecting and assessing current evidence on future conditions, and therefore on average can perform t.his task more efficiently than, say, the processors of wheat (grain mills ) .

Each speculator may be described as making a set of estimates of the probabilities of various conditions of supply and demand

,.

t I

I

100 Pric£ng wr:th Fixed SttPplie.~

. f t d•Jt" These estimates may be assembled into a fl t 3 gl\'t'll . II ~II'C . ' "· ' . fr<'qucn<'y ci t ~! nbutwn surh <iS.

PIIODABILIT \'

II 05 II 10 0 . 20 0 35 0.20 0 . 10

EXPECTED PIHCE

!3 . 00 2 50 ') .,. - · - :> 2 .00 1 80 l. 60

Tl , rane expected price is then simply the sum of the products le El\e " b b'l'. h' h. •201 , of the expected prices and their pr~ a 1 .1t1es, '~' JC 1s • . m this

T he confidence with which th1s estimate 1s held may be mea-cnsc. . d b · ~urN! by the dispersion about this expe~te ~vera.ge; o viously the specu lator will have more ~on~de~ce m this. pnce ($2.07) being appronchcd with the above chstnbutwn t han with

PROBABILITY

0.38 0 62

EXPECTED PRICE

$3.00 1.50

which a lso hus a mean of $2.07. Presumably he will make larger commitments on his pl'ediction the greater his confidence in it.

If the commodity is one that has no futures market-no market in which contracts for future delivery are bought and sold-the trader will buy wheat if the present price plus carrying costs is le s than $2.07; he will get out of the market if this is not the case.1o With a futures market, however, he will sell contracts for future dclive1·y if the price he expects is below the futures price currently quoted (and buy futures contracts in the converse case), with the hope of covedng the contract (with a "spot" purchase) when it mature::; a t the expected lower price.

Each specula tot· has a different set of expectatiom:, and a different demand-supply function for futures contracts. We may add them together to get the aggr·egate demand for (say) May futures in the prcviou~ December, as a function of the price of futures con­tracts; it is denoted n in Figure 5-5. If the futut·es price is above

•• Thus, if rcul csfllte prices are expected to fall, it is imJiossiblc to sell land "short" becau~>c 1t is not homogeneous and therefore one cunnot promise to deliver a parllculur piece at some future date.

. Determi11ation pn,ce 101

·ce that spcculntors anticipate, they will supply f t the pn . u ures con-

•~ and nt lower future::; pnccs they will demand contracts traC'-"'r f f t . t ts . . .

The supply o u ~res con rae IS prov1ded by hedgers-of whom 't is sufficient to nobce those who buy the wheat from farmers and 1

ly storage. If they do not wish to speculate, they can eliminate sUP.~ risks by selling futures contracts at prices equal to at least tbeu · 1 · · ts Tl · the current pnce p us ca1 rymg cos . tetr $Upply together with be speculators' demand (D ) fix the present price of futures t 11

contracts.

Quantity

Futures Price

Hedgers Supply

Speculators' Demond (and Supply)

of Futures ----0...._ __

0 ...... 0-------­

Supplied

Quantity of Futures Demanded

Figure S-5

The skill with which this delicate task of reading the future is performed is a much-debated point. It is undeniable that if anyone can predict future prices more accurately than the professional speculators, he can make a vast amount of money rather quickly. It is also undeniable that most nonprofessionals (who, by Barnum's Jaw, a re constantly being replenished) manage to keep alive by bor­rowing money from relatives.

The public, and especially farmers, have nevertheless always been hostile toward the speculators, and wave aside the economist's argu­ments on the need for someone p1·edicting the future and taking

"This is a much simplified picture; see L. G. Telser, "Futures Trading and the Storag<" of Cotton and Whcut," Jolmwl of Polit ical Economy, 66 (1958), 233-55,

' ' •• lj ' . ,, I· ,. ,, ! '· • ,, I• . jl ,\ ., I'

Pricing with Fixed SupPlies 102 I . f . t' are wrong An cient aws agamst oresta)), risks that the pred•dc Jons 'ting-bu~ing foodstuffs on the way to . ·!;ing an regra mg, engro~- ' k t ,'th n view to resale-are an adequate proof

k •t or Ill a mar e "I . Ad S . h mar e . . This pohcy Ject am m1t to say of this popular suspiCion. ,

t l is a certain price at which com is likely to be It supposes that .Jere • b ld .

. . b ught np in order to e so agam soon after in forcsta!Jcd, th:t

18' 11~ to hurt t.he people. But if a merchant ever buys

the same mn1 r et, ~og ~to 11 particular market or in a particular market

up com c1t 1er gom k · b be ' . ' II ' t ain soon after in the same mar et., 1t must e cause m order to sc 1 ag ]'b II I ' d th . h t tl market cannot be so 1 era y supp 1e rough the be JUdges t a IC • d h t h .

I 5 Ul)on tha.t particular occasiOn, a. n t a t e price, there-who e season a . th ' d ·r th . f

.... 50011 rise If he judges wrong m 1s, an 1 e prtee doe~; ore m11

" " • k h' h 1 ' . 1 t onlv loses the whole profit of the stoc w 1c 1e employs not nse, 1c no · · J •

1 . 1 · 11er b11t a part of the st.ock rtself, by t 1e expence and loss 111 t 11!' man , . H h ·

h. 1 ss" rl'l\' •lttcnd the storing and keepmg of com. e urts hnnself w 1c 1 nrcP. .. . • · · , I f milch more essentially than he can hurt even the pa rticular t 1ere ore, · . .

people whom he may hinder from supplymg themselves upon that part.1cu-Ja r mnrkrt day, bce<'III!'C they may afterw~rds SU J~ply t_hE.'Jnselves just as cheap upon any other market day. If he Judges r•gh.t, mstead of h~rting the great. body of fhe people, he renders them a ~ost Important service.

The popular fear of engrossing and forestalhng may be compared to the popular terrors and suspicions of witchcraft."

Smith's comment needs only a minor qualifi cation. The proposi­tion that speculators cannot as a group make money by inducing price fluctuations or withholding supplies is correct if they possess no monopoly pOWel'. In actual fact, any large or persistent degree of power to control prices has not been attainable in the large com­modity markets, simply because the trade of buying and selling is one which it is easy for anyone to enter. Smith is too kind to those who suspect speculators, however, when he compares their at­titudes with those once held toward witches, for there was no proof that the witches had not entered into compacts with the devil.

RECOMMENDED READINGS

Hardy, C. 0., Risk and Risk-Bearing, Chicago: University of Chicago Press, 1933, Cbs. 11, 12.

Working, H., "The Theory of Price of Storage," American Economic Review, 39 (1949), 1254-63.

"The Wealth of Nations (New York: Modern Libmry ed.), p. 500.

problents 103

PROBLEMS

• rtre gi,·en till' informnlion: the lolnl stof'k of ,. . 1 )' ou · - . . • · I commochtv is . the demand functJ~n IS q = 80- P, and the supply function is . ~

JOO. Derive the combmed demand curve of buyers and sell q 5 +? ~·{ount.ifort Longfield (1834) argued that the practice ~~~· th . b

~· ~· . f II .) e nc ·ng wheat m years o sma crops and resrll ing it to tl of bu)'J · 1e poor ut ·ce did not reduce the cost of wheat to poor consumers ~

half pr1 . . . .. . . . , a~ compared I I . ,,·ng the poor bu~ cllrc>ctl~ .1t m.•rk<>t pnrE.' Comp·1r .... "O .

1 . wit 1 111 . . . · • ' J ' ur ana ys1s

. 1 his (Lectures on Pollt1cal Economy. London School Reprints 1931 w~1 • , p 56). d . •

.3 Tlw market. dem~m curve. IS p·q = 1000 (a constant demand I -t· · · 1 1 d . · e a:s IC-. f _I)). Denve t H.• c emun curve I or one of '> 10 "nd 4o fi

1fV o - . . . ~. • ' ' m~, ali of equal _stz~, w1th t.he aggregate mdustry output of 200 when the finn in questiOn Js operatmg at the same output as other firms. (Thus with

10 firms, each o~ the otl~er 9 firms h~ts an output of 20 = 200/10.)

4. On 11 certam mornmg you find til(' following foreign exchange rates quoted:

P IUCES

u.s. £ Dollars Sterling Francs

Pound Sterling 2 80 1. 14 .0 French francs 0 2025 0 . 0714 1 0 American dollars I. 0 . 36 5 .0

(a) What do you do to make money?

(b) Suppose no one bothered with arbitrage, and the rates persisted. What, if any, economic objrctions arr tht>re to t hese nonequ ilibrium quo­tations?

5. The la rger the number of t raders in a market, and the larger the dollar volume of transact ion~, the smaller will be t.he sptf.'ad between bid and ask prices for :t commodity. Ex1)lain whv.

6. It has beer~ ob;:;crved thnt. t he best~ gradrs of products (oranges, apples, and the like) are sent to large cities and are not readily available to consumers in the a reas in which they a re produced . Explai~ why.

i. In a mnrk<'t in which carrying costs are negligiblE.' (such as common stocks), you are t old t h(> price of the commodity a t tinw t-say, p, = SIOO. If the market consists of intE.'IligE'nt. traclr rs, will it be of nny value to a speculator to know whnt the price was a time unit earlier'? (That. is, would it be useful to know whether p,_, had Jx.en S50 or $200?) :ti'Iore genernll;.', can repetitive pattf'rns of prices owr time exist ?

" '• ..

\

,I

•' ..

chapter six

t:;osts and Production

It is necessary now to look more closely at the nature of costs.

THE NATURE OF COSTS

Occasionally one walks into the shop of a lazy man and observes identical goods with two prices, and is told that the lower priced items were in an earlier shipment that cost less. This is fooli sh merchandising unless the cost of remarking the price is more than the rise in price. H is also symptomatic of the layman's tendency to ident ify "cost" with outlays actually incurred or historical costs.

Hist-orical costs have powerful sway over untutored minds. The Internal Revenue Service insists that corporation assets be so valued. The public uti lity commissions consider historical costs a relevant or even decisive item in setting rates. Men incur additional Jo;:sc. trying to "get thei r money" out of a venture. They a ll fly in the face of a basic principle of rational behavior, "By-gones are forever by-gones."

It is easy to manu facture cases in which historical costs are seen to be irrelevant to price. Smith produces a commodity for $3, .Jones for $4-will they receive different prices? .Johnson builds a bouse for $20,000 which termites mostly devour-will it sell for $20,000? I lmy a rock fo r $10, and it proves to be a diamond of remarkable purity- will I sell it for $10? Some Indians of questionable char­acter sold Manhattan Island (which they did not own), for S24, a typical exploitntion of tourists. The examples are sufficient to how that actual historical outlays need not govern values.

104

11.T ture of Costs 105 The Jva •

Y case of course, there WI\S a mj scalculation of some "'"rt·

1 ever ' . ov . n hould have been more effic1ent; Johnson should have beaten

.Jones 8 termites; the seller should have known it was a diamond

off ~h~ossi bly nature should have hidden it deeper in the ground); (an Dutch should h~ve bought t he G~eat Lakes. But even with per­the foresight histoncal costs can be Irrelevant: they exclude inter-feet ( accountants reckon costs) whereas n wine should sell for c est as · f C · h · t more after a year, 1 IS t e carry m g cost (as a per cent per cen )

1 t year's value . of ;:e basic concer~ of cos~ is therefore .something different : the

of any product ive serviCe to use A IS the maximum amount ~~s!ould produce elscwherl'. The foregone a ltcrnalive i the cost. ~ote that the alternative cost sets the value of the resource to uae A. it docs not by itself set th<: cost of producing A's product. To de,termine the cost of production of A's product, we mu t know also the amounts o~ resources_ use~ to produc~ a given amount of A, and this additJOn~l relatJOnflhlp (summanzed as 11the production function") is exammed later.

The a lternative uses of a resource depend upon the use for which

the cost is being reckoned:

1. The cos t of an a<'re of land to agl'icultural uses is the amount t.he land could y ield in nonagricul tural uses (res idences, parks, and

so on). 2. The cost of an acre of lanrl to the wheat-growing industry

is the amount it would yield in other agricultural crops (oats, corn, and so on), a s well as in nonagricultural uses.

3. The cost of an aere of land to wheat farmer X is the amount the land could y ield to other wheat fa rmcn;, as well as a ll non­wheat uses.

If all land were homogeneous jn all relevant respects (including location , fertili ty, and the like), obviously all three of these alter­native costs would be the same. For if land yielded more in nonagricul tural uses tllan in agricultural uses, some of i t would be transferred to the nonagricultural uses, and the t ransfer would go on until the y ields in all uses were equal (under competi tion). Equality of yields of a resource in every feasible usc i~ necessary to maximum return for the individual owners of the resource; any discrepancy

..

., t I .. I

f'

106 Costs a11d Prod~f:ion.

in yields is (with competition) an opportunity to someone to increase his income.

But if the land is not homogeneous, it is not necessary that th alternative costs be equal. Suppose that due to locational and ot~:: factors, an acre of one type_ of land :"ill yield $50 in wheat,

330 in other farm crops, and $5 m nonagncultural uses. Then the co t or the land to the whe~t ind_u:try is $30 an ~ere-the best forego~e alternative.1 This cost IS deciSIVe to the lands use: even if a declin~ ing demand forces the yield in wheat down to $31, the land will not be transferred to other uses. But from the viewpoint of any tenant wheat farmer, a rent of $50 is the cost because at $49.9

9 it will be rented to another farmer.2

This definition of cost clearly avoids the paradoxes encountered by historical costs. All productive services which are identical nee~ essarily have the same alternative cost, no matter what the differences in their historical costs. It is also a powerful weapon in analyzing fallacies, of which a few samples may be appropriate.

With conscription an army pays its soldiers whatever it wishes and it is sometimes said that the relatively high wage rates of American soldiers make national defense more expensive for the United States than for other countries. The cost of a soldier to an economy, however, is his foregone product as a civilian, and this is not directly affected by his rate of pay.3 The dollars which are given to the soldier involve a real cost to the community only to the extent that higher wage rates lead to the employment of more tax collectors.

A variant of this same argument is encountered in the request of various groups (Rural Electrification is one) to borrow from the

'The surplus of earnings over what can be earned in the best alternative is called a rent. As the name suggests, economists first attached this concept of returns beyond those needed to hold a resource only to land. The concept has since been generalized to include such returns even when rccei\·ed by laborers or owners of specific capital goods.

• A superior farmer, it might be believed, can get more than the average yield from the land. So he can, but as will be shown later, it is the (value' of the) marginal product of land that constitutes its yield, and this marginal product will not differ in equilibrium between superior and inferior farmers.

• Since no conscription s~·stem ignores certain factors (such as occupation) which are partially controllable by the individual, the higher the rate of pav the fewer eligible conscripts will seek to alter these factors to post~one military sen·ice. This sort of burden-avoiding behavior leads to some tmsal­location of resources.

.. ~. Nature of Costs

f,~e 107 edcral government rather than directly in the capital m

f se federally guaranteed bonds can be sold at low . t arket be~ cau } t t f h er m .erest rate IJere again t 1e rue cos o t e capital to the societ . , ~·

ld Produce elsewhere! Y 15 'vhat 1t wou . f

rrhe alternative uses o a resource will often be d'ff J. • 1 h t 1 erent and . fact fewer, m t le s or run from what they are in th I ' 10

· 1 f · . . e ong run. This is obvious y true o spec1ahzed machmery: during its life it

be used only for the purpose for which it was d · d can . . es1gne , or Scrap But over t1mc It earns depreciation reserves ... h· h b as · . " IC can e

reinvested in othe1' forms of cap1tal. The same situation holds with respect to I abo: : a cm~pent~r h~s as alternative occupations only those fields whJCh reqmre h1s sk11ls or are Jess skilled (he can be-orne an unskilled laborer, for example). But given sufficient tim ~0 be retr~ined, ?e can. work in .a sash and door plant or becom: an electriCJan. G1ven still more time, every young man who other­wise would have entered this occupation will enter one of a hundred others with demands for a comparable quality of labor. · We have a lready refened to the "short run" and the "long run" for example in connection with demand curves; let us look mo;e closely at these concepts. They do not refer to clock time, but to the time necessary for people to adapt fully to new conditions. When automatic machinery took over the making of glass contain~ ers, there was a great reduction in the demand for glass blowers, who until then had been among the elite of the artisans. Those in the occupation experienced great reductions in earnings, and the younger (and more easily and profitably retrained) members went into other occupations. The older workers held on until earnings fell even below what they could earn as unskilled laborers. Eventually all disappeared, except for a handful who continue to produce cus­tom products. The true long run-the·period when all reactions to the decrea~e in demand for glass blowers had been completed­varies with the question we ask. If we nsk about the long run with respect to the number of glassblowers, it is a period suffi­ciently long to allow enough withdrawals so those remaining in the occupation earn enough to attract young apprentices. This

• An egregious example of this fallacy is contained in the following passage: "By taking upon themselves a large share of economic functions the ~tate and municipal authorities to that extent released a. vast amount of pnva.te effort and capital." [W. H . Dawson, The Evolution of Modem Germany (Lon­don: T. F . Unwin, 1914), p. 208.]

l!

108 Costs and Production

might he 30 yrnrR. If we ask about the long run with respect to th retraining and relocation of young glass blowers, the period ma c . . d y hnve been seven years. The short ru~ IS easter to efine: not all adjustments to the force we are studymg have been made; or more simpJ~r, it is a period short~r than the long run.

T here is a ·widespread tendency to look ~t only the short run altematiYes in judging the cost of a commodity (when alternatives are considered at a))). When F rance froze rents during a substantial inflation , there seemed to be no serious costs in the alternative sense Dwellings are durable and specialized, so the supply can be assumed to remain the same with low rents as with high. For a week this is true. Over time, however, a landlord can and will (and did!) reduce maintenance, as a device for withdrawing capital from this unprofitable field of investment. Over a still longer period the sup­ply of houses will shrink- none will be built {privately) and the elements will erode those in existence. In the long run houses can be built and maintained only with resources that have many other uses, and no scheme of financing can avoid the alternative costs of these resources. The a lternative cost theory is sometimes rephrased as the theorem that there is no such thing as a free lunch even in France.

Nonmonetar1J Alternatives. The alternatives to a given use of 8 resourcte> often include also nonmonetary elements. In the employ­ment of labor, they include riskiness, the conditions of work (clean­liness, 3 YS. 9 coffee breaks, and so forth) , prestige, and similar factors, but not the prospectjve increase in earnings with time which is a monetary element. In the employment of capital, riskines~ is the main factor, although in some areas the abi lity to with­draw funds rapidly (liquidity) is also importan t. These nonmone­tary clements obviously must be reckoned with monetary returns in analysing the allocation of resources among uses.

It would be an immense boon if one could always translate non­monetary elements into "monetary equivalents." We would obvi­ously prefer to say that the alternative cost of a man to the legal professions is $14,000 or its equivalent, rather than $12,000 plus the amenities of being a professor.

Within limits it is possible to make direct estimates of the mone­tary value of these elements. For example, the longer vacation of

t e of Costs The Na ur 109

Upation can be appraised at the time rate of the b . nn occ . astc salary 5

d income in kmd (a~ food grown and consumed on farms) ' an raised at appropnate market prices. can be apP · t ·1 bl f

Th·s method IS no ava1 a e or elements such as st• 1 pre 1ge11 or

. k of death. H ere we may de~ttce the monetary equivalent b rts aring returns to the factors m equilibrium if there is f Y cornP .1.b . f ree com-

·t·on If in eqm 1 n um a pro essor earns $3 000 less tha d petJ 1 · . • . . . ' n a en-._. after adJustment fot dtfferences 10 t raming, income in ,_, d

tJ ~·· t th t tl . . h IUD I

d c:o on we may asser a liS IS t e money value of th an ~ ' e non-monetary returns of ~he one occupation r.elative to the other. There

. difficult, but not msoluble, problems m determining whethe at e . ..1 d . . ran Ul'!ibriurn has eXIsteu urmg a gtven period. A more import t

eq . . . I . I h . an Hroitation m prmCJp e ts t 1at t e. occup~t.IOns may not be equally open to men of equal ~ncl appropnate abthty: this is obviously the difficulty wi~h. com~armg Sup1·eme Court Justices and lawyers or comparing a~rhne ptlo.ts (who h.ave a strong union) and other pilots.

The equilibrium dtfference m money returns will measure the difference in nonmone~ary elements only at the ma rgin. If the equi­librium money labor mcome of a farmer is 20 per cent less than that of a comparable urban worker, there will be many farmers for whom nonmonetary returns are larger, and some who would not leave farming if incomes fell to 50 per cent of the urban level. In our terminology, the eamings of these ardent farmet·s contain rents.

The nonmonetary returns are seldom an invariable part of the use of a resource. If men love a rural setting, industrial plants will move to the country to supply this desire (or, what is simply an­other way of viewing it, to pay lower wages). If workers wish the opportunity to acquire additional training, the employers will in­stitute programs or ullow time off to take courses. If lenders are fearful of losing their· capital, they are supplied with senior obliga­tions by the borrower.

$This is presumably the proper basis beC'!tuso the alternative cost of leisure (at tht> margin of workin,:t another week) is the salary that could be earned. The question of wht>ther working time is nclunlly ~Subject to the worker's control is discussed later.

• This is possibly an overstatement . Wen.Jthy donors h ti\'C often been incited and rewarded with knighthoods, ambassadorships, LL.D.s. and the like. These ~arkets are believed lo bP somewhnL imperft>cl, but have not yet been studied 1n adequate detail.

' •:

110 Costs and Prodtt t. c ton

For a gratif~;ngly large numbc~ of economic problems, the non monetnrY clements need not be estimated. Often thev are esc:ent· ~

- . . • - taU • irrele,·nnt. as m the. ehotce ~·hether to grow rye or wheat on a fa ~ or to inYest funds m chenncals or paper and pulp. Often tll , rrn,

· 1 · d f · h e~ are stable oYer substantia peno s o bme, so t at the more v 1

f monetary elements will dominate the mm·ements of resourceo a~le example, one "·ould haYe expected the preference for investi~g ~r home rather than abroad to be stable as between Canada and th t United States, so total returns would move from year-to-year by ;h: same amount as monetary returns-until the recent ·era of d' criminatory rules imposed by the two nations under the benev lis­. f . t' 1' o ent mftuencc o economic na tona 1sm.

Priva t e Costs and Social Cost s

A chemical plant, let us assume, collects waste products and d" I h . h' h lS-

C 1arges t em mto a stream w 1c flows by the plant. The cost t this plant of disposing of waste is then the cost of pumping th 0

waste to the stream (or, in more precise language, the cost is the foregone alternatives of the resources necessary to do the pumping)e If pollution of the stream reduces the income of other people (de~ stroying recreational uses, making the water unpotable, and so on) there are additional costs borne by others. The cos~s to t he indi~ vidual firm are termed private costs, while the sum of costs to everyone is called the social cost of waste disposal.7

There can be no doubt of the existence of these external effects of an individual's behavior. In fact, in strictest logic there are very few actions whose entil·e consequences accrue to the actor. If I edu­cate my children well, the community (it is hoped) will benefit by reduced crime, more enlightened citizenship, and so forth. If I grow an attractive lawn, my neighbors are pleased; if Smith dresses shabbily, the other members of the United States Senate become annoyed.

One of the most tendencious questions in economics has been: when social and private costs diverge appreciably, will competition lead to correct amoun ts (and prices) of goods? Will not the chemi­cal plant, under competition, sell at a price which does not cover

'The terms nre due to A. C. Pigou, The Economics of Welfare, 4th ed. (London: Macmillan, 1932), Part II, Ch. 9.

The Nalt~re of Costs

Costs of pollution, so its costs will be t 1

111 the . . d oo ow and 'ts

larue (with given emands for chemicals)? I output too "' . , To answer the question, let us shi ft to an th

• 1 1 . o cr exnmpl . h' Penc: to have a ong ega! lustorv that f e, w Ich

haP ~ . . d • ' o wandcrin region hitherto evoted to unfenced fa . g cattle.8

In n. H' ' rms growmg rr • cattle rai~er comes: IS .cattle will, unless fenced in b:am, a

der into the neighbormg grain fields and d ' occastonally wan . amnge the cro

'f"king account of tim: damage from the . 1

. ps. "' • ' SOCia VI~Wpo· t th of the farm for cattle IS desirable only if th d .. m e

use d . 1 e a ditional t . come of the Jan Is arger than that in growing . b ne 1D ( ) 1 gram Y the lesR f the two amounts: 1 t 1e annual cost of fencin th ~er 0 t 1 • . · g · e cattle farm r (2) the damage o t 1e netghbormg crops. Let • 0 attle raising just meets this test. us assume that

c. . 1 If the cattle raiser 1as no responsibility or only p t'

1 .

. ' ar Ia respons1-b.1Jitv for the costs Imposed upon others bv his wa d · J ' • J · • n ermg cattle

I·t appears that he will earn a larger rent in cattle th . . ' . an m gratn

As a result, more farms Will be converted to cattle a d th . · d . , n ere Will

be too much meat an not enough gram in the communit We mean a sp~cific thing by too much meat and not e~~ugh grain

Suppose the soctal costs of 100 bushels of wheat and 400 pound~ of meat are the same-the same resources can produce eith Th

. (f tl . . er. en if their pnces or 1ese qunnt1ttes) a.re not equal, consumers will buy relatively more of the cheaper product. Perhap; the equilibrium is reached when 500 pounds of meat sells for the same price as 100 bushel~ of wheat. The consumer is then indifferent, if one bushel of wheat IS adde~ and 5 ~ounds of meat taken away from him. But given the soctal costs, 1t would be possible by reducing meat output 5 pounds to obtain 1.25 bushels of wheat, and the consumer would consider this 0.25 bushels a clear gain.

This is in fact an instance of a general theorem: consumers will be best off (on the highest indifference curves) when the relative prices of goods are equal to their relative (marginal) social costs. Where private costs differ from social costs, obviously this optimum position will not be reached, because producers will gear output to their private costs.

In our case of wandering cattle, it is clear that a legal require-

• The discussion to follow is based upon the profound article of Ronald Coase, "The Problem of Social Cost," Joumal of Law and Economics, 3 (1961).

1 l2 Co.sfR and Producti' on ment that the cnttlr raiser bcnr. the cost of fencing or damage h> crop. will make pri\·atE' and soctal costs equal ; n contrary law (it

woulcl npprsr) will not. T3ul ~upposc. to rcn'rSC' the whole situatio thnt llw :urn han originally been devo~,ed to cattle rai~ing and no:: ~' "'ht'at farmer <'n l<~rs. The nrg~mcnt 1s completely analogous, but th i~ t ime we rcnch thE' con<'lus10n that the wheat farmer should p:ty for thr ft'ncing! It is his arrival which creates the probletn of wnndering c.'altlc, nnd therefore to get t.hE' true (social) cost of hi, wheat wr should t ake nccount of the damage he inflicts on cattle r:1 i~1·r~ if thry ::,<hould for cxnmple have to ('rect. fE'nc.'cs. " re need two Jnw:!: one imposing f('ncing costs on grain growers, the other impo:-inl! t.h<' co~t s on cnttlc misers.

The.' fundnmcntnl symmetry in the relations of cattle and grain fnrmers. no mntt<'r whPre the law plac.'e, the liability for damages. deH'T\'<'i' cl:1boration. Let us consider morc rlosel~· the intruding cat­tlr rniser. He hns, lrt us nsRmne. the fo!IO\ving production ~chedule lnll qu:1ntitics per yenr):

t"WTTLE TOT.\.L :oiET I'R I\'.\ TE RET\ ' R:-.1 I>AMAOE TO ORAl S F'.\RMERR

\) $ 9-l ! () 10 lOll 2 I I 105 3 12 109 6 13 111 10 14 ll2 15 15 Ill 21

If he c.'onsiderE'Ct only his prin1te net returns, he would have a herd of 14 rnttlC'. for thrn his return is maximizNi. But since he must compensate for damage to grain . he will stop before this point. If he has (say i 12 cattle and contemplates a 13th. he will h:n·e to p:1y grain growers an additional S4 for the additional damAge. Simi­larly. he will reduce payments for damages to $3 if hi:' reduces the hrrd to 11. (If f<'ncing costs. sny, $6 n year, the alternatin will be adopted and a herd of 14 reared .)

When the cattle raiser increases his herd from 10 to 11 , his reve­nue rises by $5, but thi s is at a cost of $1- thc marginal damage to grain grow<'rs. R enre his net gain is $4. Similarly he adds $4 to reYenue. and i3 to cost (for damages) by the 12th animal , a net gnin of $1. T he thirteenth animal adds more to cost ($4) than to rc,·enue ($2), and will not be rea•·ed.

~ I " .,

Natttre of Costs 'fhe 113

If the tnw puts the burden of damage on the . 'II b 12 F · n · tl · gram grower th

d ··ill st t e . ot O\\ 1<' gram grower ... ·II ff ' e J t•r '' · :-; "1 o cr hi • I to the margmnl damage if he does not J·nc m sums qllll rease the h d I

<' 1 .,rd is 12, for cxmnple, they will offer up to $4 ' f h ~r · f the t~ · 1 ('I· t e WJll t

I . t.hirtt•enth anmm . amce he foregoes this r . b ~0 adl a . . . . I eceJpt v addm • 13th annnal th1s 1s t 1e cost (for costs arc forego 1 · . g thc . 1 . 1 h 1 . ne a ternatJ\'es)

1~Ulner m w uc l t e aw asstgns liubili ty , •.. ·111 t ff · The n • . . . . · ' no a ect the I t·ve ))l'IYnte nHtt gmnl costs of production of cnttl d . rc fl 1 . • • e an gram B It this procedure obnouslv leads to the cor t ·. \ · . · . . rec soc1al

It--the re:::ults whtrh would nnse tf the cattle and · f rrsu ;:, ' • gram arms e own<'d bv the snme man. The Coase theorem th•Js 8 ·t 1 wer · . . . , sser s t tat

der perfect eomp<'tltton pnvntc and social costs will be 1 un k 1 1 . . equa . It. is a mort> rcmar a • ~ proposthon to us older economistt: who h:wc belie\'Cd the oppos1te for n generation, than it "·ill appear to tht' young r~a.dt>r who was nc,·et· ,,·r~n~, here.

The propos1hon thnt . the .composJt.tOn of output will not be :\ffected by the •.nn~ncr m w.lnch the law assigns liability for dam­age sct>mS aston1shmg. But ~~ should. not b('. Laws often prow• to be ttnimportnnt: the laws wluch spec.'Jfy that, the seller or, alterna­ti\'ely. the buyt>r should pny a retnil sales tax are wholly equi\'ldent in effect. The :1ssignment of rcsponsibiUty for damagt'·. similarly, ran be ignored: assume that the same farmer grows grain and rat­tle, and it ia ob,·ious that his determinat.ion or output will be inde­pendent of the assignrncnt. Either it will be profitable to raise both rnttle nnd grain. and then one "product" will "pay" the amount nt'cessary to maximize the sum or outputs of the two (no matter what. the legnl anangements), or it will be unprofitable. and one of the product~ will not be raised."

The proposition must , to be sure. be qualified by an important fact. When a factory spews smoke on a thousand homes. the ideal solution is to tnrnngc n compensation system whereby the home­owners pay tht> fnctory to instnll smoke reduction dc.'\'ices up to the point where the marginal cost of smoke reduction t'quals the sum of th(' marginal gains to the bomeownt'rs. But the costs of

' One product, sa~· !'att le, rna~· impose (for evt:>ry pos..;ble number of cattle) more costs on graiu thnn the nrt yit'ld from thl' c:mle. R ow.-,t:>r. the ca lli<' land is either ( l) alrc:1dy in grain, and eouJd not be competl'd ior by cattle. or (2) h:ts no u;,e E' Xl'<'l'l t o grow C':\ltle, and th<'n the )'ayment must bP made (with litis as.~ignment of liability) for fo~one profils from cattle gru­ing, and in either case the \lSe of hmd is not afft't'll'<l.

'

.. ·. '• . .. .. I · •I r. . •I ;, ,., ..

Co11ttt and Produ,cu 114 •On

. t" n mav be prohibi tive-of getting the people togethn. thts trnnsac 10 · • t . ...r, • 1 111aaes and so on-so only n sta utory mterventio or assessmg (a "' I 0 0 0 If f 0 n

~. f ·"ble The statutory pohcy ts ttse ar from snnple ~-may ue ens1 . • . . . "U

d ·. . tl c amount of smoke reductiOn that 1s soc1ally optima) CVlSI' ·

1 . k d t" th

depends upon the technology of smo e re uc 10n, e number of people involved, and so forth , and none of these factors remains

constant over t ime. . . The difference~ between pr1vate and soctal costs or returns have

vidcd a fertile fi eld for public control of economic activity. In pro . . t' . t h' fact one can attribute most hmtta wns on pnva e owners tp or con-t rol of property to this source.10 Theee controls are of every degree of perspicacity, ranging from ~raffic _controls (where .private con­tracts between rapidly convergmg drtvers would be dtfficult to ar. range} to petroleum import restrictions (designed to conserve the supply of domestic petroleum I).

Isolating the Product of One Factor

If the alternative cost of a unit of a productive resource is its maximum product elsewhere, it is necessary to isolate its separate contribution from that of the other resources with which it is almost invariably used. Can this be done? On its face this seems difficult, and a considerable number of people have said that since wheat cannot be harvested unless there is land in which to plant it and men to reap it, any division of the product between land and men is arbitrary. Let us see.

Variable Prodttction Coefficients. Let us define the production coefficient of land in growing wheat as the amount of land necessary to grow one bushel of wheat-it is a number such as 1/60 acre year. Similarly the production coefficient of tractors might be 1/ 6,000 tractor year, and that of lab01· 1 man hour (or 1/ 2,000 man year). These produr.tion coefficients are merely accepted names for input-output ratios.

The production coefficients are in general variable: there is no unique quantity of land (or ot.her input) necessary to produce a bushel of wheat. One can use Jess land if he uses more fertilizer

"Alt.hough most public controls are due to this source, they are not always the most important controls. Some measures have purely ethical bases--the redistribution of income, the censorship of some forms of behavior (gambling, for example).

... rature of Cosf.R 'fhe ,. 0 115

and less labor 1f he u~>cs more machinery "'h h labor, . II . h ~.. . . l e P enomen or ~ titution IS we -nJg u r,lqUJtous. One can sub t"t on

f suos f I . s 1 ute news o dvcrtisement~; or SFL csmen, m selling goods AI . -Per a . I . ummurn ca

pa b t"tuted for stam css steel, more efficient engin. n b su s 1 d b . es can he sub e d for fuel, more ura le machines can he sub t· -

stitute s 1tuted for airmen. . . . .

reP "th variable pr·oduetJOn coefficients 1t is possible to ' te d W1 . w11 own

h dule of outputs co1·respondmg to various amounts f 11 sc e . o nny one

0 t ror example. lnpu '

Q U ANTITY 011' lNPUT A

35 36

OUTPUT

60 61.5

h rc the quantities of the other inputs have been held const t w e . 1 d t f . an . We define the margma ~ro uc o. mput A as the increase in total

roduct divided by the '?crease m the quantity of A-here it is ~-5 units of ~roduct per un~t of A . .

The margmal product IS then the (margmal) contribution of a it of any input to the total product, and the total contributi un 0 f th 0 0 • on

is the quantity o e mput times tts marginal product (or 36 X 1.5 = 54) .n

At this point an experienced teacher is torn between two desires. One is merely to say rather complacently that thus the separation of the contribution of one input has been achieved, and that is that. Most reasonable men wtll accept this conclusion, especially since it provides a tool-the marginal product-that turns out ~ be immensely useful. The other desire is to expl ain the variety of objections that have been made to this procedure, and answer each one-knowing full well that once seeds of doubt have been sown they love to grow. I shall compromise by giving two examples of the critiques.

The first critique asserts that the extra product of 1.5 obtained by using the 36th unit of A is also "really" due in part to the other inputs which are being held constant in quantity. If our ex­ample is in farming, it is said that the land is being worked 8 little harder if we add a unit of labor. This is quite true, but the contribution of the other inputs to the increment of product is so

" The question whether the total contributions of all the inputs will exactly add up to the total product is considered in subsequent chapters.

"

~~~~~------------------~---~,----------------------------~._

~ ~ 116 Costs and ProdUction 1'/le Natv.re of Costs . 117 ~ small as to be negligible. Unfort unately the proof of this assertion classica l economrsts, for example, assumed that ca .

The ·er·e used in a fixed proportion but. (through 5

b . prtal and lnust. he mathematica1.'

2 b 1·" u strt t "

I h h h h ls 0) 'n vnf'iable proportion to output In th"rs c u ron for The second critique asserts that a t ~ug t e 36t unit of A tnay

1 nd 1 '' • ase a margi

1 produc<' only 1.5 unit!', t!te pre~ious un~bts ~f A bprodhuced more, and ~oduct can be found f~r1 a ;m

1bined dose of "capital and !abo~~ •

. t 1-8 irnr>roper to apprntse therr contrr ut10n y t e contribut· P t for each separa e Y· a ras used as a first a . • r . b" . . . ron bUt no fi d ffi . nts C d t' ' pproXJmation of this least important u01t. T rs argument rmphcrtly assu...... . ally xe coe ere o pro uc ron. By 1900 mo t . •

ffi . . bl ..... es unrvers I iable productio ffi . s economrsts either that the production coe crents are not vana e or that th used universa ~ar I f fi d ~ co~ crents. I n rerent years there ('nt.repreneur who is conducting the enterprise has made a mistak e been a revrva o xe pro uctron coefficients in con t'

e )las d ll' t t t" d r ' nee ron It would be pos~ib le to have 35 men engaged in sowing and rea.pin · '"

1"th 50 -calle. 1~PU -otul pu nnf fmear programming analyses.

nnd use the 36th man on ly to repair scarecrows, which (let us a:~ The questron IS _mos Y one o act, and of a kind of fact not sumc) y ields a. much smaller marginal product. But then labor i easilY enumerated ~n a census_. Moreover, while i t is easy (J con-being used inefficiently: if the 36th man's work is less efficient tba: . t re) to show t at every rmportant production coeffic" . t h

k h. ta k h ld b · JCC .ud s·r·nce 1925, only those variations that occurred 1·n th Ienb as Lhat of his fellow wor ers, rs s s s ou e reassrgned. Perhap vane . . . e a sence he should spend half of his time in sowing and reaping, and mak: of technologrcal progress are m quest10n, and they do not carry only basic repairs in scarecrows. Whatever the assignment, as long separate labels. . . . as the men are homogeneous, each one should be making the same Perhaps a maJonty of econom1sts-certainly a majority "f "t marginal contribution. It is for this reason t hat the correct phrase would be a tie with~ut my vote-helieve that almost all produ:tio~ is 11the marginal product of 36 men," not 11the marginal product coefficients are vanable. They r·each this conclusion on various of the 36th man." bases. One is that counter-exnmples are hard to find. Pareto for

This leads us to a basic problem: there are many ways to grow example, said that only so much gold leaf can be hammered' out wheat, even using the same inputs. The farmer can plow sha llow of an ounce of 1~o ld, so the coe~ci~nt of_ production of gold in gold or deep, he can fer·tilizc uniformly or unevenly, he can harvest early leaf was fixed. But ~ctually rt 1~ vanable: in. Germany, where or late, und so on . Which method will he use of this vast array labor was cheapet· relat.1ve to gold, rt was pounded thinner so there of feasible techniques ? E ach technique may have a different mar- '"ere 350,000 leaves to the inch; in the United States, wh~re labor gina) product for each input, so our concept of costs ultimately was more expensive, ther·e was less pounding and only 262,000 leaves rests upon Ute choice of productive techniques. to the in ch.u But this game of specific cases never ends. Moreover

The economists' answer is to assume that the entrepreneur w.i ll it is a game that is rather unfair: a possible case of fixed production use the !Jest known technique, which is the technique which yields coefficients can be invented in a minute, and may require a month the Jargeat product with these given inputs . This is of cour·se a sub- to refu te. stantial simplification of the problem, and in effec t says: let us The more important reason for believing that the production co-put the problem of advances of technologica l knowledge into a sepa- efficients are variable is that a vast amount of experience suggests rate rompartment, to be studied later- preferably by someone else, this to be so. We observe that farmers use mor·e fert ilizer when ~ince it is a very difficult problem; and let us only gradually intro- a crop restriction program reduces the land they may t ill. We ob-duce the differences in technical knowledge possessed by different serve t hat some firms in an industry use better labor than others firms in an industry. Provided we eventually redeem these pledges, or mechanize di fferent processes, or use different raw materials, 0;

no one can quarrel seriously with the "best technology" assumption. employ differ<'nt advertising media, or displuy n hundred other Fixed Prod1u:lion Coefficients. The question of whether production forms of substitution of one input for· another. We even have some

coeffi cients are variable or fixed has had a long history in economics.

"Be!! mathematical note 8 in Appendix B. "C{)ur~ d'ecorlfm1ie politiquc (Parid, 1897), II, §714, 717. "U. S. TarilJ CommiBSion, Gold Lea/ (1926), v. 6.

• .l

s ws

Costs and Productton

118 . t this effect. but on the whole t hey con. formal statistical findmdgs ~l"tl·vely recent part of t he evidence for

rn~· nn re" stitute a very 1 ~

variability. t' coeffi cients are variable-and this of ·r all produc lon t . h Even I k ·-there remains the ques I On: OW van-

one can no~ 1/ 11 course no . 1

fficient ranges only between and l/1 2 I 'I If techmca coe f

ab e · a h hnological coefficient of pro e&.<:Ors per stu-( hiY the average ...,c . . . roug : . b . ler for many questiOns to assume 1t IS fixed.

dent) · .1t _m~Y fie ~tm~an we isolate the contribut ion of one input Row 1f 1t 15 x ' 1 · f th h · ' d t? N t by marginal ana ys•s, or en w en we 10• to the pro . uc t byo a unit the product rises in proportion (if there crease one mpu , 11

sed mounts of other inputs) or not at a . are unu .tha . 'dly fixed proportions however, it is possible to de-

Even w1 ngJ ' . . . the contribution of each input, essentially by a companson

term•ne · . · h b of different industries. The Iog1c of th~s approac may e presented bv means of the analysis of a very stmple economy. Suppose that u; this economy there are 1,000 men nnd ~00,000 acres of land, each homogeneous. There are only two posstble outp~ts each pro­duced by a different combination of men and land, WJth no substi-

tution possibilities:

1 man + 50 acres produces 100 bushels of rice;

1 man + 200 acres produces 100 bushels of wheat.

If the economy concentrated on rice, half the land would not hi! employed; if it concentrated on wheat, half the men would not oo employed.

Suppose, in fact, that rice has been selling for S2 a bushel, wheat for S3 (and these constant prices are given by t he export market). Then if only rice were produced, it would have an aggregate value of 1,000 (farms) X 100 bushels X $2 = $200,000. If 1 man were shifted to wheat, his product would be 100 bushels X $3, or $300, and the reduction in the value of rice would be 100 X $2, or $200, so national income would rise $100. Let this shift continue until 333.3 men are raising wheat on (333.3 X 200) = 66,667 acres, and 666.7 meo are on the remaining 33,333 acres. Now if one more man shifts from rice to wheat, he will still produce a p1·oduct of $300, but the 200 acres he requires wiJI lead to a reduction of 4 rice farms whose product is $800. So we a re at equilibrium with full employ~

119 bl£171~

pro th'trds of the labor forcf• on rice farms. National · h two- · \\' It

meot. . S233 333-. coflle IS ' were to be added to the economy, say by giving til 50 acres ld h' f h l f 1 . one more man cou . 1 t to w eat , anti national

P golf courldses:se $100. Hence this is t he urn that would be paid

u wou Tl h . )' . . ·ncorne f l50 acres, a nd t e 1mp 1c1t rent 1s $0.67 per acre. ~or the use ;h r hand . 3 m ore men we re to withdraw from work . If, on the

0 e wheat farm would be possible, and its higher yield

then one rn~~e parti ally offset the decline of rice output {4 timu ($300) :~u national income would decline by $~hence a roan's $2()()), 8 •orth $500/ 3 = $167. services ~re ~- c it p rices represent alternative products in the proper

These ~;p ~easure the value of output foregone · when a unit of sense: t · . withdrawn from any use. The reason we have been

~ource IS h . h 8 re- fi . d these products is that t e van ous uses of t e resources able to ~~ substitute between products even if not directly in the UoW us IN d 8 t ' n of any one pro uct.

produ_c 10

ethod of isolating products is intimately related t~ a ThiS m · d th " h d · " f d known as linear programmmg, an e s a ow pnces o

rnetho t hod are the im plicit alternative costs of inputs.15

that me

RECOMMENDED READINGS

Ronald "The Problem of Social Cost," Joornal of Law and eoase, • Economics, S (1961 ) . , . . .

' 'Ec: nomic Empty Boxes, symposmro m Ec011omtc Journal b)' J . H. C~npham (September nod December 1922), A. C. Pigou, nnd D . H. Robertson (March 1924). Reprinted in Readings in Price Theory.

Knight, F. H., "Falla.~ies in the Interpretation of S~cinl C~st," Qu~rter~y Journal of Econom.tcs, 38 (1924) , 582--$06. Repnnted m Readmgs m Price Theor1J.

PROBLEMS

I. Under what conditions would historical costs always equal alternative costs?

2. Does it. cost n smgcon more to operate on a rich person than a poor person?

"Sec almost any other book on economics; also P. A. Samuelson, "Pro­fessor Knight 's Theorem on Linear Programming," Zeitschri/t fur National­okonomie, 18 (1958), 31~17 .

t

.. I

I . ..

f ••

I ~~ :t

'·~ ., I

.:

120 Costs and Produ 1.: c~·,on

3. Wha t would happen to the value of men and acres in our . (p. 118) if the lnbor force increased to 1,200 men? example

4. Yon :He told that 100 bu~hcls of wht>at cnn be produced bv . 4 mnn-ho.urs and 2 acre-years or by 3 man-hours and 3 acre-ye~rs~lther the mnrgmal products of men and land be determined with th· . Can mation? · 18 lnfor.

5. Explain or denounce the propositions :

(n) Thcre is no such thing as a free lunch. (b) There cannot be two expensive lunches.

ebapter seveo

Production: Dlndnishing Returns

At a given time there is a set of "technological" possibilities 0 · l d f pen to any potentta pro ucer o any commodity. These possible tech-

)

·ques are commonly labeled "technological" without quote mark nl f h d" . s, and we shall hence ~rt tspense w1tb them, but the quote marks should serve to remmd us t~at t he methods of converting coffee beans at a port war~house mto coffee ground to specification at a grocery sto~e cons1st of m?re ~h~n the technical details of the ways of roastmg c~ffee,_ puttmg It mto bags, and transporting it to buyers. ProductiOn mvolves a lso the carrying of inventories which are not too large (for they are expensive) or too small (or sales will be lost), the hiring of workers of all descriptions and getting them to work w~ll, bo~rowing money and collecting debts, advertising and quarrelhng w1th the Federal Trade Commission, detecting changes in consumer tastes, and making out tax re­turns. The plebian phrase, 11know-how," better describes this set of possibilities.

An inventory of all known ways of producing goods-using production in its widest sense to include methods of organizing economic activity-is referred to as t he "state of the arts." This inventory contains many methods that no one will use because they are obsolete : they yield goods that are no longer desired ; or yield desired goods but require larger amounts of all inputs than other known methods. It contains a lso many methods that cannot be ranked unambiguously as superior and inferior: process A uses more machinery, process B more labor-so which is more efficient will depend upon the prices of machinery and labor. This inventory

121

' • .. ; [:

:j I.

}· '

' >l

I' ,l

r ll

i~ [

122 Production: Diminiahing Ret urn8

of knowledge grows over time as new discoveries are made. We shall nevertheless assume that it is fixed.

Even in the absence of. new disco~e:i~~· the "state of the arts" is an immenee collectwn of possJblhties, and of the m varied sorts. In fac~ it contain.s all pu~Iished ,knowledge and :~: vast empirical experience reposmg only m mens heads. It is si . larly indescribable in its variety: it contains the methods of mak~t­doughnuts (on a large and small scale) and airplanes, of collect~ng delinquent accounts and recruiting employees, and what not. tng

The ~tude~t should therefore be suita~ly impresF:ed to learn that economists dtscovered a general law relatmg the quantities of inputs and the quantity of output for any productive process. The dis­covery of this law, due to T. R. Malthus (of population fame) and Edward West (who deserves to be as famous) in 1815 w

h h . d . h h' ' as one oft e er01c a vances m t e tstory of economics. It turns out that much more can be said about the relationsb'

of output to one of several inputs than nbout the relationsh~p of output to all inputs, so we begin with this case. This rei: t.~onshi~the law of ~iminishing returns--answers the ques­tiOn: m what proportion should t he various inputs be com­bined?

DIMINISHING RETURNS

The law of diminishing returns may be stated quite briefly:

As equal incremcntto of one input are added, the inputs of other productive services being held constant, beyond a certain point the resulting incre­ments of product will decrease-that is, the marginal products will diminish .

The law is not a tautology, but an assertion a bout the real world. As such, it must be interpreted in a particular way--even the physi­cal Jaw that freely falling bodjes have constant acceleration does not. work well if the body is in a tub of molasses. In our case the conditions are:

1. That there be other inputs whose quantities are held constant. If all input.~ vary, we have the problem of economies of scale, discussed in the next chapter.

. . hiM Returns Ditntrl-"8 . 123

tate of technological knowledgP is given Th . . 'fhe s ' . · <' vanous m t

2. ~ibil it ies arc all available at the iiHm!' time Ob . 1

. pu -t pos' · 1· d · \-'lous v 1f an

0utPll 1 1nit of labor IS app Ie to a fann next vcnr and ., . · .' d·(ona t . h . . · • ' " nPw mventton

11d 1 1 the product nsc more t an 1t chd when n man was dd d h' ltlllkes . · no contradiction of the law. 11 e t 1!1

r thiS 15 • I . h . vea , proportions m w 11c mputs can cffrrtivclv combine a . bl · 3 The . · re vana f'

: other words, th(> <'Ot>ffi ~1ent~ of pr?<~uction nre variable (p. 114)• or I

0 1 as rell:'vance evrn tf th1s condthon fails but we shall d' ·

h laW l . • • • ' ISCUSS 1' e iJnportnnt situatiOn of contmnously va nablr proportions. onl~· th<'

duction is a. process, not an act, so all of the inputs and out-pro fl · f · e rates of ow per umt o tJme: man-years, bushels per

Puts sr . ts d and so on . If economts use completely meticulous language

)rear, h . th' fl ' ould therefore emp. aslZe JS ow nature by speaking not theY w f h' · th · '

h. ·ng 7 men, but o mng e serv1ces of 7 men for a year · of tn '

f producing 2,000 bushels, but 2,000 bushels per year. They not o . I d 't . ot this metiCu ous, an 1 1s customary to refer to productive are n h . . "factors" rather than t eu servtce~.

This carelessness has on o~cas1?n le~ to error. For example, it h been said that labor (servtce) ts pen shable but capital (a build­. as or machine, say) is not. Yet surely if the services of a man :g a machine arc not used this year, there is a loss in either case. It will be roughly true that the man's fu ture services are no larger because of this year's unemployment, but machines also rust or become obsolete and in any case a year's services which are post­poned 10 years are worth much less than they would be this year! We shall not examine the relationships between services and the capital goods which yield them until we reach the theory of quasi-rents.

Elaboration of the Law

Let us begin with a simple numerical illustrat ion of the law of diminishing returns. In this numerical example (Table 7- 1). a series of amounts of labor (M = m an years) are used in cooperation with an amount of land (L = acre years) which we hold constant. Di­minishing returns sets in with the fifth unit of labor.

'Future services must be discounted to obtain their pre&'nt value, so a dollar of services 10 ycnrs hence is wort.h only Sl/ 0 + 0.1)'" = $0.39 if the interest rate is 10 per cent.

'

,,

~ 124 Production: Diminishin n

. g ~eturn . It. ~11 be noted ~hat the average product of labor .

8

dtmtmsh only after s1x units of labor are employed beg~ns to marginal products begin to diminish at different po·' tso aver~ge and t d ' ff · m .sand dt ·

a 1 ercnt rates. Unttl well into the present ce t Intnisb diminishing returns was often stated in terms of ~ ~ry the la" of marginal products, and they were treated as equiva~ t aWverage and

en . e see that Table 7- 1

AVERAGE PRODUCT ---=::: MAN YEARS TOTAL PRODUCT PER MAN YEAR

MARGINAL PRO DOc-r

0 0 OF A M.\.N YEAR

0 1 5 5 2 13 6 . 5

5 8

3 23 7 .7 4 38 9 .5

10

5 50 10 15 12

6 60 10 7 68 9.7

10

8 75 9 .4 8 7

9 81 9 10 86 8 .6

6

11 89 8 . 1 5 3

12 91 7 .6 2 13 92 7 .1 1 14 92 6.6 0

15 91 6. 1 -1 16 88 5.5 -3 17 84 4.9 -4

they are not equivalent, and in fact only marginal products are of interest to the economist.

We ~an demo~strate the importance of marginal products at once by asking the stmple question: if the wage rate of labor is 6 units o~ product, how many laborers should the owner of a plot of ground h1re? The arithmetic is performed in Table 7- 2, which is based squarely on the data of Table 7-1. The owner wiiJ wish to maximize his surplus, which is achieved when he hires 9 men-which is of course where the marginal product of labor equals its cost. Marginal

. . · .. hi'ng Returns Dtfl~.tnt"

d ts are always the guide to maximu 125

ro uc . d . . m profits . . p ··bereYer a plo uctlve :.-ervlce has a d'ff or tnmttn"""

0st: '' · ' crent m · .,..... c t in two uses, we can mcrease total product Thu a~glllal prod. uc uJD· al product of 10 on one farm and 8' s, tf labor had

tnar., • on an th 11 • g one laborer from the latter to the f 0 er, trnns-ferrlD b Ortner farm . 1 .

e total product Y 2, and the gains conf wou d In· creas) until the marginal products are equal mue (at a declining rate ·

Table 7- 2

:::==--NtiM!JEll OF

TOTAL WAGE BILL )1.1.1~-YJ:ABS

AT 6 PER MAN-YEAR TOTAL PRODUC'I' SURPLCS OV!:R

I{I!U)D WAGE BILL

1 6 5

2 12 13

-I

3 18 23 1 5

4 24 38 30 50

14 5

36 60 20

6 24

7 42 68 26 8 48 75 27 9 54 81 27

10 60 86 26 11 66 89 23 12 72 91 19

When we are speaking of "applying" laborers to a plot of land, we can equally well speak of "applying" a plot of land to the la­borers. When the marginal product of men declines in Table 7-1 , we can say it is because there are more men per acre, or fewer acres per man- only the proportions are important. The law of di­minishing returns is completely symmetrical, and it is a matter of indifference which input we hold fixed and which we vary.

The symmetry can be illustrated by deducing t.he marginal product of land from Table 7- 1, on the assumption that 10 acres of land were in the plot. We may proceed along these lines: As an approximation (to be discussed in Chapter 8) , if eight units of labor on 10 acres yield 75 units of product, then 9 units of labor on f X 10 ( = 11.25) acres will yield l X 75 ( = 84:.375) units of

t

·. 'l

.. •I .

126 Production: Diminishing Return

8

(Th t is proportional increases of all inputs lead to Pro product. a ' bl II h ~ . 1 · crea.ses of output.) The ta e te .s us t at 9 men on port10na 111

0 · ld 81 units of product. We may now calculate the margt' 1 acres y1e · . . ~

nal product of land by con~panng the outputs wtth 10 and 11.25 acres, holding labor at 9 umts:

84.375- 81 = 3·375 = 2.7 per acre. 11.25 - 10 1.25

When we move from a ratio of labor to land of ..fer to one of h, we found that the marginal product was 6 per man. Now, as we reverse the movement and go from a ratio of labor to land of~ to one of ~'5' = -.A, we find that the marginal product of land is 2.7 Per acre.

We give both marginal product curves (with L = 10) and th€ total product curve in one diagram (Figure 7-1 , based on Tabl£ 7-1) . As we move to the right, the ratio of labor to the land rises as we move to the left, the ratio of land to labor rises. The diagratn is divided into three stages, which correspond to three possible stages of returns:

1. In the first stage the marginal product of the land is negative. 2. In the second stage the marginal products of both factors are

positive and diminish as the factor increases. 3. In the third stage the marginal product of the labor is

negative.

The first and third stages are thus completely symmetrical.2 The entrepreneur will seek to be in the second stage, where

neither input is being used in so large a quantity as to reduce the level of output. Even if labor is free, he will go only to the end of the second stage, and even if land is free he will stop at the beginning of the second stage. This latter condition was approached in colonial days, when land was almost free. The colonists were properly lavish in their use of land relative to labor, despite the frequent complaints of European visitors who were accustomed to the more intensive utilization of more expensive land and trans-

• T~ese J?recise rela tionships between average and marginal products hold only 1f ?' gJven proportwnal change in all input.s leads to an equal proportional change m output; see mathematical note 9 in Appendix B.

127

F igure 7-l

ferred their notions of appropriate technique to inappropriate rela­tive prices of labor and land.

In our examples we have assumed that if the ratio of labor to land is sufficiently small, no product will be obtained. This is not impossible: one man-hour applied to an entire 160 acre farm will yield nothing but a brisk stroll. No1· is it necessary. Suppose we apply a variable amount of fertilizer to given quantities of land and labor. If no fertilizer is used, some product will nevertheless be obtained, so the total product curve begins some distance above the origin. An exa-mple is given in Table 7-3.

128

POI'I>DS OF

FERTILIZER

0 43 86

129 172

• Pu 43 pounds of fertilizer.

Production: Di-m1'nishing Ret UJ·n.s

Table 7- 3

BUSHELS OF WHEAT MARGINAL ---= PRODUCED PRODUCT •

18.3 28.6 10.3 37. 1 8 .5 39.0 1.9 39.5 0.5

otiii RC& : The e•amplo is taken from F. L. Patton, DiminirAing Rtlur11 , • (New York: Columbi" University, 1926), p. 34. "' Al/l'iculturo

We hu,·e so far assumed also that there is an initial s ta f · · · 1 ge o Jn('rea'Smg margma. returns to labor and this is also possible bu unnecessary. Margmal product may begin to diminish with the fi t

't f t h · bl · h' · rst um s o e var1a c sei'VJce; t 1s 1s also illustrated in Table 7-3 although the size of the increments of fertilizer is so large th ' we cannot be sure that an initial stage of increasing marginal r:~ turn~ hns not been ovel'looked.

The converse is also possible: t he initial stage of increasing margi­nal product may be so broad that t he demand for t.he req · d

d · b · mre pro uct. IS o ta~ned ~efore the second stage is reached. But if the product1ve serviCe bemg held constant is divisible it would be _

. h' un necessary even m t 1s case to empl?Y it with a negative marginal P.roduct. Suppose we need only 13 umts of product, given the prod uc­tion sc~ed ule of Table 7- 1. Using again the approximation that proportional changes in all inputs yield proport ional changes in o~tput, we. may proceed as follows: 6 units of the variable service w1th 10 umts of the constant service yield 60 units of product so H. X 6 ( = 1.3) units of t he variable service with H X 10 ( = 2.' 17) umts of the constant service will yield H X 60 ( = 13) units of product. H ence by throwing away (10 - 2.17) = 7.83 units of t he constan t service we can save (2 - 1.3) = 0.7 unit of t he variable servitc, still obta ining 13 units of product. If t he fixed service is divisi.ble, the entrepreneur will not operate in a region of increasing margma.l rcLums to t he variable service (and of negative marginal rctmns to the constan t service). a

. ' H would .be imprecise to say that hy this device we have coDve>rtcd increns­lllg rr-turn11 m to ronslun~ marginal . returns to the \'ariable> ~'CI'v icc, for we nrc not holdmg the qunn hty of land muse constant.

.. h'ng Returns v im·t1l1$ t 129

Phrase " diminishing returns" has become part f d.· 'fhe I th t h o or mary

ge so peop e now say a t ey stopped reading a b k be Janguath~Y reached the poin t of diminishing returns I t · boo

1 -

ause 1 b · IS ope ess c fi bt against popu ar usage, ut one should at least notice th t to gt always this usage is nonsensical unless reference 1· be' a ahnos . . l . s mg

d to dimimshmg tota, not margmal, returns. One should · d d Jllll e ( h' . . . m ee

eading a book even t IS one) 1f he 1s losmg ground unl stoP r . . . . , ess it is ground that 1s. ~ po

1sit(Jve n~1sa1 n) ce, but commonly the person

that the a dd1bona margma pleasure or instruction is not means . . uffi ·ent to justify the time for further reading. I recommend the

s Jlc~ing language, especially with elderly aunts: I stopped reading fo 0

· · 1 t'l't the book becau~~ Its margm a _u 1 1 Y per min~te had fallen below the marginal u~1hty of alternative uses of my t1~e, including sleep.

Tb. language 1s not only correct but has the mteresting effect of .IS . l always shifting the conversation to s eep.

The Role of Adaptability The Jaw of diminishing returns requires that we hold constant

the quantity of one (or more) productive factors as we vary the quantity of the factor we are studying. In its most literal sense, this constancy implies t hat the quantity and form of the constant productive factors be unchanged: if we vary the number of men building a house, we nevertheless hold the numbec and type of tools constant. This is perfectly possible, and will of course usually yield fairly sharply diminishing returns, because if the tools appropri­ately equip n men, a larger number will have to resort to more primitive methods of work or tool-sharing.

There is another sense in which a factor may be held constant : its economic quantity (or value) can be held constant. We can hold the house-building tools at $2,000, say, but vary their form so that they are most appropriate to whatever quantity of labor we employ. With fewer men, we use fewer and more elaborate tools; with more men, we use more, but less elaborate, tools. Or conversely, if we are examining the marginal productivity for tools, we can hire fewer but abler workmen (with the same aggregate payroll) with fewer tools, and more hut less able workmen with many tools.

This broader sense of 11constancy" is obviously more appropriate when we are studying the behavior of an entrepreneur who seeks to maximi ze the output from given resources, if he can in fact

lt

'

.,

t• '' :•. , ;

130 Production.: Dimin.ish1:ng Returnll

change the form of the constant factors. And normally he can tnak this change if given time: sooner or later the particular facto~ need to be replaced and they can then be replaced by more appro­priate "constant" factors.

If the fixed productive factor need not be changed in form 'Wh the quantity of the variable produc~i~e f~ctors is changed, the fuc:~ factor is called adaptabl~. Ada.ptab1hty JS complete when the form of the constant factors 1s such that, whatever the quantity of th variable factor~', the maximum output (with the known technolo~ gies) is achieved.

The difference between the products obtainable with partial and complete adaptability is illustrated in Figure 7-2. The extrem case of zero adaptability, it may be noted, would arise with fixe~ proportions-where the constant factor was litera1ly incapable of being used with more or less than a critical quantity of the variable factor-and in this case the total product "curve" would simply be point P~.

We shall later argue that the productive service which we arbi­trarily hold constant in order to exhibit diminishing marginal re­turns is often actually fixed for the entrepreneur in the short run. Then he cannot make any magical transformation of the constant productive factor- it requires time to wear out such factors (if they are durable) or to rebuild them. Since the firm will nevertheless usually have a fluctuating output even in the short run, the entrepre­neur will seek to have a flexible productive system-one which op­erates with tolerable efficiency over a considerable range of outputs. This flexibility can usually be achieved (at a cost): for example, it is possible to design an oil refinery so it can vary substantially the proportions in which gasoline, fuel oil, and other products are obtained from given crude oil. In terms of our diagram, the flexible plant will have a lower output at Xo because, if versatility is ex­pensive, a larger quantity of the constant factor is needed, but the marginal product will not fall so rapidly when the variable produc­tive service is increased.

The Proof of the Law

The law of diminishing returns is, as we have said, an empirical generalization , not a deduction from the laws of matter. An .empiri­cal law (as we learned from the Jaw of demand, p. 24) cannot

. . hi1W Returns DifTltn.t.S 131

p

0

Product Curve with Adoptability

Xo

Figure 7- 2

Product Curve with

Partial Adoptability

v

be proved by producing instances of its operation. T?is is ~ot to say that such direct empirical evidence is irr~levant: m. part•cular the Jaw was immediately accepted by econom1sts when tt was first proposed simply because it seemed so clearly operative_ in agric~­ture. We could now produce a vast number of illustrations and m fact do give two samples in Figure 7-3 and Table 7-3.~ A method

• Figure 7-3 is based upon "Trials of the T .S.M.V. Polyphemus," The l~ti­tution of Mechanical Engineers, Proceediii(IIS, 121 ( 1931), 183 ff. The equation of the total product cun·e is

Y ,.. -128.5 + 2.740X + 0.0005110X'- O.OOOOOOM79X', where Y is brake horsepower and X is fuel input (pounds per hour).

I

' .: I

~

1: ·~

·:

·~ . '· .. .. •• ;.,, i•l l .

132

0:: w 3 0

3000

ft. 2250 (f)

0:: 0 I

w 1500 ~ <{ 0:: CD

0:: w

750

3 3 0

~ 25 (f)'

~ 2 I

w 1.5 ~ <{ 0:: CD

Production: Dim·inishing Ret urn8

o~~~~--~~~----L---~--~-----200 400 600 800 1000 1200

FUEL PER HOUR (Pounds) (b)

Fig ure 7-3

. . ishing Returns o~mt.Tl 133

ting the Jaw that is especially relevant to ec . of. te~ provided later in the chapter: onomJc analysis

wtll 1e ·ge number of attempts have been made to j\ a1 · . prove the 1

d ·iving it from self-ev1dent facts. Perhaps the aw bY eJ . . • • . . most famous

f as<:umes the oppos1te of dnmmshmg marginal t Proo · - . re urns and

d es that all the wheat m the world could be grown · fi' de uc · . h' m one ower t It Proceeds hke t 1s: suppose we have increas'tng . ~ · . ~~~

ducts on a 10 acre farm: pro

VARIADLE SERVI CE TOTAL PRODUCT

0 0 1 5 2 15 3 30 4 50

(The total product is then i V + t V 2 where V is variable service.) We proceed:

If 2 units of V on 10 acres yields 15, 1 unit of Von 5 acres yields 7.5.

Again: If 4 units of 1' on 10 acres yields 50,

2 units of V on 5 acres yields 25, 1 unit of Von 2.5 acres yields 12.5.

It is evident that by decreasing the quantity of land we are in­creasing the total product from given quantities of the variable service. Using our equation for total product,

1000 units of V on 10 acres yields 2,502,500,

1 unit of V on 10~0 acres yields 2,502.5.

Since -nfr:nr of an acre is still a very big flower pot, let us do this once more:

1,000,000 units of Von 10 acres yields 2,502,002,500,000, 1 unit of V on 10-5 acres yields 2,500,002.5.

It is clear that we are doing very well by reducing the quantity of land : 10-~ acres is a plot of 5.2 sq. inches. The result should not surprise us unduly, however : if there are constant returns to scale (so reducing every input by [( per cent reduces the product by K per cent) and if there are increasing average returns to one

-134 Prodttc fion: Diminishing n t

11 e 1Lrn8 factor. th<>rC' must h<> negntive marginal returns to the oth r·<>ducing the latter naturnlly increas<':< the total product (p. e;2

7so

But unf01'tunately for t.he proof, ther·r is no basis for sayin th ) · thcr(' must be constnnt returns to scale, as we shall see in th g at chapter. So the proof is inconclu~ive, 1\S proofs concerning the next world have a habit of being. e real

SHORT-RUN COST CURVES

In order· to isolate the marginal product of a productive · h I ld th · · h serv1ce

wed ave 1e b e q1 ~adnt1t1es of t e ~ther factors constant. This pro~ ce ure can e app re to any combmation of factors· an · ( . . y one mput or group of mputs) could be varied , the remainder bein h

1 con~tant.5 g e d

In actual life, however, it is usually the case that the entrep _ n c~r can vary t he quantities of some inputs much more easily red qurckly tha_n ~he quantities of others. The proprietor of a f~c~~y can vary wtthm a few days the number of employees he hir·es th rate of supply of raw. materials, the number of hours be ope;ate: t? e pl ant. It rna~ requ1r~ ~eeks, however, to hire specialized execu­hv.es, or to obtarn speciahzed machinery (which may have to be hutlt to o.rder), or to ~nlarge the factory building. The propt·ietor of a retatl store can mcrease quickly the number of sales clerks and the supplie~ of goods, but it will take longer to enlarge the sto.rc. ThC: propn ctor of an electric generating company can expand q.wckly h1s use of fuel, but requires several years to obtain an addi­tJOnal generator.

This is loose language: when a proprietor says that he can quickly buy more steel sheet, but requires 7 months to obtain a n~w st~mping machine, he is not being prE-cise. At a sufficiently high pnc<', one can buy a stamping machine from another company and haYe it instulled jn 24 hours ; at a very high cost one can have a new machine built in a month by working around the clock. When we ay that in the shor·t run sonw inputs are freely Ynriablc, we mean that their quantrty can be varied without affecting their price ( for given quality ). When we say that othe1· inputs arc not freely variable we mean that their quantities can be varied within the

• When more th nn one productive service is variable, they must be combined in the most efficient proportions, which may vary with tbe rate of their use. This problem is discus.."Cd below, p. 146.

SSt

t Run Cost Cttrves Shor-

. b 't k 135 . tirne unttr- e t a wee I a month or a y given . h . . . I ear-only t .d ... bl<' change m t etr pnce: 1 f we try t 11 a · a con.

Sl eJ" J' I I . o se the S"" . I' h·ne it bas ttt e va ue m other uses· t'f ,.. ... eta 1zed

18c 1 ' • we try t b 11 • rises sharply for early delivery. 0 uy more,

prlCC . b')' Fi ·tv and var·ta I 1ty a re matters of degree Th

:XJ • • • • • c plant's 1 f electricitY can be ~~creased mstantaneously (withou supp Y ~ price}; it may reqmre five years to find a gifted dt ~change :der to sirnplify. th~ fo~al theory I economists define '~t~~e;. In

as a period w1thm whtch some inputs are variabl th hort run h e, o ers fixed Cl arlv there are many s ort runs, and the number of f

1 . · e J • • • ree y \'art

ble productive servrces mcreases as the period f t· . -a o 1me 111 lengthened. . .

The rate at wluch a firm expands Its use of "fixed" f to I th t f . d h ac rs de-

pends not on y on e cos o rapt. c ange but also upon how Ion utput is expected to run at a high or low rate. Suppos fi g

o " (fi d f to ) . e a rm has a "pl~nt xe ac rs approprtate to a rate of production

Of 100 umts of output per week . (The determination of th · ht . k . h e rrg

amount of plant t::s ta en up m t e next chapter.) If now l30 unit.s is the desired output (due to a rise in price), the finn will im _ diately begin to increase its ~la.nt_ if thjs new rate of output is~~­pected to last for years. But 1f tt 1s a short term fluctuation, which will probably be followed by an output rate of 70, it will be supplied only by varying the use of variable factors (and prdbably by inven­tory changes). In general no variation in plant size will be made if the fluctuation in output is expected to be temporary. In addition, e\·en a permanent change in output, if it comes unexpectedly, will for a time be handled primarily through changes in the "variable" productive services.

The cost curve appropriate to these temporary changes in output is the short run marginal cost. We may prove the primacy of mar­ginal cost from first principles. The cost of any action (such as increasing output 10 units) is the alternative use of the resources required to achieve this action. The short run fluctuations of output by definition involvE> no change in the ''plant'' (fixed factor:; ), so there is no foregone alternative to the more int.ensive use of the plant.0 The only for·egone alternative is the amount spent on addi­tional units of variable services.

• If the plant will wear out (aster at higher rates of output, the extra cost is chargeable to the increased oulput. This cost {called lli'ier cost) IS usulilly minor.

)

'

136 Production: Diminishing Ret"~ ..., ns

The definition of marginal cost is

C _ Increase in Total Cost. M - Increase in Output

Sinec the increase in total cost is equal to the increase in the number of units of variable Rcrvices times their price (which is constant to the firm under competition), we may rewrite this definition as

Increase in Quantity of Variable Services . . .

MC = . 0 t t X Pnce of Variable Services Increase m u pu

Price of Variable Services Marginal Product of Variable Services·

Hence marginal cost varies inversely t<> marginal product, and the law of ciiminishing marginal product is equinlent (under competi­tion) to the law of increasing marginal cost.

For reasons which do not bear close scrutiny, it is conventional to define a considerable variety of short run cost curves for the competitive firm . They may be illustrated with the arithmetic in Table 7-4, which is based upon t he production schedule in Table 7- 1, plus the assumption that units of the variable service cost $5 and units of the constant service $4. The definitions of the various costs are:

I. Tota l fixed cost = quantity of the fixed productive service times its price.

2. T otal variable cost = quantity of the variable productive ser­vice t imes its price .

3. Total cost = total fixed cost plus total variable cost. 4. Marginal cost= increase in total cost divided by the increase

in output.

5. A ,·erage fixed cost = total fixed cost divided by ou tput. 6. Average variable cost = total variable cost divided by output. 7. Average cost= average fixed cost plus average variable

cost = total cost di vided by output.

The last four curves are illustrated in Figure 7-4. We have said that onJy the marginal cost curve is relevant to

short run changes in output: we can go a step farther and say that only that portion of the marginal cost curve above average

OU',)a>ooor-..or....ll),,,r....o.,. 0 s~CC:(')~~~ -:~~=:~-:-:~ ~C"'') N _...., ________ _

000...,.11)01'-oC>CQO>r....u:..,.t'?~ oor-..ooo~ll)ll')..,...,...,....,..,."~' 8 . . . . . . . . . . . . . OOCQ ........ ooooooocoo ...

or-..""""oo-~coooc-~co-co 0 1'-o C0 II') \0 L") L., .. ., L") .. .., <0 <0 r-.. r-.. ~ooooooociocicioo ..

OOOOOOOOO::!::!See:: ~__,.,.....""""' __ __,_...,

137

••

I ' I ~

' I r ~

138 Production: Diminishing Return

8

..... C/l 0 u

0 16 32 48 64 OUTPUT

Fig ure 7-4

MC

AFC

80 96

variable cost is relevant. To show t his, we must first show that a competitive firm will operate where marginal cost equals price. It operates at t his output because profits are t hen maximized. The demand curve of a competitive fi rm is a horizontal line: its output is too smal l to affect t he market price. Hence, when the firm in­creases output by one unit, it increases

1. Receipts by the price of the unit. 2. Costs by the marginal cost of the unit.

Hence profi ts will rise after a unit increase in ou tput if price exceeds marginal cost; and profits will rise after a decrease of a unit in output if price is less than marginal cost.7

' The rule may be derived algebraically. When output rises by Aq, profits rise by

pAq - !C(q + Aq) - C(q)J,

where C(q) is t he cost of producing q. H profits arc at a maximum, they will not either incrcn.sc or decrease with a small chnnp;e in output, so t.his exprclil!ion must equal zero. ltewriting it,

p • C (q + Aq)- C(q) , Aq

and the expression on the right is of course marginal cost .

t-JlU1~ Cost Cwrves 139

ShOT te this rule in Figure 7-5. When the price is p ·1r ·Hustra ,, We 1 , nds its output from Xo to A, it will add RST more the firJ11 expato receipts; if it contracts output to B, it will reduce · t than . d

to c~s 8 b RMN more than 1t re uces c~sts. ~Recall that the area receipts Y ·gina! curve between two pomts IS the change in the

a mal . ) under . en these pomts. wtal betwe. falls below Po, the firm faces a different choice. Wben ~ t if pnce X ( h · vU . p . f the firm operates at 1 w ere marg~nal cost equals

price IS ~, I

p

AVC

Pt

0 X1 8 X0 A 0

Figure 7-5

price) it will have total variable costs of_ OX, times X,F, which exceed the recei pts (OX1 times P2 ). By closmg down the plant tem­porarily (reca ll tha t short run curves are appropriate only t~ tem­porary fluctuations), it will save money. Hence the firm Will not operate below a price of Po.

We define the supply cut·Ye of a competitive firm as the amounts it will supply a t va rious prices. This supply curve is (in the sho~t run) the finn's marginal cost curve above minimum average varl­able cost.

., , ., ' I

! r. ~ i

I i t

140 Production: Diminishing Retu.rn8

The Suspicious Character of Average Costs

F Cost curves were presented in Figure 7-4: average fi"ed our . , average variable, average. a~d margmal costs. ~ verag~ fixed cost is wholly uninteresting: It 1s the c~st (per umt of time) of the "fixed" factors divided by output. It 1s always a rect-angular hyper­bola and it is always useless. Average variable cost, we found, had one ~se: to determine the minimum effective point on the marginal cost curve; otherwise it too is dispensable.

Average cost is rather more popular in economics, and deserves fuller-but not necessarily kinder- treatment. The problem it poses is simply this: it cannot be trusted to stay put. Suppose a finn is making very handsome profits or losses on the usual average cost calculations: price is well above average cost or well below it, where average cost of course includes interest at the going rate on investment.8 Suppose further that the profits or losses will persist for a considerable time. We claim that there will be a tendency for average costs to rise or fall t<l where they equal price.

To understand this shiftiness of average costs, Jet us ask why this competitive firm makes an unusually large or small rate of return on its investment. for a considerable period of time. The an­swer must be that it has superior resources (including possibly man­agement) so its costs are comparatively low, or inferior resources, so its costs are compat·atively high. But then these superior resources are really worth more, and the inferior resources less, than the values at which they are carried on the books. If the resources are owned by the firm (say, a piece of land), there may be no tendency to write up the value of a superior resource to its true value, because accountants are conservative. On the other hand, the account.a.nts will not object strongly to writing down the value of the inferior resource.

'Vhether the resources are revalued or not, another factor leads to movements of average costs. If the firm is sold, ·its price will be determined by its expected earnings. If these earnings are high, the firm will sell for more than book value, and if earnings are low it will sell for less than book value. If the buyer values the

• The "of course" should not lend the student to believe that it will be included in usual accounting procedures; a.ccountant.s have been unwilling to include interest on investment (other than interest on debt) in cost.

Cost cu.?·ves 14 rl~~ . 1

ShO t its <'ost to him, then by definition it Will ise a .1 earn the

nterpr f return-average cost wt 1 move to equality Wt.th . e te o . . 1 • Prtce. going ra used no spectahzec resources, the valuation of .

firtu h b fi . . tnputs If a ch simpler, for t en Y de mt10n the alternative p d d be mu . h ro -

woul rce would be Itg cost to t e firm (and industrv) 0 f a resou . . . nee

uct o . d ·esources enter, however, there ts no valid basis f . )tze ' h d' . h . or ~pecta . alue other t an 1scountmg t etr future earnings and • . thetr v . -

fiJCtng t begins to follow prtce. a.veragel~~~ions of assets will not affect marginal costs becau~e the

Reva . 5 do not depend upon the firm's output. Suppose there aJuation ' t t b f · · rev . . the industry s ou pu ecause o an mcrease m demand

. rtse tn ( . f ' 1S a . n superior resource say, a p1ece o land) should be culti-so a gtve t'ntensively for maximum profit. If the plot is cultivated

t d more . 1

· va e . sively it wtll have a arger margmal product (by the

re mten ' u·p . F' tn° d. 1·nishing returns; see l Y.l L m 1gure 7-1 ), and should I ' of ltn . f l f h ;'"revalued upward. Rut e:en

1 1 .;,~e o

1wner o ldt ~ plot mistakenly

. use it more intensive y, 1~ va ue wou nse--for the value fat led to t is determined by what others would pay for it. Hence f an asse bl h h . 0 t becomes more valua e w et er or not Its owner varies the asse

outp~t. ctual amount of asset revaluations is unfortunately almost T ~ ~ly unknown.9 The effects of restraints imposed by accoun­

comp e d tax Jaws are in the direction of preserving historical costs tantstsa~s historically made and recorded ). Historical costs, if rigor­( cos) adhered to eliminate certain methods of capitalizing gains ous v ' .

d ·losses but introduce other departures from the alternative <lost an ' . fit b h . lo concept appropriate to maxnnum pro e av10r.

The Proof of Rising Short-Run Marginal Costs

We have pointed out that marginal cost varies invers~ly. ~th the marginal product of the variable factor, s? the law of durumsh­ing retums implies that the short-run margmal cost curve has a

• The most extensive study is Solomon Fabricant's Capital Congumptiou and Adju~trnent (National Bureau of Economic Research, ~938), ~sp. Ch. 12. Of 272 corporations reporting during 1925-~4, 66 made . rapttaJ wnte-ups, 140 capital write-down~the period wa.s obv10usly dom10ated by the Great

Depre~ion. . · · 1 t dealt 10 Many of the problems encountered in analyztUg htstonca cos s are with in the literature on national income and wealth.

142 Prodllction: Dirn£ni8hiflg R eturn8

po!'itiw !'lope. It would appear thnt this ends the mutte f but it does not. r 0 Proof,

A ~f'ril':, of ~ull ist icnl studies lun~c found that short-run mar . ro::t 18 npproxnnatcly constant unttl "capncity" is appro h d gtnat pnoity in t.urn is u~unlly defined 1\s the output at whic:c e ·~a­COl't..s become \'ery inclnstir. 11 T he typi<'lll mnrginul cost marginal

d. to t l . )' . I . curve nc oor mg 11s tlt't·nturc, IS t 1nt Illustrated in Figure 7-6 Cl ' -· early

p

MC

I

o~-----------------------------------0

l. hi~ lit fii'HI III'I' dl'lll t '~ llln 141tol'l •l'llll V1didiLy of t.hu ltLW of dilllilliHh· 1111:( l't' l lll'l lli , I ~

Hnllll't' l.llnn dt• lvt• iulo Uu' Ml.nl.lrdii'ILI Mlud lt•M whinh yidd huri­~ollfnl r~ laul'l • l' llll IIIHI'~i1111l 1 • oHIM, 1 ~ It IM potH• II ~ Ic· lo lt•Mf t.lu• vu lldlty

"\\'" "l.nll q1 11111tol wU h 1!.11' de•llnil luu lnl1•r "Ntttii iii'IHIII 1 ' ~ " '"1' 11 •11 nud , • .,r.,tt•lll'i''' "''' jth' t•ll 111 ,1 , ,l lllll thl\•11 , '"'''''"''''II/

1111• 1 illlllftJifl ~ I Ne111' V111'k ' .M c•l It nil' II III, 1\IIIU). "'l'ltn nlllllu•lt l1111 1• ''""" P I II te•l1a•d "" l u1111 c~ ltlll 'fll' hill~ • • Ill I 1,,, " lnll• lll•nl

f'lll•t•l lll lt ' li, llllc l t ltllutu lelll llltiiii iHI 1111 10 1tf11111te t, 11llh llell 1letf11 llc•lln\ l cll ccllhl•l

~t~l cln

:, ria

t*RtUt Cost Curves s~or . 143

. cost curve indirectly. If margiMI costs a r thiS - . re essential\ o to the output at whtch they rise ranidlv u d Y con-tnnt up h . I' • ' n er comPet't'

s 's output (set w ere margmnl <'Ollt equn\s price) ·n be t ton '' flr~tn t nt nil prices above' this con~tnnt tnarg1nal Wt t nearly ron:- nn h . F' cos . and zero

I ·er prices. T us m tgure 7-6, the output of lh c. .

At o\\ p d p b c nrm vanes I

t \)rices between 1 nn ~ . ut falls to zero 1\t . titl• c n . I t d' 1 . prtces \lnder

'~'her<' mnrgmn cos s tsp ny tlns behavior then h Po· ,:y . t t f th . d ' ' s ort-run . tions in the ou .pu o e m ustry will come abo\tt 1 var'n l . t' . h a most

I ·,vrly throug 1 \'1\rla tons m t e number of plant in 01'\n t' r>:<' us . d'l . .-~ra ton t ·r tnnrginnl co!i\ts rtse sten 1 y w1th output much of •h . d · flu 1 • • • • ~ e m us-

' fluctuation m output w1\1 come from fluctuations ·1n th t try s . . · e ra e

£ Ut11

ut of each plant , nnd httle from fluctuations in the numl 0 0 u )('f

of opernting plants. .

I this form, the hypothesis tlmt short-run marginal costs are 11

d · d'\ constnnt cnn b<' teste n~nmst rca t y obscrvnblc fnc~ . As an ex-nmplc, <'onsidcr the Amcl'lonn cotton spi~ning industry. The output of the inciustt·y mu.y be mcnsm Nt hy spmd\chours, thl' "plnnt" by native spindles, t\.nd the output per plnnt hy "hours per ncti\'e spin­dle". 'T'hen the pcrcentilJ7;C change in output (spindlc hours) from

0110 qunrt.t'r yctu to th<' next ':ill be. appr?xitMtoly cqunl to the

um of thl' pcr<'<'nt.ngc chm1~€'s m Mltve t~pmrlleR nne\ in hout'tl per :pindlr. l& Thit~ ('1\\oulnlion hns bcl'n mnde hy quarters from Au~st 1945 throuf(h .hm<l 1959, Krpru·atoly for thr southern states (where U\C' in1)ul\try hnl\ J.(t·own 1\li ~thtly ) tllltl fur tlw Nl'w En~tl l\nd l!h\tcs

"Thr• nntunwnt, it 1111\Y l11• nolt•tl, t•nn lw nxle•tu le•tlnl~n lo nont·OtnlH' Iitivc• flrtn~ whi11h npt'l'tll t• mort• tlmn nn" plnnl within 11 11111rkl'l 11re•n. \lnle·~ lht• pltlnllt lut\'1' '''llltll t'otlltl nnt. umr~innl ~'""' "· n 111\IIIIIIIOli~t will miuimi11• t'OI!b "'' oprrntinK lhr• IIIWI'r nulf~tinul 1'11111 plrmt nt "c•ntuu·ity" nntl 11111kmll 1111 n;lnpl nl imnt to t•hnnl(iiiK output in I hr plnnt with hi~tht•r nllll')linnl r0111a.

"'1'1111 uulpul. of 1111 in eh111l1'~' i11 I) • Nrf, wlwre• N i~ tlw lllllnlwr 11£ plnntA opo,rnl illll , 'I lh t• 11111 pill l'llf pltllll. 1\v clt•l\nlt,i<ln ,

t)(J - N ll•l -t qt.N IIIUI

~\1/ 1\N I .

" ·"

144 Production: Diminishing Returns

(where the industry hns been declining very substantially). We may tabulate the average of the 55 quarterly changes: 10

Section

Southern st,ates New En~tland

PER CENT OF CHANGE IN SPlNDLE

HOU RS Dl:l'E TO

Change 1:n Change in Hours Active Spindles per Spindle

9 .2 21 .8

90 .5 76 .5

The conclusion is clear: even in the declining branch of the in. dustry the overwhelming part of changes in output is achieved through variations in the rate of operation of plants (here, hours per spindle), not by variations in number of active plants (here active spindles) .11 In this industry short-run marginal costs ar~ rising: I suspect that in most industries they do so.

RECOMMENDED READINGS

Friedman, M., Price Theory, Chicago: Aldine, 1962, Chs. 5, 6. Stigler, G. ,J ., "Production and Distribution in the Short. Run," Journal of

Political Economy. 41 (1939), 305-27. Reprinted in Readings in Income Distribution.

Viner, J., "Cost Curves and Supply Curves," Zeitschrijt fur Nationaloko­nomie, 3 (1932) , 23-46. Reprinted in Readings in Price Theory.

PROBLEMS

1. A producer with two plants wishes to produce a given output at the lowest possible cost. Under what conditions will he close down one of the plants?

"The source of the data is: U.S. Bureau of the Census, ''Cotton Production and Dist ribution," Bulletins 186, 189, 193, and 196 (Washington, D. C. : U. S. Go\•ernment Printing Office).

" In the declining branch of the industr;~·. one would expect a larger roll' for plant reductions simply because the industry is declining. And when short-run output changes nrc dh•idcd into increases and decreases, we find that the role of plant changes is more important in the case of declines of output:

D~r<Giion of Chan(le in QUtJrlulv Outpul

Increase Decreue

New EnjJiand State• l•£RCENT OF CBAWOE IN SPINDLt; -lrOURS UUI! TO

Cha71ge in Acli•e Chang• in Hour• per Spit~dl.e• Spindle

20.3 82 . 2 23 .9 68. 6

P 0blent-S . . r given the followmg product10n function:

145

z. )'ou nre I 0 1 2 3 4151 6

oToFA --------- I 7 l~pv- __- ------- 100 101 103 105 106 .8 108 4 109 9

OT · 111 3 ov'l'P tile m1u"inal and average product~ of A.

praW · "' (a) the marginal and average products of B (the other pr 1 f (b) praWTen units of B underly the foregoing schedule u~e ()(thuc IVt>

f tor) · ( 133) · ~ e con-ac · rns to scale equatwn p. . stnnt retu

nom\' consisting of farms has the unusual production function 3. An eco .

for each farm: NUMBER OF MEN

1 2 3 4 5 6

etc.

MARGINAL PRODUCT

20 15 19 14 18 13

etc.

had 10 farms and 40 employees how would you allocate them If vou . am~ng farms? If wages are $40, construct the margma] cost schedule of

output. . . . I . . . I . 4_ The law of dtmmts ung rPtnrns was ?rtgma ly stated as an Iustorical

I that is it asserted that the margmal product of labor on land aw, ' . f

tld decline as population grew. I tnte, what would have happened ~0

\ 1 ) aggregate agricultural land vah~es, and (2) prices of farm products relative to manufactures, o,·er long penods?

I

I

chapter eight

Produedon: Returns to Seale

No such sweeping generalization as the law of diminishing returns has been found for the relationship of output to inputs when all inputs are varied. We are accordingly driven to consider alternative possibilities: when all inputs are increased in a given proportion, output may increase in a greater or lesser or equal proportion. The economist must then determine, when he is analyzing the automo­bile or shoe or radio repair industry, whether it has increasing, de­creasing, or constant returns to scale, and we shall discuss later the methods of empirically determining economies of scale.

THE PROPER COMBINATION OF INPUTS

Let us begin by asking a basic question: if we wish to produce at a certain rate, in what proportion shall we use the various in­puts? This question is not answered directly by the Jaw of diminish­ing returns, for it told us only how many men were needed to pro­duce a given product, given that they worked on 10 acres of land, or (since the law is reversible) how many acres were needed, given a labor force of 8 men. There are many different combinations of inputs that will yield t he desired product, and obviously the cheap­est combination will maximize the producer's profits.

The cheapest combination obviously depends upon the relative prices of the inputs and in fact the least cost combination is given by the rule : a dollar's worth of any input should add as much product as a dollar's worth of any other input. For if a dollar's worth of input A has a marginal product of (say) 5 units, and

146

Y' Combination of Inputs rhe proper 147

B only 3 units, then we can that of

B y $1 less of B, suffering a decline of product of 3 un·ts

(a) B~Y $0.60 more of A, obtaining 3/5 of the marginal pr~d~ct (b)

11 ·~worth or 3 units of product, and

f do ar ~; ' o a p cket the $0.40.

(c) o

. 1 maY be stated as an equation of minimum cost: 'fblS rue

Marginal Product of A = Marginal Product of B Price of A Price of B

Marginal Product of C P rice of C

ll ·nputs no matter how many. for e. 1

' · · hi I f · · -.rh the price of one mput mcreases, t s ru e o mtrumwn cost ''v en 1 f h. · ( h · l

that we must use ess o t 1s mput t us mcreasing its ~s~ . · . 1 product) and more of the other mputs (thus decreasing

margJDa their marginal products)·. .

This analysis has obv10us analog1es to .t~e problem of the_ ~n­dividing his income among commod1t1es m order to max1m1ze

sumer f · d. ff t. faction. I n fact the same apparatus o m 1 erence curves can ~ 1~ed with the obvious modification that now we shall call such

e rves i~oquants (equal quantities), and define the isoquant (Figure ~~1) as those combinations of inputs which yield the same product. When we reduce the quantity of one input (A ) by a small amount (~ . ...4), we reduce the product by ~.4 times the margin~! product of A ( = MPa). Thus if the margmal product of men 1s 6, when we reduce the quantity of labor by 0.25 (one-fourth of a day, say), we reduce the total product by 0.25 X 6 = 1.5. In order t.o offset this reduction, we must increase the other input (B) by such an amount (6.B ) as to produce this much, so

(~A < 0),

along an isoquant. Hence the slope of an isoquant is

D.B MPo ~A= - MP."

Corresponding to the consumer's budget line, there will be an outlay line for the entrepreneur. With a given expenditure Eo, hP

"

' I •' ..

~:

' l· t , r. ,I t

~

r

l

~ t rns to SCIJle: The Simplest Case . / ,.. tant Re ll 149

Productwn: Returns to~'-

1

C0115 y implies that

0

148

B

v Figure 8-1

can buy all com binations of A and B such that

Eo= A Pa + BPb,

A

and there will be a different outlay line for every amount of ex­penditure. We draw thtee outlay line1> in Figure 8-1 (temporarily ignoring TV) , each higher one representing a larger total expendi­ture. The en trepreneur will choose outlay line FO because this is the lowest line which touches the isoquant, and in general the lowest outlay line to yield the desired product. is tangent to the isoqua nt. But the slope of the outlay line is '

Pa - pb'

1 For a constant outlay, .1A · P. + .1B · P. = 0,

60

...: he tangenc 11nd t Pa MPa

-= - - · I pb MPb

. of our condition for minimum cost. The proposition t}er foiJD · t ' f ·t · ·

11no l , • 11 be used of an mpu 1 1 s priCe n ses is illustrated thAt Jess ~\1 the price of A, leading to the new outlay curve TV

. creasmg . . , ' bY JP . cessarily tangent to a convex 1soquant to the left of

I . h IS ne " '

110 : ·nal equi librium.

2 • •

the 011gi d nt will find many d1fferent uses of th1s technique which

The stu e . h I ' 11 employed where one w1s es to ana yze three variable~

is genera. ~ourse to solid geometry. (Here the three variables are "thout 1 e · · d"ff

W1 . uts and output; w1th consumer m 1 erence curves they were two lDP nodities a nd uti lity. l two con11

oNSTANT RETURNS TO SCALE: ~HE SIMPLEST CASE

Th ·mplest possibility with respect to economies of scale is that e s1 . . d · ·

1 e Done . when output IS mcrease m any proport iOn, exact y there ar . . . . . I roportiona te mcreases of nll mputs are required. Then If

equa P · · ff I b I fi ' : ces of 11roduct1ve factors are not a ectec y t 1e rm s rate the pu d · · t 1 of output, as they will not be un e1· competitiOn, to a costs vary

proportionately with output. . Constant returns to scale are commen~ed ~pon a very simple . und: if we do n thing once, we can do It tw1ce. If we use A and ~~0 produce P, why ~hou ld not 2A a nd 2B produce 2P? Perhaps thry should, but it must be emph~si~ed that there may be c_heaper ways of producing 2P. Where pamtmg was done by hand, 1t may now be feasib le to use a spray gun; where a man per·for·med tasks X nnd Y, it may now be fear-ible to have him specialize in task X with a gain in efficiency. These are questions of fact , and. we cannot state tha t in general they will be, or will not be, possJble. If these exa mples suggest that at most we must double in~uts. to double output, that also is not true. For the task1> of c-oordmat.mg a larger entel'pl'i~:>c may inerease so mpidly t hat large ~nterpn.ses are inefficient. vV e sha ll examine these possibilities of mcreusmg nnd decreasing returns shortly .

• See mathematiC'ul note 6 in Appendix B on thl' rrlation~h ip of diminishing returns to convexity,

150 Production: Returns to S cale

If there arc con~tant returns to scale, obviously marginal . · costs will be con tant for all outputs when the mputs are in proper

t · Pro-

portion. For K per cent more ou put reqUJres K per cent mor · d · th · f d · f e of each mput, an smce e pnces o pro uct1ve actors are consta

to a competitive firm, total costs also rise by K per cent H nt . · ence average and margmal costs are constant.

1-(/)

0 <..>

SMC

LMC

0~--------------------L-----------~ A

QUANTITY

Figure 8-2

·we have identi fied cost curves which reflect complete adjustment ~f all inputs w.ith the "long run", and those which reflect changes m part of the mputs wit h the "short run" (p. 134). Henc<' "short­run" marginal costs will rise (because of diminishing returns) even though " long-run" marginal costs are constant. Consider Figure 8-2. At output A, a certain quantity of each input yields minimum mar-

t r118 to Beale: The Simplest <.;ase 101

·nt Re tt co11sta ge) cost, AK. If we vary part of the inputs we d avera SMC '

.119

1 (aO . the marginal cost curve, . glhllJI obt.DI~ t that shor t- run marginal costs may be greater or 5 It is evldenl g-run marginal costs, depending upon the rate of

than °0 · te h srtl

111)er j\t the point where the tw~')cudr.v~sd 1dn b. rs~ctt, t . e ~arginal

11wut. )ant ("fixed factors 1v1 e y 1 s pnce 1s equal

0 J'()(luct of t.he r product of the variable factor divided by its price. ~0 the Jl]arginauts the marginal product of t he plant rises and the ~t Jarger 00~ t of the variable factor falls, so t he long run mini­Jllllrginal pro ~~tion is not fulfilled ; the opposite relation holds be-

cost con muiJI ·ntersection. )oW the 1 h h the long-run average and marginal cost curves of

£veD t oughorizontal (and in fact identical ) under constant re­tbe firi11 are) no such relation need hold for the industry. As we

to sea e, . turns . Chapter 10, the mdustry cost curves are affected also shall see 10 ·n the prices of inputs (which are constant to the indi-b changes t f . ! fi m) . Nevertheless, even or the mdustry constant returns \'lduall r.

5 the overwhelmingly popular assumption in scientific

to sea e t D I f t' . work. The so-called Cobb- oug as unc ton IS

p = aCa£1- a,

h P l·s product, C is capital, and L is labor. This production

-~ . function yields c~nst~nt return~ to. scale/1

and 1t has ~n ~lmost onopolistic position m economic hterature. I ts popularity ts not

~ue to its demonst rated validity as a description of actual produc­tion functions , however. Rather, it is used because (1) it yields diminishing returns to each productive factor separately, (2) it is simple to handle, being linear in logarithmic form, (3) in many investigations the precise nature of returns to scale is not very in­teresting, and constant returns is a convenient simplification, and (4} of a remarkable property of constant returns to scale which

we must now mention. Ettler's Theorem. Euler's t heorem on homogeneous functions is

the august name attached to thi s final property of constant returns. Tbe theorem is a simple one: it says that if there is constant returns

'If we vary each input in a given proportion, say changing C to (:\C) and L to (AL), we get

a(~C)a(A£)1-a = a~a+t-aCa£1-a - axCa£1- a - xP 110 the product increases in the same proportion . '

152 Prodtt.etion: Returns t

0 Scale to scale, then the total product is equal to the sum of th . products of the vnrious inputs, each multiplied by tl e rna~g~na) its input.• Thus if the production function is le quantity of

P = !(A, B, C, . .. )

and there is constant returns to scale I

P = A· MPa + B · llfPb + C · MPc + Since the theorem has been in t he mathematical b 1

hundred years, we can assume its truth and her oo cs for two I . . ' e present only

exnmp e. Cons1der the stmple production function an

p = Cli•LS/4 '

which Paul D ouglas believed to be desc1·iptive of A · f t . h mencan manu . a~ u rmg; ere P, C, and L are product, capital and lab • m mdex number form. If L = c = 200 ' · or , all

I

p = 2001/42003/4 = 200.

Increase labor to 201, and the product rises to

p = 200114201 314 = 200.749.

If now Cis increased to 201, with L held at 200,

p = 201114200314 = 200.249.

Hence the marginal product of L is 200.749- 200 = 0.749 and that of c~pital is :o_0.249 - 200 = 0.249. The sum of ma;ginal products t1mes qunnbtles of factors is

200 X 0.749 + 200 X 0.249 = 199.60,

which is approximately what Euler's theorem asserts. T he small discrepancy in product arises because we u~e finite increases in the inputs: the theorem holds strictly only for infinitesimal changes.

Euler's theorem entered economics in order to solve the problem whether, if each productive factor is paid at the rate of i ts marginal

• The definition of a homogeneous function of degree /.; is thA.t if P = f(A, B, C, ... ),

)..kp = f(X.A, >..ll, XC, ... ), where X is any positive number. When k is unity, the function is homogeneous of the first degree, and this is our definition of constant returns to scale.

t nt Returns to Scale: The Simplest Case cons a 153

d Ctivity, the total product would be sufficient d Pro u · d 'th 'd an onlv ffi . t It was rece1ve WI cons1 erable hostility· E 1 J su -cJen. k. d that "Justice is a perfect cube said the a. . c geworth rc­rosr e . h ' nctent sage· a d

tional conduct lS a omoge~~ous .function, adds the , n rs t, The modern savant , Ph!hp WJCksteed by nam b modern c:avan . h . r . e, a andoned ~h argument, but t e s1mp tctty and manageability of th h t e t' h e c e orno-eneous func Jons av over orne any. scruples on realism and the g ·mmensely popular among economtsts to this day Y areJ ·

, 1 • ble Returns to Scale yar1a h ll • f

Phrases sue . as economies o m~ss production" testify to the widely held behef that as an enterpnse expands its scale of opera-

t . ns it will be able to reduce average costs. Popular beliefs a .IO ' 'd . . re seldom a safe gm e m econom1cs, and here they are especially sus-

ect. Laymen observe that more electricity (or transistor radios pr electric dishwashers) are made than formerly, and that prices ~ave fallen (or, in a period of inflation, risen less than a comprehen­sive price index). These observations are correct, but the passage of time also allows technological advances to take place, so the effects of scale of operations and technological advance are not sep­arated. R eturns to scale (like diminishing returns) refer to the be­havior of output relative to inputs when the "state of the arts" is given.

Increasing returns to scale arise when a doubling of output does not require a doubling of every input. The causes of increasing re­turns are:

1. There may be some unavoidable "excess capacity" of some inputs. A railroad has a tunnel which is essential for given traffic, but cnn handle twice as much t raffic. The emphasis here is on "un­avoidable." If the railroad has unused locomotives, in the long run they can be sold or worn out, and hence do not give rire to increas­ing returns.

2. Many inputs become cheaper when purchased on a larger scale. There are quantity discounts because of economies _in larger transactions. Often equipment costs less per unit of capac1ty when larger sizes are ordered (see T able 8-1).5

h . t t increase as the cube • Containers have the property that t ctr con en s of dimensions, the surface (and material required) as the square.

154 Production: Returns to Scale

Table 8-l

. f B 11 l ' curiuu Induction Elec tr-ic 1\iotors, 1800 rpru l' rJrC." o a - • "'

(Fe bruary 1950)

IIORSEPOWEII PRICE PRfCE PER HORSEPOWER

1.0 $59 $59 .00

1.5 69 46 .00

2 .0 80 4Q . 00

3.0 89 29 .67 .; .o 106 21.20

7 .5 139 18 .53

10.0 176 17 . 60 25.0 327 13. 08 50.0 559 11 .18

100.0 1073 10.73 1.50. 0 1633 10 .89 200 . 0 2085 10.42

500 .0 3207 6.41 1000.0 5819 5 .82

3. More specialized processes (whether performed by men or ma­chines) are often possible as the scale of operations increases: the man can become more expert on a smaller range of tasks; the ma­chine can be special purpose.

4. The sttltistical Jaws of large numbers give rise to certain econ­omies of scale. For example, the inventory of a firm need not in­crease in proportion to its sales, because there is greater stability in the aggregate behavior of a larger number of customers. a

If these fof'ces are dominant, the long-run marginal cost curve of the firm will have a negative slope-there will be economies of scale. An illustrative long-run marginal cost and several short-run margi­nal cost curves are given in Figure 8-3: each short run curve repre­sents a different amount of "fixed plant." The corresponding aver-

• See Vf . J. Baurnol, "Tite Tmnsactions Demand for Cash: An I nven Lor.v Theoretic Appronch,'' Quarterly Journal of Economics (NO\'Cmber 1952). A similar argument may be mnde with respect to risks of fai lure. See tdl'o the results on servicing of machines in W. Feller, A 11 Int roduction to Probabil­ity 7'heorv and Its A pplications, 2nd ed. (New York : \\'ile.\', 1957) , Vol. I , pp. 416-21.

~ to Scale: The Simplest Case 15S

J

t ]leturnB . . Co11st0.1~ also given tn F1gure 8-3. These average costs

rves are h . . 005t c_u lternative costs-t e mput pnces are tho e neces-

age ~cJusiVeiY a sources in this industry and exclude all " rents. '' re e p t he re f L d'ffi I ·

11 to kee ns to scale arises out o t11e 1 1cu t1es of manug-sllrpYecreasing retu~. e The larger the enterprise, the more extensive terpllS . . . . . a large ~u d inistrative orgamzat10n must be m order to pro-Jilg Jllal lts a m and for

0 QUANTITY

Figure 8-3

vide the information necessary for central decisions a~d t~e sanc­tions necessary to enforce t hese decisions. A large orgamza~o:ti~u:! be less flexible-policies cannot be changed frequently an ~

carefully controlled. . . · 1 b considered The decentra lization of a large orgamzatwn Img 1t . e . d d

a way in which to avoid the rigidity of size, and ti11S has m ;.e become a fashionable practice a t times. A fundamental contra Ic-

r

156 Production : Returns to S COle

tion is encountered here, however : as the parts of a large enter . . I . f . f I · PtJse are decentralized, t 1e gams o econom1es o sea e are sJmultane

' b ) to . h OUs)y sacrificed. It would be poss1 e g1ve eac manager of a t h h . . h. sore complete autonomy, butt en t e orgamzat10n w 1ch owned a tb . ou.

sand stores would ~ecome a mere J~v~stment t:u.st: there could be no gains from quant1ty purchases or Jomt advertlsmg.

This source of inefficiency of large size is given little weight . the popular literature : size is almost equated with efficiency. ym anyone who watches a line of automobiles start forward as a tra~t light changes will be impressed by how each additional driv c starts a little later than his predecessor, so it takes considerab~r time for the motion to be communicated to t he twentieth car ev e

h I.

1 , en

when all the drivers can see t e 1g 1t change. This same slack is encountered in large organizations, so when frequent changes ar called for, a large company is very inept. The industries ma.kin: style goods (women's apparel and shoes, novelty toys, and so forth ) are consistently dominated by smaller and more flexible companies. Again, those enterprises requiring very close coordination of skills of men are seldom large scale: no novel can be written by more than two persons (and of these at most one can be a woman), no orchestra can have 300 members and still be called symphonic. And in general in tricate decisions cannot be made well by committees

I

which is the reason the greatest of industrial and political empires must have one head, whose familiarity with the details which un­derlie his decisions becomes vanishingly small.

Capacity. The notion of capacity is widely used, but seldom de­fined precisely. Yet it is an ambiguous concept even at best. In the normal case of variable proportions, the absolute maximum at­t ainable output from a given set of fixed factors might be used-ob­viously a firm has no "capacity" limitation in t he long run when all inputs can be increased. But the maximum attainable output is never known- it is, for example, the out put of a farm or a factory when uno expense [or variable facto t·] is spared," and no one has been foolish enough to devote unlimited resources to this end.

Sometimes the technology of production seems to invite a fairly clean notion of capacity. For example, a blast fumace runs day and night, so it would appear to have a definite limit on output per month. Actually it docs not : t he charge can be varied; oxygen can be used, and the shut-down period can be shortened, so plants

.........,. , turns to Scale: The Simptest Case • stant •~e lo7

C011

t d for considerable pcriodf" at more than lOO Peril e 1. fi · . per cent

b11ve o .. Yet the qua 1 cat10ns arc mmor, and in the ·h l nell)· 1 d . . s or run

of cnP ·ty" has a reasonab e etermmate meaning here. Such cases ''cnpacl

cororoon. . h ld are un etllS clear that capamty s ou be defined in a way that It se t o£ costs-no one cares about the output that cou\d

takeS accoun

0 A 8

QUANTITY

Figure 8-4

LMC

be obtained only at literally prohibitive costs. ~o definitions have d. capacity is (1) the output at wlucb short-run aver­

been propose . t . . urn and (2) the output at which short­age costs are a a mmlm ' tinition of words is and long-run marginal costs are equal. The ?e t f the

. b t tb · s a persuas1Ve argumen or · necessarily ~:bltra~,. u e:ell, t to entrepreneurial decisions. latter defimtlOn-lt 1S more re e\ a~ We may illustrate its relevance by Flgure 8-4.

158 Productwn: Returns t eo 0 >JCQ{

On the minimum cost definition, capacity is OA · on the e d fi . . . . OB S t ' lllargi nal cost e mtwn 1t IS · . uppose an en repreneur with th •

represented by the short-1·un average cost curve wished to e plant pcrm:mently at 0/3. On the minimum cost definition he is opoper~te

· d tl · t th t · · crating beyond capacity, an liS sugges s a , gtven t1me, he will b . a larger plant. But he will not: this plant has the minimum av Uild cost of any possible plant for output OB, and the larger plan~r~ge noted by SAC' would obviously have higher costs for the d . e­output. A definition which leads us to say a firm will willinglyeslred

tl be d .t d . oper. ate permanen y yon capac1 Y seems un es1rable. The d fi . tion of capacity in terms of the equality of short- and Jon;. Dl­marginnl costs does not have this flaw: then it will always be trun that in the long run a firm will expand if it wishes to main/~e a rate of output which is beyond present plant capacity. atn

EMPIRICAL MEASURES OF ECONOMIES OF SCALE

When one looks at the size distribution of firms in a competitive (or, for that matter, noncompetitive) industry, he will always dis­cover that a large variety of sizes exist at any one t ime. We may illustrate this variety with the corporate income tax data in Table 8-2. Assets are not an ideal measure of firm size, but they will do.

We observe that there is a considerable range of sizes of firms at any one time. This could be explained by the failure of some companies to reach the optimum size, due to errors of judgment or the time required to grow to the optimum size. But the range of sizes persists over a considerable period of time (a longer period, indeed, than our tables reveal). This persistence can only be ex­plained by the fact that there is more than one optimum size.

The optimum size of a firm-we shall define "optimum" shortly-depends upon the resou1·ces which a firm uses. All firms in an industry do not have identical resources. Some have managers who are effective in running a small concern; others have managers who capably run a large concern. Some have large holdings of natu­ral resources, others buy their J'aw materials. Some are located where labor is cheaper, others where electrical power is cheaper.

h

a.age Distribution of Assets by Com"'• n s· . percen • .-- Y •:r.e m

Selected Manufaclurmg lndusLriee (1954 und 1958)

1954 ~Class A. Knitting mills

Under $100,000 2.4% $100,00D- 500,000 13 .6 500,ooo- 1,ooo,ooo 12 .0

1 000 ooo- 2,soo,ooo 19.2

2•500 ' 00o- 5,ooo,ooo 14.8

5•000'ooo-to,ooo,ooo 13.7

0'000 'ooo-25,00o,ooo 12.s j ' ' 000 Over 25,000 , ll.5

TOTAL 100. B. Engines

Under $500, 000 ssoo,ooo- 1,ooo,ooo

l ,OOO,OOD- 2,500,000 2,500,00D- 5,000,000 s ,ooo,ooo- 1o,ooo,ooo

lO,OOO,OOD- 25,000,000 25,000,000$ 50,000,000 50,000,ooo-too,ooo,ooo

TOTAL

SoollCI'J: SL4ti•tieo oflneom•, 1064, 1058.

.1

.6 2.4 5.5 6.1

32 .5 35 . 1 16.6

99.9

1958

34% 14 .9 13 . 1 18.1 16 .3 12 5 19.4 2.4

100.1

1.2 .4

1.6 3 .3 0.

20 .2 31.1 42.3

100. 1

159

~

Such differences are compatible with all firms having equal long run

marginal costs.1 . . •

If we observed the distribution of firms by Size m an mdu~try ·od of years and it did not change (random ftuctuat10ns

over a peri . . . fi f ·d ) e could make several vahd mferences. F1rst, the nns o

asl e , on . . . f t t · ould on average be operatmg m ft reg1on o cons an

every s1ze w . . d 1· · · 1 run marginal costs-for 1f margmal costs were ec m-or r~smg ong-

. · of firm is commonly defined as that which has minimum 'The optimum I'IZC soon as we allow resources to differ, i t is not

loosn!-,·brulen t oav=~~g~h~~s~~~g~~m average costs excludill(J rents will be; cqlu.althfaort P ""' ' · · r · d t •pes of rcsourei'S Imp ' the different ~r~. The var~m~ _qu~~tleSt ~~ so·~c rcsottr<'Cs will car~ more some are speculhzed to the m)ddustr.\ lthn h • e !\. verage costs iucllldill(} rt nts in the industry than they cou earn e sew er . . can of course be equal.

' · ,_

~12 a a

as ·ra we

160 Production.· Returns to ~ QCale

ing to nny size. 1 hc~t" fi rms would expand and acquire a la:ger share

Of the indu~trv'!' output And second, the firms of vanous ~,· . . . . ~ zes would be equally efficient., h<'cause 1f any s1ze were more efficient this si ze would be more. profitable and fi~·ms would tend either t~ move to thi12 preferable ~1zc or to leave the mdustry.

In fact the basic _definit~on of_ a firm o~ ?Ptim~m s ize is that it can maintain it~clf mdcfimtely m compet1t10n w1th firms of oth sizes. This test of opt imality js all inclusive: it takes a ccount ;; the ability of thr firm, not merely to produce goods efficiently, but also to introduce new technology at the proper rate, cope with changc11 in conrumcr tastes, adapt to a changing geographical mar­ket in the product or resources, and so on. A test of comparativ effici ency that iil not a ll inclusive would not allow us to predic~ the survival of the most efficient size of finn.

Some sizes of firms decline as a share of the industry; for exam­ple, corporations with assets under $10,000,000 making engines had 14.7% of indust ry usscts in 1954, only 6.5% in 1958 (Table 8-2). When the decline il' large enough or persistent enough to overcome the possibility that it is due only to random fl uctuations,s as is tr·ue in this en c, we may conclude that these size classes are com­paratiYcly inefficient. On this interpretation, the large firms in the engine industry were more efficient than the smaller firms: there were economies of flCn lc. In the knitting industry, on the contrary there was a rleclinc in the role of larger firms, so there were dis~ economies of scale.

RECOMMENDED READINGS

Douglas, P . H., "Are There Laws of Production?" American Economic Review (March 1948) .

.\farshall, A., Principles of Economics, London: Macmillan, 1922, Bk. IV, Chs. S-13; Bk. V, 3-5.

Robinson, E. A. G., The Structure of Competitive Indust ry, London: Nisbet, 1935.

Stigler, G. J ., ''The Economics of Scale," Journal of Law and Economics. 1 (1958). .

'Random forces would bf' accidental events unrelntcd to the size of firm O\"Cr a long pe riod : floods or other catnstrophcs, no unusua l num ber of deaths o_f entrepreneurs in a gi\·en period, unusual interruptions of supplies of mnte­nals, and so fort h.

161

pROBLEMS

that long-run and short-run llUirginal costs are equal where 1. prove t-run average cost curves are tangent.

nd shor . t . th " . long-suppose a productiOn Bproc~ssh, con .am~ refe machmes": A, with

z. u "t , of 20 units ; , wtt a cnpnctty o 75 units; and c with

8 "cllP3~'/ of ZlO units. Each ~:JChine ha11 ~osts of SI? plus 10¢ per a c:tpactt. these limits of capactty, nfter whtch an nddttionul machine unit uP to lo •ed. Calculate the average costs for outputs of 10, 20, and J1lust be eroP ~eral hundred units. Then detPrmine minimum cost output. 50 on, up to ~f reconciling processes with different efficient sizes is called fbe problem "

of processes. •'balanc~ Cobb-Douglas function, P = C'I'L"I' calculate isoquants for

3. '(]smg2~ 300. (For the first isoquant, since P = 100, log 100 = P"" 100, C + f Jog L and assign various values to C or L.) Draw some 2"" ! _log t ngent to t hese isoquants, Pt. = 1 and Pr = 2: (Perhaps Pt. is price hnes

8 hour and Po rental cost of mnchinrry per hom.) Calculate

, ge rate per 11 11: 1 -run average cost curve. also the ~nt~ al studies of costs of finns or plants of different size often

4 Statts JC h. h h I d L.~- d . · . h regression fnllacy-w tc as a rC':I Y U\.'CI\ enl'ountere m the e~mmt~ t e f the consumption function. It yields economies of sc:Ue simply . .:~ .. uss•on ° 0 h h th .. II ,. 0

W"" of random fl u<'luatJOn, even t oug ere rr:~ y ts constant re-bccaure ale It may be illustrated as follows : turns to sc .

(a) Consider 10 firms, with average outputs of 100, 200, . . . , 1000,

respectively. . . b) Each firm's costs in any one year are S5 per. umt (vartable costs)

(I ~"' 6mes its avNage output. Thus the firm with an average output Pus .:><~ 500 I ·~ . I t . th of 300 has costs of 300 X $5 = $1 p us "" ttmes t 1e outpu m . e

given year. . . (c) Output in a given year conststs of average output plus or mmus a random fiuctuntion. (d) The random fluctuation is obtained by flipping a coin, adding 10% of average output for each consec~tive ~NI~S ( i~ heads appear first) ~r subtracting 10% for each consecutive ta1ls (1f tatls appear first) . Temu­nate the flipping when t.he mn of heads or tails ends.

Calculate the costs in a given year. Compare graphically with average costs when there are no random fluctuations in output.

chapter nine

Additional Topics in Produc tion and Costs

The cost curves developed in the preceding chapt-er are thos I d . . . e com-mon y use m economic analysis. Yet they deal with only a part' I k. d · ICU-ar m of production process, and there are many problems f ~hich they require modification or extension. In this chapter ,~: discuss three such extensions: multiple products; external econo­mies; and finite production runs. Each is sufficiently important to deserve attention, and in the process more will be learned Of the standard cost curves.

MULTIPLE PRODUCTS

Multiple products made their entrance into economic analysis in Great Britain, so the traditional example of multiple products has been the steer, which yielded a hide and beef. It is at least approxi­mately true tha t these products are yielded in fixed proportions: a steer has only one hide. Hence if we attempt to construct a cost curve for (say) hides, we shall find that we cannot do so: we cannot vary the output of hides, holding the output of beef constant. The only possible cost function is that for a composite unit of (hides and beef), and given competition, it will be a matter of indifference to producers whether hides sell for $20 and carcasses for $1, or hides sell for $1 and carcasses sell for $20. Demand conditions will determine relative prices.

The case of multiple products produced in fixed proportions is, in fact, really not a case of multiple products so far as production is concerned. In a cost diagram, we may rels.bel the output axis (A +B), and now employ the cost curves of the single product

162

. z Products 163 ~[1tlttP e . J • no difference between calhng (beef and hide) one 'f}lere JS firll1· d calling H 20 water. product an 1 rule, however, the products of a firm can be pro-

As a gene.rable proportions. This is obviously true in many cases· d · vana · duce m t store can sell more or less of any one product· a d a.rtmen 1 f k' d h ' a ep . an make more or ess o one m of s oe; a farmer shoe fac~m ~ c agricultural policy permitting) can grow more soy­(the natJ~nl:ss wheat. Variability is also possible in many more beans an . petroleum refinery can vary the proportion of crude subtle ~aseds: ato ""~oline. Conversely, what looks to be independent d' t Jle m o"~

oil 15 1

.v activities- a firm produces steel and cement in different product! e be related by some common element: for example, plants-mafy 'sing capital for the cement plant will probably be the cost o rat

I larger the steel plant. lower, t

1

e h . portions among the products are variable, it is pos-When t ~ pto separate marginal cost for each product. Consider

'ble to denve a · T bl 9-1 '·i\r 51 · h t ' 1 data for a petroleum refinery m a e . ,. e the hypot e tca

Table 9-1

OUTPUT OF OUTPUT OF GASOLINE (GALLONS)

FUEL OIL 100 110 120 ISO

100 $2.45 S3.55 $4 .85 $6 .35 110 3.90 4.80 5.90 7.20 120 5 .45 6.15 7.05 8. 15 130 7.10 7.60 8.30 9.20

define the marginal cost of gasoline as the increas~ in tot~\;o~~ divided by an increase in the output of gasoline, . ~ el qua~ ;f

110 fuel oil being held constant. For example, :h<\ ~a~;~:al~~:s is gallons of gasoline, when the output of fue OJ IS ,

$6.15 - $5.45 = $0.07 per gallon. 10

f soline or in general There will be a marginal cost curve or ga 'bl, output of the d · to each posst e for any one product, correspon mg

1 bl m in the theory:

other product or products. This poses no rea pro e we can simply write (in the competitive case)

MCa(G, F) = Po,

164 Additional Topics in Production and C osts

that is, that at equilibrium the price of gasoline will equal 't ginal cost, which depends upon the quantities of gasoline ;;tar~ fuel oil (F) produced, and similarly for fuel oil: and

MC,(G, F) = Pfl'.

The two equations can then be solved simultaneously.

Figu re 9-l

An equivalent geometrical r d . . . curves (called isocost curvesf oc: .ure IS to construct mdifference the products which b ' which represent the quantities of display one such iso~::t c~r~ro?uce? at a given .total outlay. We origin because as on . e m Figure 9-1. It IS concave to the other in the d / contmues to substitute one product for the obtained f p~o ucdJOD process, smaller amounts of the other are

or given ecreases of th . e one-margm1:1l costs of each

....

l Economies ~u~ · · th · v : ing! 1Jnder compet1t10n e receipts from the sale

t a,re 1 15 b d · h d' produc t by a firm can e rawn m t e 1agram as a straight of the pro?uc s re Apa + Bpb, and prices are constant. The firm nne: receipts :ere the isocost line touches (is tangent to) the high-

! Perate w d h' . . I t . wil

0 . ceipts )ine, an t IS IS eqmva en to equatmg marginal

t Possible re

es . z cost and ~nee. corresponding possibility of calculating the average There 1s nfoseveral products. It is worth noticing that even though

t ~o~o . cos . 1

·t is done every day. The costs whiCh are common to illlPoss:b :.~~ucts-a machine or raw material used in producing severa p cutive who manages the production of both-are often b?t~, ~n ex~ng t he products in proportion to their separable vari­d1'~1de tarn or in proportion to their sales. Such an allocation must able cos s, b · f ll · h ·

b't ry for there is no one asis o a ocat.wn t at IS more

be ar 1 ra ' . · than others. Indeed any allocatiOn of common costs to duct is irrational 1f 1t affects the amount of the product persuas1ve . . .

one pro d h d · f · · ·

d d for the firm should pro uce t e pro uct 1 1ts priCe JS

pro uce , . at least equal to its minimum margmal cost.

EXTERNAL ECONOMIES

An external economy iB a source of reduction in cost which is beyond control of the firm. One finn in a competitive industry has no influence upon the prices of inputs, so if their prices fall as the industry expands, this is an external economy. Conversely, if input prices rise as the industry expands, the rise in cost of a finn repre­sents an external diseconomy. The external factors may work upon coefficients of production as well as on input prices: for example the growth of traffic congestion in a community may force a firm to use more trucks to deliver a given quantity of goods.

1 The argument of mathematical note 6 in Appendix B is applicable with

changes of language. 2 The slope of the price line is

o.B Po o.A = -;·

An isocost curve is given by t1A . MC,. + t1B · MCb ... 0, or t1B MC,. ~--MK·

' u

------

...

. : .. . .. '.

166 Additional Topics in Production and c 08t8

Cos t Curves for Industry-wi de Outpu t Ch a n ges

T he cost curves of a firm presented in Chapters 7 and 8 w constructed on the assumption that the firm has no influence u;;e th~ ?rices of the factors .o! production it uses.3 Under competitio~ this IS of c.ourse (by d~fi.mti?n) the pr~per assumption. But when all the firms m a competitive mdustry Simultaneously increase or d _ crease output, their aggregate effect is often to change the pric:s of inputs. Since we are normally interested much more in the be­havior of the industry than of the firm, it is desirable to have cost curves which take account of the impact of the industry's rate of output on input prices.

T he direct method of dealing with this dependence of the costs of one firm on the rate of output of the industry is to draw a differ­ent cost curve for the firm for each possible price of productive services. For example, when the price of the product is OA and the output of the firm (JT, the price of raw materials may be $1 a pound, and the firm's marginal cost curve M1 (Figure 9-2). When the price of the product is OB and the output of the firm OR, the price of the raw material may be $2 and the marginal cost curve of the firm M 2 • Let us join points like T, and T2 (and the innumer­able other points we could find for other prices of the raw material) and label the curve loJ. Then M, and M2 are the type of cost curves derived in preceding chapters, and M is the type of cost curve which we wish to employ in many areas. The distinction between the two types of marginal cost curves is clear:

M, (or M.) is the marginal cost curve when the prices of productive services are constant.

M is the marginal cost curve when all firms in the industry are varying their rate of operation so marginal cost equals price.

Let us call the latter type of curve marginal cost for industry-wide changes: We argued that marginal cost curves of type M 1 have a positive slope under competition in both short and long run. If

• Implicitly it was also assumed that vario.t.ions in the industr~'s out~ut did not affect the coefficients of production. Exactly th~ ~me tech~nque whi~h will be presented to include the effects of changes m .mput pn~s on t e cost curves will also take account of changes in production coefficients.

al Economies 167

o:cterrt . v marginal cost curves for mdustry-wide chan . . trUe, 1 h h . ges wlll this tS sitive slopes un ess, w en t e mdustry expan.t- th

have po · f 11 · 1· h w;, e alSO • ductivc serv1ces a , m w 1IC case U1ese curves of pro . l ( d' may

Prices ) 1 ave a negat1ve s ope we Iscuss this case later)

1ust 1 · · d tl t f · (not ll uld be kept m mm . la curves o type M ,, which might 1t sh0

1·ginal costs for smgle-firm changes, are the only t"pe

\led ma . 'J

be ca

p M

B

A

0 T R Q

Figure 9-2

. . 'd 11 along· be cannot con-that the entrepreneUl' can md1v1 ua Y move · . d trol the rate of output of the industry and thus the pr~ce~ of ;rotsu~~ tive services. The type M curves display the co~b~ . e fe~ ts

. · · t corobmatlons o mpu the entrepreneur's selecl1on of mmnnum-cos fi f fit-maxi-

. s on the rm o pro (portrayed by M 1) and the repercussiOn h' h the entre-mizing behavior of other firms in the industry, over w lC • hort-

. th type M curves aie s preneur has no control. I n tlus sense e f 'ble marginal hand methods of describing the whole tmay 0 ?b~ss~rices of pro­cost curves of the finn (corresponding to all possl e

168 Additional 'Topics in Production and Cost~

ductivc services), for they pick out the points (like T, and T2

)

which nre rele\'ant to industry-wide changes.

The Fu nctions o f the Firm

The number of processes to which a raw material is subj ected in its transformation into a finished consumer commodity is in­determinably large. We may, for example, distinguish the makin of flour and the baking of bread, or we may distingui~h the greasin: of pans, the kneading of dough, or the lighting of ov<:>ns. The ClUes­t ion arises: how are these functions divided up among firms? What determines whether retailing will be undertaken by manufacturers or ore mining by steel companies, or credit extension by doctors? '

A part of the answer lies in the technology employed. If letters a re prepared on n typewriter, it would be extremely inconvenient to subcontract out the typing of the vowels . If an ingot must be reheated to be rolled, it is obviously more economical for t he firm that cast the ingot to roll it while it is still hot.

But technology is usually not peremptory: there is often wide scope for variety in the ways productive processes a t·e performed. The publisher of a book need not (and seldom docs) print it; the printer seldom binds the book. Then a famous theorem of Adam Smith comes to our rescue: t he division of labor is limited by the extent of the market.• Smith pointed out that sma ll villages ~ould not support highly special ized occupations. but t hnt large cities could :

In t he lone houSf's and very small villages which arc seatt<>n>d about in so desert a country as the Highlands of Scotland, every farmer must be butcher, baker and br<>wer for J1is own family. In such situations we can scarce expect to find even a smith, a ca rpenter, or a mason, within less than twenty mileR of another of th<> same trade. The scattered fRmiliPs t hat live at eight or ten miles distance from the nearest of them, must learn to perform themo:elves a great number of little piec<>s of work, for which, in more populous countries, they would call in the nssistancc of those workmen . Country workmen are almost every where obliged to apply themselves to all the different branches of industry that have so much affinity to one another as to bC' employed about the snmr sort of materials. A country carpenter deals in every sort of work t.hat is made of wood:

• 1'he Wealth of Nations (New York: Modern Library cd., 1937), pp. 17-21. I earnestly recommend that all of this book except p. 720 he rend.

Ec,..,()1TI.ies 169 ternaL v•· f k h ·

s~ . b ·m every sort 0 wor t at IS made of iron. Th f ..mtt . . . b" e ormer ountrY • penter but a JOmer, a ca met maker and even

8 cpot onlY a calrl as 'L 'wheelwright, a plough wright ~ cart anda .. carver is we < ' • I n·aggon . wo<>d· as loyroents of t he latter a re sttll more various. It is impossj. 111

!Ike!· 'fbe ernlpd be such a trarle ns even that of a nailer in the rem t JlU shou f Sc I o e ble there arts of t he Highlands o ot and. Such a workman at the nd inland P sand nails a day, and three hundred working days in the ~te of a tb~ three hundred thousand nails in the year. But in such ·car, will rn. e"ould be impossible to dispose of one thousand that is ' tion tt '• , , ~ situa 's work in the year . f one daY . . • 0

• from speciahzat10n operate m the same manner in a 'fb gams . d

e industrial society. As an m ustry grows, more and more tnoder~ performed on a sufficient scale to permit firms to

. "ties are h . actl~1 • • their full time performances: t e makmg, and repair-specialize

10hinery the designing of p lants, the testing of products

. of 111!\C ' k . f I . ' 1ng, .t. g of labor, the pac ·agmg o proc ucts, the collection h recrm m k d · h h ld" t e t. n on supplies mar ets, an pr1ces, t e o mg of trade f ·nfonna IO ,

o 1 • h on technical problems, and so forth. f · s reseal c . tnr ' illustrate this development gcometncally. Suppose the We may 5 in three processes: processing raw materials (YI), as-

firm engage 11· h d (Y ) · r the product ( Y,), and se mg t e pro uct 3 • For Slm-se~~ mg ume that the cost of each function is independent of the Pbctty. ass

te of the ot her processes, and that the output of each proceEs ra rt"onal to t he ou tput of the final product s The average is propo I · d

f Ch function is shown separately, and the combme costs cost o ea . th average cost of output for t he firm (Figure 9-3). As we

are e l' . b" t t . . t d wn the fi!mre process 1 IS su ]ec o mcreasmg re urns. have ra o • . . ,. Y~ is sub]·ect to decreasing returns, and process Y, IS subject

process _ . Th. ·t r first to increasing a nd then to decreasmg returns. IS s1 .ua Ion

y be perfectly stable in spite of the fact that the firm IS per­~~~ming function Y 1 at less than the most efficient rate and Y: at

more than the most efficient rate.~ As the industry's output grows, the firms will seek to d~l~gate

decreasing and increasing cost functions to independent (atlXlhary\

• This second assumption allows us to measure all processes along one axis; it has no effect on the argument. . . . _ y and sell

• If the firm is a monopoly, it cannot specu1hze m process 'h fi ~ to other firms. I t would be cheaper to buy r , from se,·eral ot her trhms

I · 1 but if the cost .. of t e o er than undertake it subject to < ecreasm~ re urns, - h · lif,· processes would be higher if y, were not performed (contrary to t e SimP · -ing assumption in the text), y , cannot be delegated.

170 Additional Topics in Production and Costs

industries. For example, when one component is made on a sm lJ scale it may be unprofitable to employ specialized machines a ad labor; when the industry gi'Ows, the individual firms will ce n making this component on a small scale and a new firm will spec·a~e ize in its production on a large scale. Thus, when the firm bla -uys

p

AC

............. ...._ ___ _.....

A

0~------------------------------0

Figure 9-3

Y, at price OA, its average costs fall to the broken curves shown in Figure 9-3. Conversely, the firms will make only a part of the processes (Y:) subject to increasing cost, and buy the remainder from independent firms. . A related explanation of the division of functions among firms 1s that those activities will be undertaken by a firm which are cheaper to administer internally t han to purchase in the market. The transactions between firms are not free: there are costs at-

.. e production. Runs . . J 71 f rr1tf arching for prices, closmg contracts coli t'

to se"' . 1 .1. . ' ec mg Ched d 0 on 1 Of course tile coorc mat10n of activities 'th' tfl an 5 · • WI m

""'111ent7, 1 not free: men and machmes must be nssigned t k P"' tS a so . d as s the firJll . t ...-.anner and supervJse to ensure that the effi · t tfic1en ... . . Cien .0 liD e

1 .,,eeL When a firm ~upphes only a part of its need

I . fol o.. . F' 9 3) h . . s P)e.n iS . 55 (curve Y 2 m 1gure - t e nsmg costs of intern 1 e proce b . 1 . a {or so11l . ore in fact t he asJc exp anatJOn for partial recourse

d. atJOD .. k t t . coor 10 The cheaper mar e ransactJons become (due to im-to purchase. ledge of prices and greater security of contracts) the

d knOW • 1 . prove .11 be the comparative roe of market coordmation-firms

ter Wl • I' d grea more speCla 1ze . «ill becom~rnal economies depend less on the growth of the indus­

Some ex that of the entire industrial system. As the economy than on 1' trY 8

it becomes possible to estab J5h a much more complet~ trans-groW '. system, a complex of types of banks and other financial

ortatJOD · 1' d d d · P . . 5 catering to speCJa 1ze nee s, an e ucat10nal system · st1tutiOD . . 1 In train highly speCJahzed personne , and so on. These external that can h d · · th h · es are perhaps t e ems1ve reason at t e law of diminish-economi d f t' . . . . eturns does not hol or an en Ire economy ; It 1s h1ghly proba-~~= ;hat the American economy would be less productive if it were

smaller.

FINITE PRODUCTION RUNS

The traditional Jaws of production are oriented to the problem of infinitely continued production: the farm will grow wheat this year, next year, and so on indefinitely. Many production decisions, however, involve a. given volume or period of production. For ex­ample, the firm is to print 10,000 copies of a book, or produce 300 planes of a. certain type; or, in the event of a fixed period, it is to supply (at a fixed annual rate) some item for 2 or 5 years.

The traditional theory does not directly cope with production for a finite run. For t his theory is based upon continuous, unending Bows of productive services, and under this rondition it is a matter of minor detail whether the productive resources which yield the Bows are durable or perishable : in either case they will be replaced when necessary. If the farm is to produce for only lO years, how-

. '~e R. Coase, "The Nature of the Firm," Economica (1937); reprinted m Sttgler and Boulding (eds.), Readings in Price Theorv.

172 Additional 'Topics in Production and C 08f8

ever, and then be abandoned, it is clearly more efficient to use the natural fertility of the soil than to maintain it. If only 5 un'i of a product are to be made, less specialized or less durable 1 8

chinery will be used than if 500 units are to be made. llla-In the case of finite production runs, a theory of costs of g

interest has been devised by Armen Alchian.8 His analysis rre~t o~ the vari~tion of total output (volu~e = V), the rate of prod~c~ tlon per penod (q).' and n~mber of penods over. which the item will be produced .< m) ; m the stmple~t case these vanables are connected by the equation, V = mq. Alch1an has proposed a series of propos·­tions concerning the behavior of total cost of the volume to be pr 1• duced, of which the following are the most important: 0

1. The average an~ marginal co~t per unit of total volume decreases a.s the total volume mcreases, holdmg the rate of production per unit of tune constant.

Let the cost of a given total volume be the sum of discounted future expenditures. Then the proposition may be illustrated by the printing of a given book: once the plates have been made, addi­tional copies (a given number per period) can be struck off at a relatively constant additional cost. The total cost (ignoring inter­est) wi11 be approximately

Composition Costs+ Number of Copies X Printing Costs per Copy

so the average cost will be

Composition Costs . . N b f C . + Prmtmg Costs per Copy, urn er o optes

which decreases as the number of copies printed increases. There are usually some producers' goods which partake of the nature of stamping dies. In addition there are economies from 11learning": as the length of the production run is extended (as it must be if V increases but q is held constant) -a variety of economies are un­covered by experience.

2. The marginal cost of output rises with the rate of output if volume is held constant.

• "Costs and Outputs" in The Allocation of Economic Resources (Palo Alt.o, Calif.: Stanford University Press, 1959); see also J. Hirshleifer, "The Firm's Cost Function : A Success£ ul Reconstruction?" Journal of Busineas (July 1962).

· Runs . . product·wn . 173

FtTltte 1 nJe is held constant, an mcrease in the rate f 1 vo u . . f h o output l f totn . . lies a shortenmg o t c number of production .

· d unP · · h Pettods I' pertO ·t·on asser ts that 1t 1s c eaper to produce a "'v '

pe ·opoSI 1 h . .,. en num-tbe pi . . (say) 4 years t an m 3 years. This pro ..

so 01ts 10 • f d. . . 1 . POSition r of u assertion o 1m1ms ung returns. be t'a.llY an . .11 . essen 1 ·nal cost curves are 1 ustratecl in Figure 9.

4 Th 1s rnargl . .

1 . . · e

'fhese t f volume IS of spema mterest-1t is the theoret· 1 . 1 cos o 1ca margtna.

If)

~ --' --' 0 0

0 Vor q

Figure 9-4

explanation for the almost universally observed phenomenon of quantity discounts. Whether we look at aggregate vol~me-the. cost of a book of which 1,000 or 100,000 copies are prmted-or at the size of an individual transaction-it costs less per copy to sell five copies than one-we find strong confirmation of the effects

of volume on cost. has spe-The relationship of marginal costs to aggregate ~~lume ,

. . f mod1tles These ne" cia\ relevance to the mtroduchon o new com . · d th . . . . . dl tlrough tJme than o , e commodttles fall m pnce more rap1 Y l

174 Additional Topics in Production and Co8f8

prices o f established goods, and the more rapid fall is due to the large increase in volume. Once the production of the commo<li ty has achieved a subst an tial scale, these economies are exhausted and the t raditional cost curves of infinite production runs become

appropriate.

RECOMMENDED READINGS

Alchinn, A., "Costs and Outputs," in The Allocation of Economic Resourcea. Palo Alto, Calif.: Stanford University Press, 1959, also A. Alchian and W. Allen, University Economics, Belmont, Cal.: Wadsworth Publishing Co .. 1964, Ch. 21.

Coase, R., "The Nature of the Firm," Economica (1937) ; repnnted in Stigler and Boulding {ed~.). Readings in Price Theory.

Stigler, G. J ., "The Division of Labor is Limited by the Extent of the Market," Journal of Political Economy. 59 (J une 1951) , 185-93.

Young, A., "Increasing Returns and Economic Progress," Economic Journal, 38 (1928) , 527-42.

PROBLEMS

1. An industry produces A and B in fixed proportions (lA with 3B). Average cost is constant at $5 for l A + 3B. The demand functions are:

8 q.

p. = 4 - 10'

Qb p. = 60- 3-

Determine outputs and prices in long run equilibrium (assuming competi­tion ). Compare the effects of a tax of $3 on A and S1 on B.

2. Let tot al costs of p roducing A and B be

A A 2 B B2 AB c = 10 + 2 + 10 + 5 + 25 + l(f"

What is the marginal cost of 10 units of B when A = 20?

3. Construct the marginal cost curve for industry-wide changes from the production function in T able 7- 1, t he costs in Table 7-4, and the information that the p rice of the variable service is related to the purchases of the industry by the equation, p. = 83 + Q./500 and t here are 100 firms. The marginal costs in Table 7-4 a re then valid when the price is 55, the purchases of Q. are 1000, and the output of the industry is 8600.

175

problems !\. . C. Jlarberger .) Product X is prod~ced by two factors (Pue _to ·A nd B. These factors must be used m fixed proportions

.t. rodncuon, a cipe: lA + 18 produces lX. The industry is competi~ f P the re · · d h. 0 f(iing to h

110 use outstde the m ustry, w tie factor B is so widely

~cC0 A ns 1 · f · f · · . "t"actor . d\tst rv thu t t tc p n cc o a umt. o B IS not mfiuenced tt'·e. s: ·d the tn . J • • , _ d 0utst c . ttr)ut in the X mdustry. The pn ce of B is Sl . There

u::C . • S JD 0\ r · h . · · b" "3nnt10~t of factor A, all of whtc are_ a\:\llablc at any pnce above · 1~ nut 5 •hich arf' 3 vailable at a pnce below $0.50. The demand

!lre ne of ' \ ~-oo ~.50. no d t X is XP' = o,o . .. f r pro uc

rve 0 · · d · f X ? cu .11

b the equilibnum pncc an quanhty o . What WI e .

(ll) .11

be the equilibrium pnce of factor A? of facto r B? What w1 · .

(b) 0

excise ta.x of 20 per cent of the pnce to the consumer (c~ SuP:\;hat will be the price of X paid by the consumer? What is t0lp0 · ·ce receh·ed by the producer? How much X will be pro-·u b the pn . WI e h t . ·

111 be t he price of factor A ? o£ factor B? ednv a w . .

due · t hat a monopolist takes over mdustry X, and that he is (d) Supplos~ no entry will take plncc and no government will interfere as:sure~ t

111 ra tions so long as he charges a single price for all the units

wtth }us ~pefact deJ1jvcrs. Whnt will be the price set by this monopolist?

of X he ·n10 be t he outpu t of commodity X? What will be the price of

Wbat wt -factor A? of factor B?

chapter ten

The General Theory of Competitive Priees

Everyone knows that prices are set by supply and demand much smaller group, but one including careful readers of th · A

d' k h e pre-ce m.g pages, nows w at factors govern supply and dem d 0 task IS to gather these pieces of analysis and fit them into an . ur

· t f h · a general p1c ure o t e workings of competitive markets.

THE GENERAL PRINCIPLE

A competitive market must fulfill certain conditions if it is to be in equilibrium:

1. Each firm must be operating at the output which it deems most appropriate to the cond]tions of cost and demand.

2. The total quantity all firms wish to sell at the market price must equal the total quantity an buyers wish to purchase.

When these conditions are fulfilled, the price will be an equilibrium price--that is, it will have no tendency to change until supply or demand conditions change.

The first condition-an appropriate output of each firm- is in turn fulfilled when two conditions are met:

1. Each firm is in t he industry which yields it largest profits. 2 . Each firm is operating at the output where marginal cost

equals price, which is the output which maximizes profits in this industry.

Quite clearly we are judging the "appropriateness" of an entrepre­neur's decisions by whether they maximize his profits.

176

General P·rirz ciple 177 ']'ht t to which the entrepreneurial behavior

8~n . . fi . can be 'fbe b efforts to maximize pro ts 1s a celebrated d b .

. ..olained y onolllists. 1 We shall nevertheless use this assue att~ng ~d~~ . ~~ gro\10 elMnsive defense, and on two grounds. First, and most im-~tbout . ields 8 vast number of testable conclusions and b

t It y ' 'th b . 1 y p0rtall ' e these conclusiOnS agree WI o servatton. Second, 00 other $1ld larg d goals have yet been developed and given empiri 1 «ell-define ca.

suPPo~ conditions of competitive equilibrium are readily trans-'l'h~ diagram (Figure 10-1). For the firm the demand curve

lated Into a

p

0 r t ( 0)

p

MC

q 0

Figure 10-1

T (b)

s

0

0

is a horizontal line, by our definition of competition that the firm be sufficiently small relative to the industry so variations in its output have a negligible influence on price. We may pause to notice that if our demand curve refers to this month (we shall soon look closely at the time dimensions), then the demand curve of the firm will be independent of next month's demnnd. Even if an unusually

'Even business men do not like this formulation. In one field study, when they were asked whether they maximized profits, they indignantly reject~ the suggestion and pointed out that they were s.incerely religious, public­spirited, and so on-as if these trails were inconsistent wi th profit-maximizing. But when the question was re formulnted as: would a higher or lower price of the product yield larger profits'l, the answer was, usually, no.

.. ·,, 1·. ; .

'.

_ ..... ,.

"~.·- .. ~ ·' . -

.. :.....:...;.. ,

• - . 1 1

. . . i

·-r 178 The General Theory of Compet "t. . h" . . . . t we Pnces

1gh pnce th1s month \nil lend to a reduction in i d next. month. the indh·idual firm cannot influence nt ustry demand ( I II' nex month's · say, JY se mg more cheaply now). Hence th d Pnce a t. · fi . . e emand curv

compe 1tn·c rm 1s mdepcndent of future c d'f e of shall see that ~his is not true under monopoly. on I Ions. Later we . Tbe firm wtll operate at the output where its mar ina mt-ersects the demand curve. If we are exam· . g( 1 cost cur\"e h IJ) f . mmg as we usu II

8 a orces that 1mpinge on all firms in the indust th ~ y cost curve should be that which incorporates th ?·t.s e margmal economies--what we call the margl.n"l o te fe ec_ of external 1 " c s or mdustry ·

c 1anges (see pp. 166f.) 2 The firm operates at output Ot . f ~WJ~e OA , and at Or if price is 08. The marginal cost curve t~ Prtce IS out the firm's supply curve. us traces

If we sum horizontally the marginal cost curves of th fi we trace out the supply schedule of the industry (curv S) ~f rms, are 100 identical firms, then OT = 100 Ot and similaerl f th~re outputs. The industry demand curve D i~ of course a coynvor t~t er

t' 1 · . '. ' en 1onal neg~ _•v: -s op1~g curve. The mtersect10n of S and D establishe th eqUJhbnum pnce. s e

This becomi~~ly Ei~ple apparatus contains the essence of the the­ory of compet1t1ve pnces. We can, and shall clutter up the exp · t" . kj ' OSJ-IOn m ta ng account of time periods, and of the entry and exit

of firms from an industry, but the essence of the analysis will not change.

T wo Normative P roperties

Competitive p1·ices are widely admired: by customers, for they connote the absence of monopoly power; by lawyers. since the anti­trust laws are designed to achievp competition; and by economists. The economic advantages of a competitive price are two.

First, the division of output among firms is efficient in the sense that with no other division would the same output be so cheap to produce. Consider two firms which were not in competitive equi­librium (Figure 10-2) . Firm 1 is operating at output Ob, firm 2

'If a force were to impinge on only this one firm (say a tax on only this firm, or only this firm introducing a. technologi<"al improvement) w~ should of course use the marginal cost curve for single firm changes in output.

i ~-~

5

X' a

, Principle oe11era• 179

fhe . t od. Clea rly competitive equilibrium is lacltin ~t ontPll . not selling nt the same pric~:: . If we reduced ~because .tile {irJlJS able ab its costs would fall by abmn If \\'e m· t e outpul

1 v . . . creased th of firnl of fi.r!11 2 by cd ( = ab J' It~ costs would rise by cdsr . Clear\e· 0utrnt f firm t would fall by more than tho~e of fir

2 }

sts o . ~ m rose the co sts of the two firms would dcchne for the gh·e t , ' sO w~l~ n ~~

f

0 0 b d c 0 Figure 10-2

output. In competitive equilibrium marginal costs of all firms are equal, and thus no reduction in total costs would be possible by reshuffiing output among firms .

Second, the output of the industry is "correct." T he price is such that marginal cost equals price. The price is, for each consumer, the measure of the importance of an incremento[ the commodity-a demand price of $2 is implicitly a statement by each consumer that

- :

d " 6 -~ ,,_ ~ ----

. ~":· . --i

~~ ~;. ·.J .... . ~ .. _. .... _

-·-~

.·-1 ·-··· <;l ·· · ..J

·:J

180 The General Theory of Competitiv p . e rtce8

a marginal unit of this commodity yields $2 of utility • Th · e tnar · nal cost is the value ( = alternative cost) of the resources ne gJ.

to produce a marginal unit. If price exceeded marginal ~e~ary it will be shown to do under monopoly), then consumers woul~ (~s by expanding output: a product worth about $2 is obtain dgatn sa~rificing the sma_ller alternative produc~ ( = m~rginal cost)~ ri~ gam from expandmg output would perstst until price had r .

11 to margtna cos . . I t a en

These felicitous properties of competition are the basis for usi competition as an ideal. But it is a limited ideal, quite aside fr ng a qualification for decreasing cost industries to be discussed shor~~ The ideal takes the d istribution of income for granted, and if thi · distribution is unsatisfactory to a person, he may accept as idea~ only that competitive equilibrium which rul es with a satisfactory distribution of income. The ideal also takes consumers' desires for granted, and if a person disapproves of consumers' choices (and of their right to make their own choices), the competitive solution is again objectionable.

In fact almost everyone will make both of these criticisms of competition on occasion. No one believes that a destitute family should starve (income distribution) or that a consumer should be a llowed t o feed poison to his family (consumer sovereignty). Yet in a society where there is tolerable acquiescence in the existing income distribution, and consumers are believed to have a right to much freedom of choice, these normative properties are of great importance .

THE LONG AND THE SHORT R UN

Marginal cost is defined as the i~cre~e~t in ~tal cost divided by t he increment in output with wh1ch 1t. Is a~soc1ated. Hence we shall have as many marginal costs for a gtven mcrement of output

'Recall that at equilibrium, P. M U. Pb,. MUb'

and if we call all commodities other than A money income (B), !10 Pb - 1 (the price of a dollar is 1 dollar),

MU. p - . • - MU1aeomo d ice falls

• We say "about $2" because as output expand~, ~he dcm~ otit~ut lea& and with continuous demand curves even a one-urut mcrease 1

to a small fall in price-perhaps from $2.00 to $1.99999.

and the Short Run 181

']'h8 f;orr11 1 vant ways of producing this increment. If the fi reree . . 1

rm 5 there ~ Isnt overtime 1ts margma costs will be governed by 11 eratcs ~ts P1 wages, materials, power, and so forth . If the fi :e 6ddi~1008Jant, marginal costs v.:m also inc~u~e interest on : P&Jlds tts . P stment and appropnate dcprectatJon charges.5 If a

eJC "I mve . 1 t . dditiOD" . nstructed, margma cos may mclude the salary of s nt ts co

neW pia rintendent, etc. ne~ supe ·u normally handle short run fluctuations in output 11

f be ~rm i:1 rate of operation of the existing plant (and by bold-

by varytng . ) Investments in durable assets will be made on the . tortes · . jng 1Dven persistent changes m output. We call the short run

· f more · fi d t k · basts o. "thin wh1ch the rm oes no rna e lrnportant changes the penod w~ rable factors ("plant"), and the long run the period in i~ mor~ch uthe size (and e~istence)_ of plants is fr~ely ~ariable. within wh horl- run is of no mterest tf a firm can qUickly mcrease ClearlY the

8

11 inputs and it is basically an empirical judgment d crease a ' . .

&nd e 1 there will be Important resources whtch cannot be · genera that

10 built in (say) a year. The long run may also be longer

rn out or . . wo t. s than for expansions, or Vlce-versa. for contrac tn n marginal cost curve of a firm will rise more rapidly

The shorl -rgu run marginal cost, because the law of diminishing h the on - .

t an .11 b ld more strongly, the more mputs are held constant. returns wt (~or single firm changes) must rise with output in the Both _curves. if competition is to exist-if marginal cost fell with ffecttve regiOn . d t• . )

e b t lling price did not (and 1t does not un er compe 1t10n , output u slde increase indefinitely with increases in output and the Profits wou · n · 1

ld acquire a significant control over pnce. out marg1na firm wou for industry-wide changes, which incorporate effects of cost curves . . . external economies, may either nse or fall Wlth output.

The Fir m and the Industry

The industry's long-run supply curve, like its s~ort-ru_n curve, is the sum of the marginal cost cu rves of the firms m the mdustry · Ita slope will therefore be governed by two factors:

•u the additional plant were to be used for only one_y~ar (e,•en_th~:b i! might last 10 years with care), the appropriate ~eprect~h~n r~.e ~ fractron cent. If the additional output is to be produced mde~lllle r· 0 r . 10/ 0 + 0/10 by the now unpopular straight-line depre<:tatJOn ~n~u a~ ff the ... + 10) = 10/55 by the sum-of-digit formula) should c arg o first year.

L •

t I I

182 The General Theory of Competitive Prices

1. The slope of the long-run marginal cost curve of each finn (for industry-wide changes) .

2. The price at which firms enter or leave the industry.

\\'e have nothing to add on the first score: the firm will operat ::iOtnewhere on its long-run marginal cost curve.8 e

The price above which firms will enter the indust-ry, or below which they will leave, can be different for every fit·m (existing or potential) in the economy. It will take a higher price of aluminum pots and pans to attract a firm from cotton textiles than a firm from aluminum toys because the former fi rm's familiarity with the basic technology is less. It may take a lower price of trucks to attract a firm from agricultural implements than one from the hand tool industries because the large capital requirements are easier for the former firm to meet. It will take a higher price to attract a bachelor than a married couple into the corner grocery industry, because the latter has a captive labor supply.

The number and versatility of existing firms is so lat·ge, relative to the number in any one industry, that one would generally expect the number of entrants to increase rapidly as the price of the indus­try's product rose. Only if the industry employed specialized re­sources (say, a special kind of land) or if (what is ruled out under competition) there are barriers to entry would one generally expect numbers of entrants to be unresponsive to price in the long run.

The empirical evidence suggests that in fact a large part of the increases in output of a growing industry come from the existing firms.r Our geometry tells us that the existing firms wiJI produce this additional output only if the long-run marginal costs of existing firms do not rise with output. This line of analysis therefore sug­gests that the long-run marginal costs in most industries (for sin­gle-firm changes) are relatively flat.

• One minor point ma.y be noted. If the marginal P

cost curve for industry-wide changes falls with output, the firm will still operate where this marginal cost equals price. T he indh,idual firm never has a choice. of where to operate on the curve for industry-w1de P

changes but the curve for single firm output changes leads t~ this output. The accompanying graph illus- 0.~.--..:===="'-';; trates the point. . . · c · l d

1 For manufacturing industries some evidence IS giVen m my. ap1ta an Rates of Return in Manufacturing Jnd1tstries (New York: NatiOnal Bureau of Economic Research, Hl63), pp. 31-34.

d the Short Run ~e [;oflg a·11

tf Character of . k,si111er .

183

Qtllc I dus trteS 1be ..etiti"e u ffort is devoted to assisting or burdening com-rnttlr~ nt of e . . ff '-"' Jarge sJll00. The assistance may be a protective tan , a sub-

f. 1·0 dustnes· ninental service. The burden may be a tax 'live gover . . ' pet! r ::oJlle free compulsory industnal safety deVIce. Usually

,idY; ~IJluJll wage, or ha firms in the industry will reap the gain or 11 1~11n~lieved that ttl· e measure at least in part. This belief is usu-jt JS den of le . ' !Jeitf tbe bUf but only temporarJly.

11 correct, il y

SRMC (Af ter Tax)

fsRMC (Before Tax)

I LRMC

I /(Af ter Tax)

B /, LRMC '-r, (Before r

w J r-:.:~=---n.A~- Tax) pl-----7""~~ ~p 0.

0 (ol

0

w (..)

0:: 0...

0

Figure 10-3

( b)

s (After

Tax)

0

Consider a firm with the long- and short-run costs displayed in panel A of Figure 10-3, and selling its product at price OP. If a tax is now imposed on each firm, its costs may rise as indicated. The price will rise by a smaller amount than the tax if the demand is not completely inelastic (see panel B). Marginal losses of AB per unit of output will be incurred by t he firms. With the passage of time resources will leave the indust1·y because t.hey can earn an amount elsewhere equal to their long-run mat·ginal cost to this in­dustry. Eventually the short-run marginal cost curves (and with them, their sum, the industry's short -run supply curve) will shi ft to the left enough to raise price to long-run marginal cost. The

184 The General 'Theo,.y of Competitive p . ?"!ce8 contraction of output of a plant will be to some output large th

TC, because price will rise above 07' as the number of fir~ an 1. Tl fi ' 11 · b · · 8 de­c mes. 1e rms Wl agam e earnmg a compebtive rate of r t .

The analysis of a subsidy is completely symmetrical. e Utn. Only short-run gains or losses, therefore, can be given to the fi

· 't· · d t Tl · 1'llls m a competl 1ve m us ry. 1ese gams may of course be larg . . durable assets without alternative uses have on average a rema·e·. tf · fi · 1n1ng hfe of 6 years, a rm may gam 3 or 4 years' return if the Pol" .

prevents the contraction of the industry,s or if it takes 3 Year~~~ build a new plant, extra gains may persist this long. 8 0

Even these temporary gains or losses will not be incurred ho\ _ ever, if the developments are fully anticipated. If the tax is ~nti~~­pated, investment will have fallen appropriately by the time it ~ imposed. Similarly, if a tariff is expected, the industry's investmen~ will have risen to where only a competitive rate of return is ob­tained when the tariff is imposed.

T here is one group who may reap permanent gains or losses from policies designed to help or burden an industry: the owners of spe­cialized resources. They will not. have alternative uses for their re­sources, so their returns will vary directly with industry output. T hus the permanent beneficiaries of a subsidy on zinc will be the owners of zinc mines; the permanent losers from rent ceilings will be landowners.

Is t h e O utput of Decreasing Cost I n d u stries Op timal ?

We have said that a competitive industry has an optimal out­put--when marginal cost equals price, resources are satisfying mar­ginal demands in this industry as important as these same resources could satisfy elsewhere. D ecreasing cost industries, however, pose a special problem.

Consider the long run cost curves for single-firm changes, Liv!C1 and LAC 1 in Figure 10-4. Let us begin with a price of SIO, and an output of the firm of 1,000 units per week. Average costs are 89.60, and the "profit" of 1,000 X $0.40 = $400 is the payment to the en-

• The duration of the short-run gains will depend ~pon how much the _indus­try would have to contract, as well as how fast 1t would contract, m the absence of the favoring legislation.

nd the Short Run 18

!;. Lang a u

The f . his scarce services.9 Total costs of produ t' 1eur OI c ton are treprel 9.60 = $9,~00. ~ . .

1 000 :>< d 1and mcrcase:s and pnce nses, the firm's output .11 I oW CD . s· tb" . d \Vl If n ) 1 400 umts. mce IS 1s a ecreasing cost ind t , (saY ' d tl us ry,

rise ~o fall in price an 1e cost curves for single firm chan some inputs ges

p

10.2 10.0 9.8 9.6 9.4 9.2 9.0 8.8

L

SMC (Social Marginal Cost l

~---L------~~---0 1400

F igure 10-4

shift downward to LACz and LMC2. The price in the new equilib-. . S-9 80 and the average costs $9.40. (The long-num we assume, 1s " · . l t d as

run ~arginal cost for industry-wide changes lS a so prese~teh de h · arginal costs Wl · -the locus of intersections of t e vanous m

. . . t scarce, there would be • If this type of ent.repreneur~al service were n~ t 1 000 that marginal . · h · d tr" each operatmg a • ' sufficiently many firms m t e m us J ,

and average cost would be equal.

-~ c ,

186 The General Theory of Competiti n . ve •rtc e8 mand.) Total costs are now 1,400 X 9.40 = $13160 H

' . ence th marginAl cost of output (for· industry-wide changes) is e

$13,160 - $9,600 1400- 1000 S8.90.

From the social viewpoint, it would be desirable for the · d to expand because price ($9.80) is in excess of marginal :n ~stry one firm will find this expansi9n feasible because when it os · ~0

1 . . 1 expands output a one, 1t rece1ves on y 1/n of the reduction in input . that results from the rise in output-the remainder goes to the P::~es (n- 1) firms. er

Decreasing cost industries therefore operate at too small an out­put. The extent of the departure from a socially optimal

0 t

. . . U PUt wtll depend upon the rate of fall of mput pnces; or more generall on the extent of the external economies. Y,

It might be, and in fact has been, argued that by a symmetrical argument increasing cost industries will be too large. It is true that when the firm buys more of an input subject to rising supply price it will ignore the resulting rise in its price because this rise wili be borne by the other firms. The arithmetic is indeed strictlv parallel : let the supply of the input be •

Q UANTITY PRICE TOTAL OOST UAROINAL COIIT

100 ,000 S10 SI ,OOO,OOO $155,000

110 ,000 10 .50 1 , 155,000 10,000 - $15 .5()

The firm will consider $10.50 to be the marginal cost of the input, since its purchases do not affect its price.

But the conclusion is false: increasing cost industries are not too large. The alternative product of t he input must be $10.50, when 110,000 units are purchased by this industry, or the input could not be obtained at this price. The extra $5 is a rent accruing to the suppliers of the input who had previously received only $10.11)

No product is foregone as a result of t his price inc1·ease-it is a transfer payment, ultimately from consumers of the .product . to owners of the input. The difference between the decreasmg and m­creasing cost industries is this: the price increases of inputs do not

"Their receipts r ise by 100,000 X $0.50 = $50,000 and $50,000/10,000 - S5.

d the Short Run /JoM an 187

The t foregone product\ whereas the price decrea~e" f . sen · 1 · d · ~ ., o mpuL repre anomies m t 1eu· pro uct1on on a larger :seal sent ec e. repre

·se in Analysis £~ere• . . .

,\11 ratus of competltlYe pTJcc theory i the staff £ l' f The appa . o 1 e for

i-t. he uses 1t much more often than any oth econorn :. . . . h b . er part the ledge and 1t 1s t e as1s upon which mo~t of hi~ f .

· knOW ' ;j anc1er of hiS d is erected. A thorough command of the apparatus com ~ wle ge . 1 I. e::l ~no using 1t frequent y, uut we must be content here ,.,·th I, from . . .. 1 on ) . 1 analys1s of a gcner al problem, the effects of protection artla . d · 1 · a P . lture in an m ustna soc1ety. of agr1cu

0 (a)

0 0

Figure 10- 5

Agricultural industries, both in. the United State:: and el::ewhere. often given assistance by pnce support program!;. A govern­

:ntal agency (the Commodity Credit Corporation is our leading · strument) will lend at designated prices against the product on m . h .. what are called nonrecourse loans (loans wluc permit no M5t'58-

roent on the farmer if the agency fails to recon•r the full nmo~t of the loan). The program is presumably initiated wh~n the .m­dustry is earning less th:m the rate of return in other mdustr~es.

Hence the initial position for a firm and the industry are s~meth~ng like the situation portrayed in Figure 10-5, A and B. wJ~h pn~e p0• The support price is set at p1 , and it obviously serYes to mcren:e output and diminish purchases, and to increase consumer expendr-

·~.-~.~ v-188 The General Theory of Competitive p

11ce8 tures if demand is inelasti~. In fact the increase in producers' ccipts will be the sum of t(!.

Increase in consumer expenditures, Q1p1 - Q1p0 Governmental loans, (Q2 - Qt)Pt· '

In each period of time(say, ~rop year) the governmental sto ~ will rise by (Q~ - Q~), assummg there is no entry of new fi c

· f ·t· fi 11 dth rms or expanston o ens mg rms, an at costs of productio d not change for a farm. If technological progress lowers costs

0 0

shifts the industry supply curve to 8', of course the governme:~

Quota

MC AC

P, I--~.__-~~..-£..­

Po 1------,.,.,c...-+-+---

0 q

s"

~t------~-+-~ Po 1-------~~

~t-----::::;;~=t--+-~ s

(b)

Figure 10-6

0

stocks increase more rapidly. Eventually there will be complaints at the growth of the governmental stocks (whether for reasons of expense or the outrage of some primitive ethical code) , and produc­tion controls will be imposed. The controls may be direct output quotas for individual farms, or more commonly- because of the short-run fluctuation of yields due to weather changes-quotas on the acreage devoted to the product.'~ The situation is now illus­trated by Figure 10-6, where Qs is the sum of the quotas of all

" The latt.er assumption is especially unrealistic, but. is made to simplify the discussion.

"Since one input is being fixed, but others are free, the farmer will substi­tut~ other inputs (fertilizer, better seed), so output will not fall in proport.ion to t he reduction in acreage.

and the Short Run 1'he LottO . .

rT"l e annual mcrcase m governmental stocks 00, .. dec 189

J. 1 . . • ' n reases rar~~~ _ Q 1 ). There 1s ~ savmg to consumers, but governmental to d'tures fall by (Q:~ Q:~).Pl · eJ{pen

1 accept without questiOn the desirability of giving the P _

Let us . . h h' d . . ro th increase m mcome ere ac teve . Tlus mcome incre ~<

d ers e . ( ) . a~e uc typical farmer lS Q:s P1 -Po 7nml1.8 the additional costs of

(or 8. the larger quantity (q3- Q1), which is the area bounded

groWlng and .'4fC in Figure 10-6A. The objections to giving this in-by Po• Qs, . h'

d . come m t 1s manner are

crease m I. Producers are using an unnecessarily large amount of resources

duce the output: to pr~ Marginal costs will inevitably vary among firms-violating

(a tiroum property discussed earlier. th~~f. If an inp~t i~ controlled, the ~ubstitution. ~f other inputs

.11 lead to the v10lat1on of another optimum condttton: that inputs Wl ed in such proportions that their marginal products are propor­~e us! to their social costs. Here too much fertilizer, and not enough t1ons land, will be used. . .

2. A portion of the output tS unnecessary, and ts measured by vernroental purchases. Storage costs should be added.

go 3. The price is above marginal cost (even accepting the combina­tion of inputs used) so consumers would gain by an expansion of

h lS pure ases.

The first two components represent resources wa.sted ; the third represents the consumer loss due to an inappropriate composition of output.

Tbe same increase in income could be given to the farmers by other devices:

1. Output quotas could be made sufficiently small to raise prices and reduce costs the desired amounts. Then component 2 of waste would be eliminated; the other components of wast.e would rise.

"They would gain roughly t he n.mount indi<·ated by P

the shaded nrea in the accompn.nying figure. Thr increase in output (Q, - Q,) would require resources which would produce roughly p.(Q,- Q,) worth of " product e lsewherE', which must bt• (oregon<'. ;./otice ~r-~~ that this is n measure of th<' utility gain to consumrrs: the money gain (i f de mand is inelastic) represents o only a lransfer from farmers. c, "•

,. 190 The General Theory of Competitive p I

rtce8 Query: would the price still be Pa 714

2. The government guarantees each producer a price p1

but th market could be allowed to become free, so the price would f e to p 2 (Figure 10-6B). This scheme would eliminate the first t a.ll components of waste, but retain the third (with price below ~0

mar­ginal cost).

Query: how much should t he guaranteed price be to keep fal'lllers• incomes constant?u

3. Prices and output could be freed, and a direct subsidy p .d Then all components of waste would be eliminated. at ·

Query: is the su bsidy now larger or smaller than in case 2

?aa

We should notice that this third policy, and in fact a ll policie raise other economic (to say nothing of political) questions. Eac~ policy implies a different income distribution, immediately for fa rmers and consumers, ultimately for everyone through the itn­pllcit taxation necessary to finance the policies. The quota systems will benefit landowners who possess quotas, but not tenant farmers. The <iircct su bsidy system (policy 3) and the quota systems must face explicitly the problem of dividing the benefits among farmers· the subsidized price system (policy 2) need not. All systems except the subsidy system will yield target· benefits to farmers as tech­nology improves (and cost curves fall), which may be a factor in the opposition of farm groups to the direct subsidy plan.

RECOMMENDED READINGS

Knight, F. H ., "Cost of Production and Price Over Long and Short Periods," Journal of Political Economy, 29 (1921), 304-35; reprinted in The Ethics of Com7Jetition (New York: Harper & Brothers, 1935).

"To keep the questions tolerably manngcable, n.ssume that the cost cun·es stay put, that is, there is no substitution of other inputs for land. Assume a l80 that we are interested in "profits"; it some of the farmer's wage and interest income must be separated out of the cost curves, the geometry be­comes complex. Then a farmer's receipts fall by p,(q,- q,) at price p, and costs fall only by the area bounded by p., q,, und /HC in Figure 10-6. Hence price must rise above p, to maintain his profi ts. I

"The rise in income from expanding output to q, would exceed t.hc rJ&' in costs (since M C is less than p,), so the IJI'ice would fall below 1>• if profi ts were maintained. .

.. The subsidy is smaller. The costs of the extra produce (q,- q, ) whwh could be sold only at a price less than marginal cost, need not be incurred.

. '7 I • a

problem.s . . . . 191 A. Pnncrples of Economrcs. London: Macmillan

1922 B

;\l:tr.::h311, ., ' I k. V,

' Cbs· l--5.p H. The Commonsense of Political Economy. Lond . G . k~t('€(1. . ' \ ' I II Bk on. eorge Wr<' ·" & Sons. 1934, o. , .. :J. Rutledge

PROBLEMS

ral problem in pricing. (This is a summary of a problem 1 A. gene . . . . . con-. ·ed b the late HE'nr) Srmons, m Econom1cs 201: Matenal., and p b-

stnrct dass Discussion. University of Chicago, n.d.) ro tems f~rd str:r consisting of 1,000 firms producl's a standardizoo product

i\n 1n u • I d · · 6 owns and operates one Pant, an no other size of plant can Each .1;m'Thc variable costs of l.'nch firm nrc idcnticnl and are given in be bul. : ·ug table: the fixed costs of each firm are $100. the adJOIIlJ

TOTAL VARIABLE TOTAL VARIABLE

oUTPUT COST OUTPUT COST

1 SlO 13 $101 2 19 14 113 3 27 15 126

4 34 16 140 5 40 17 155 6 45 18 171

7 50 19 188 8 56 20 206 9 63 21 225

10 7 1 22 245 11 80 23 266 12 90 24 288

The industry demand curve is pq "" S255,000. Calculate the marginal and average costs of a firm, and the demand schedule of the industry for prices from SlO to $20. (See p. 238 for the cost equation.)

PAUT I

(a) Draw t he supply curve-that is, the sum of the marginal . cost curves-and demand curve of the industry on the same graph (Figure I) . Read off the equilibrium price and quantity. Prove that the answer is correct by comparing quantities supplied nnd demanded at (1) a price Sl higher, (2) a price $1 lower. (b) Draw the cost and demand curves of the individual firm on the same graph (Figure 2). Accompany these graphs with detailed textual explanation of their construction.

•4111

192

PART II

The GeneraL Theo1·y of Competitive p . 7'ice4

Congf('!<S now unexpectrdly imposes a tax of S4 per nnit on the facturr of thi commodity. Tlw tax become ' effectiYe immediatel~anu. remain-. in effect indefinitely. A.ssume (1) no changes in the eco~oatl_d system other than tho!'<' attributable to the tax; and (2) none of ~tc chnng<·s due to the tax has :my effect on the prices of productive Bervi he used by this industry. ces

(a) Draw the new supply curve and the demand curve of the ind st . (Figun' 3). Read off the new equilibrium price. u '1

(b) Draw the new cost curves and demand curve of the individual fi (Figure 4). Explain the details of the construction of these graphs. nn (c) Why can thf.' price not remain as low as $15?

(d) Why can the price not rise to and remain at $19?

(e) Precisely what would happen if the price remained for a time at S16?

(f) At precisely what level would the price become temporarily stahl ?

What dO<"s it mean to say this is an equilibrium level? e ·

(g) Suppose t he short-run equilibrium price to be $17. How would you answer the query: "I don't st>e why every firm should produce 15 units per day when the price is $17. I t would make just as much if it produced only 14, for the 15 unit adds just as much to expenses as it adds to revenues." Pre<:isely what would happen if some firms produced 14 units per day and others 15 units ?

(h ) Would short-run equilibrium be reached at a higher or lower price (and with larger or smaller output) if the elasticity of demand were lower (lrss than unity)? If it were higher (greater than unity)?

(i) What would happen if demand had an elasticity of zero ? An elasticity of infinity?

PART Ill

As Figure 4 will reveal, the new mmrmum average cost is $19. The short-run equilibrium price is 817; hencl' this industry becomes unat­tractive as an investment, relative to other industries. As plants are worn out, therefore, they will not be rPplncrd: plants wiU be junked sooner: and I'Vt'll maintenance will he reduced . To sim plify the problem, we assume: ( 1) each plant has a lift> of 1000 weeks ; (2) the plants in the industry are staggered so that, at thf.' time the tax was imposed, there is one plant 1 week old, one plant 2 weeks old, and ::o on; nnd (3) at the time the t ax was imposed, 20 plants were so nenr completion that it was impoF:Sible to divert them to other uses. Thrsr nre completed nt

problems 193 k intervrus. H ence, for 20 weeks the price will st

onr-W~c;e gradually as entrepreneurs fail to replace worn_:ytatla$17, and then n- . . u P nts.

What will the s ttua tton be at the end of the twenty-fifth (a) m· terms of "gre:lter than" or " less than ") week'? AnS\"er ·

( W]len 120 weeks have passed (900 plants left) will the . be (b) or below $18? pnce Above

II w manv weeks must pass (how many plants must be scrapped) (c)

0the pri~e rises to S18?

before (d) Will t~e o?utput per plant increase or decrease as the number of

(ants declines . ~e) When 220 weeks have passed (800 plants left), will the price be above or below $19? (f) !Iow manY plants must be scrapped before the price rises precisely

to $19? . . (g) What would the pnce be 1f the number of plants declined to 750? What would be the output per plant ? What would happen to the num-

ber of p!B.nts 1 (h) What happens .to .t~e short-run supply curve of the industry as the number of plants dtmmtshes. Draw, on the same graph (Figure 5), the supply curve when there are 1000 firms and 800 firms. Compute elas­ticities of supply for these two curves at a given price.

(i) How could t he pro~ of adjustment, and the final equilibrium, be different (1) if the elastletty of demand were greater than unity; and (2) if the elasticity of demand were less than unity? (The significant points are price, output per plant immediately after the tax is imposed, and number of plants and total output at the new long-run equilibrium.)

2. The same problem with multiple products. Assume that the cost schedule in the foregoing table is for outputs of commodity X. and that for every unit of X , one unit of Y is necessa rily produced. The demand curve for X is pq = $170,000, and the demand curve for Y is

PART I

p = $22 - _q_. 1000

(a) Verify that the industry lS m equilibrium. The marginal costs of X and Y cannot be calculated separately (p. 162), so the supply curve of the industry refers to the equal quantities of X and Y forthcoming at any price. Hen ce draw the d emand curves for X and Y and add them vertically to get the price per unit of X plus Y. (b) Then, for t he individual finn, draw the demand curves for X and Y and their sum against the costs, to find profits.

194 The General Theory of Competitiv h .

e n,ces PART II

A permanent decrease in the demand for X now takes pcctcdly. The new dcm:md curve is pq == SIOO,OOO. (a) Find the new price!; of X and Y and the loss per firm.

(b) What would be the effect on short-run prices of a demand for X? For Y?

PART III

Place une)(_

more elastic

Make the snmc assumptions about plant life and the rate of entry exit of firms as in Problem 1. and

(a) What will the prices of X and Y be when there are only 900 fl. in the industry? What will losses per firm be? rrns

(b) What is the number of firms consistent with the price of X plus tb price Y equal to 815? Is this the long-run equilibrium? e

(c) If a technical change now permitted the proportions between X and Y to be variable within considerable limits, would you e>.-pcct the price of X to rise relative to that of Y?

cltaJtter eleven

Tlte Theory of Monopoly

t 8 now make an abrupt transition from the industry of many Leu fi 1'1' fi ·

t that of one rm. 11s rm may owe tts sheltered existence firms o I . . h ffi . atent the fact t 1at 1t 1s muc more e c~ent than any !;mall toaP ' .

1. . . ' ~

r1va. , 0 . 1 r to other circumstances w nch we shall d1scu~s m the next chapter.

MONOPOLY PRICE

A monopolist is no less desirous of profits than a competitive fir and is in a somewhat better position to achieve t.hem. The

m, polist will by definition face the industry demand curve, and m~o onscious account of the influence of his output on price. When hta ? creases his output, the resulting fall in pl'ice will be borne e me · · I I · I b by himself alone-not, as. under competJtlon, a m?st exc U~Jv.e y y · 1 Marginal revenue IS therefore less than pnce, and 1s m fact nva s.

given by the equation,

marginal revenue = p ( 1 + ; }

I ·~ the elasticity of demand. It follows immediately that w 1ere 11 t::s · •

· ""onopolist will willingly opernte where margmal revenue smce no "' · · 1 t' is negative, he will never willingly operate where demand IS me as 1c.

Maximum profits are obtained when an increment of output ~dds as much to revenue as to cost, that is, at the o~t.pu~ w~ere .mar~mal l'evenue equals marginal cost. ·we ill~strate this prmclple Ill Figure 11-1, where output will be ONI and pnce MT.

195

196

p

0

MT 1'71

L __

M Figure 11-l

Monopoly and National Income

:: -~

The Theory of M on opoly

MC

0

The Earl of Lauderdale criticized those writers who said that a nation's wealth was the sum of the wealth of its citizens:

The common sense of mankind would revolt at a proposal for augment­ing the wealth of a nation, by creating a scarcity of any commodity gen­erally useful and necessary to man. For example, let us suppose a country possessing abundance of the necessaries and conveniencies of life, and uni­versally accommodated with the purest streams of water-what opinion would be entertained of the understanding of a man, who, as the means of increasing the wealth of such a country, should propose to create a scarcity of water . .. ? I t is certain, however, that such a projector would, by this means, succeed in increasing the mass of individual riches.'

• An l nqui711 into the Nature and Origin of PubliC' Wealth (Edinburgh : A. Constable, 1804), pp. 4~.

,,

M opoly Demand Curve

the on 197 . g a monopoly of water and selling it however

~ rnun · 1 · ' , would 1 d l' o duction in naltonn mcome, the noble Earl to th ea a re fi · 11 e contrary to ply is super cw Y easy: the income or th · 'fhde ~ese but the (real ) income of others who muste monopolist ul rJ I • • now pay r

«O ould fa ll. Yet thts sounds hke a simple tramsfer r or «ater w . ' t t h' h o command

the commumty s ou pu , w tc would leave aggreg t . over ged The reduction of real income would occur becaa e mcome

0 cb8D · . use wants u . usly satisfied no longer were sattsfied, with no corresp di PreVlO h (' · on ng

e in output elsew ere m fact a reduction if reso increas • urces nre ...v to bottle and guard t he water). If we constructed . neceSSB• J • • a pnce

. d to deflate money mcomes, tt would compare the cost of th 10 eX d d b f I · · · e

dl of goods pro uce e ore monopo y wtth tts cost afterw d bUD e . . . . . d ld . . ar ' and the nse m thts prlce m ex wou tmply a fall m real income.

'fhe cost and ~emand curves need not ~e the same for a product if it is roon~pohzed as t~ey would be. 1£ a competitive industry produced it; 10 fact they Will proba~l_Y d1ffer (more on this shortly) .

B t if t he cost a nd demand cond1t10ns were the same we could u . f '

Sure the misallocation o resources which results with monopoly rnea A h . f 10 Figure 11-1. t t e margm, resources necessary to produce ro h . I nit of t he product ave a margma cost, and hence an alternative au h ' . d product, of MN. In t ts m ustry however, they produce a product which consumers value at MT. Hence i f output were expanded one unit the product added here would exceed the product foregone else~here, and aggregate income would rise by NT. As additional units were produced, additiona l but declining gains would be achieved until marginal cost equalled price. The approximate tri­angle NT R measures the rise in income that would be achieved if output were to increase to the competitive level.

THE MONOPOLY DEMAND CURVE

T he demand curve of a monopolist must have a negative slope. Ii a firm is the only producer of a commodity, and consumers dis­play normal demand characteristics, the firm can sell more at a lower price. Only if there is at least one other producer of the iden­tical commodity (oligopoly) will the monopolist's demand curve be horizontal over a significant range of outputs.

The slope of the demand curve will in general depend upon how good t he substitutes for the monopolized good are, and how many

198 The Theory of Mono l

Po !I substitutes there ure. The producer of any commodity is limit in his price-making ~ower by ~he availability of other Ptodu:: which arc close substitutes for It. H ence monopoly can arise (' the absence of collu~ion an~ong producei·s) only if the product ~~ the fi rm is substantially different from the products of all oth firms-that is, if the cross-elasticity of demand for the output ~~ this firm with respect to the price of each other firm 1s small. We should therefore say that the maker of any one brand of furniture is not a monopoli~ because, i f he raises his prices, consumers Will shift to other brands. Whether the maker of nylon is a monopolist depends upon the extent to which consumers will shift to silk or rayon i f the price of nylon rises relative to the prices of silk and rayon . The telephone company if' definitely a monopoly because telegrams, letters, bridge parties, and messengers are poor substi­tutes. If there are only a few producers of the good substitutes, we call the market structure oligopolistic.

This raises the question of when the substitutes arc good or poor. Suppose there is only one grocery store at point ~· but a road runs through A, and there are identical rivals on ~lus road .at B and C, and the cross-elastic.ity of demand for groceries at A. wtth respect to prices at B or C is 0.05. Then we would say that A IS a monopo­list: he can raise his price 20 per cent and lose only 2 per cent of his customers to B and C (al though he 'vould lose customers also to other products).!! Suppose now that 50 roads run through

't) t · als Jt'ke B and C on each road. Then there are 100 A w1 1 wo n v . .' 1 d 'th 20 per cent rise in the pnce at A, sales at each nva s an w1 · a . · d

of th~se other ~tores will rise 1 per cent-that IS, the quantity . e-A '11 nl."h H ence the power of a firm to set pnces manded at w1 va - · b f

d u on both the closeness of substitutes and t~e ~urn er o depe~ s p d rs of poor substitutes may hmlt the firm substitutes; many pro uce h s a few good substitutes. .

as roue a . . r iet in calling a firm a monopoly If Although there IS no Impro:. . t Y f -100 there is also little pur-

its demand curve has a~ elas ~~~ y o opoly ,~·ill only tell us why this pose in doing so. The t Ieory o ~~~~·e level by about 1 per cent firm's priee exceed~ thed comfpe I Initude is not very interesting in r = p(Tit;) L and thiS or er 0 ma g

. h mn" be taken as about fi of equal SIZe t en , .,. J 1 c nt :If the various rro.s are ·.... · ' will let1d to roughly n per e. equal to 'I••·· Hence a 20 pBcr redntcn::_~n th~s to a fall of only 2 per cent m . · l 6s a t both an • ..u• . d' . B n se m pure 1as.. . 1 ote lO 10 Appen IX .

purchases a t A. See mathemattca n

\

f opoly Demand Curve The 1l on

ld where the best measurements of mar..n l 199 wor . o . In I .,.na cost h s a 1 per cent err t. genern we shall wish to . ave lll.ore

than . ovolving demand curves which are n L think Of mono-])' as 1 . ' d d . o extremel I

p0 e monopolists eman. curve W11l depend u . n Y e astic. 'fh d terminants: the pr1ces of substitutes and po the conven­

tionnl e d tastes. Incomes are beyond his cont clombplements, in. mes an b . ro ' ut th . co ' len1ents and su stltutes are frequently b e PrJces

of comP capa le or being . f}uenced. . 10 entrance of the automobile companies into th fi

'fhe 1 · fi . e nanee b · "'Y illustrate t le m uencmg of complementan, . USJ-ess ro.- b'l d • J Prices The n of a n automo I e epends upon the cost of d' ·

rcbase . ere It as We\l pu the price of the nutomoblle, and in fact for buy . upon . . (d ers on cred

1t as 1 ti'onship is ad ditive own payments aside) . th .

tl e re a . · e same ln-1 'n sales can be achteved by reducing the Price of tl

crease I d' b $10 I f 1' . le car I Cost of ere It, y . crec It 1s supplied camp t"t·

1 ' or t 1e . d . . t . e I ·lVe y

•5 no profit m re ucmg I ·S pnce further but if it ·15

s 1. •

1 there I . . . ' . upp Je ( nopohsbc terms (by dealers), a reduction m price will b

on mo Of . ene-tomobile producers. course It may be a!'<ked why a m fit a.u . · " · onop-

. financing au tomoblle sales would not attract other;; bes'd oly m ~ 1 es the autQmobile manufacturers. T he answer may be that entry is

h easier for the m anufacturers than for others, since they a roue h · d' t f ·1· · b c n el the use of t eu· ere 1 aci tbes y their dealers as parl camp b

f the franchise,S or the answer may be that the manufacturers 0

. ply were the first to be attracted by the gains. Indeed the mum· 9ffi .

effects of the entry of the automobile finance companies would be (1) to redistribute profits ?etween manufacturers and dealers, and (2) probably to _lower credit costs to. b~yers of automobiles.~ When the typical snvmgs _and loan as~ociahon e~iends a mortgage, it writes the property msurance pohcy through an affiliated agency, which is a related instance of the exploitation of complementary demands.s

• Commercial banks did c' ·entually enter into this line of finanre. ' That the entry will not lend merely to a redistribution of monopoly profit~

from finanring can be shown as follows. For a de:iler the rate of return on selling cars will be at the competit ive rate (assuming the automobile firm is not engaged also in philanthropy). but his rate of return on financing scth·ities where he has monopoly power will be tlbove the rompetitive Je,·el. Renee he will sacrifice auto sales to obtain more than a competitive rate of return from sales of finance, whereas the manufacturer "ill preier an output mixture with more rars nod less fin!lllcing: ren•nue. . 'If the insurance agency business is competitive, the profits from thts com­

bination presumably rome from the avoid!lllre of selling costs.

200 The Theory of .\[ onopoly

Advertising We could have discus-....W advertising earlier, for it will occur also

under competit ion. t"nder competition, the main tasks of a seller are to inform potential buyers of his existence. his line of goods, and his prices. Since both sellers and buyers change over time (due to birth. death, migration) , since people forget information once acquired. and since new products appear, the existence of sellers must be continually advertised. Price information poses heavy bur­dens: a store selling a thousand items would have to advertise per­haps 10,000 prices a year if it wished to remind people of its prices and notifv them of changes.

This i~formational function of advertising must be emphasit-ed because of a popular and erroneous belief that advertising consists chiefly of nonrational (emotional and repetitive) appeals. Even the seller of aluminum ingots or 2,000 horsepower engines advertises (and makes extensive use of solicitation through salesmen) , al­though he is dea ling only with more or less hard-headed businessmen.

What is true is that under competition the individual firm will not attempt to increase the desire for the product. Even if $1 of advertising would increase total sales of apples by $5, a single farmer would obtain only a t iny fraction of t he industry's return, so only a cooperative advertising program would be feasible. A monopolist, on the other hand, would obtain the full returns from the advertising and hence undertake it.

Advertising, and selling activity generally, will be pursued like any other pi"Oductive activities, until the expected returns and costs of various media are equated at the margin. I t is commonly be­lieved that advertising may first yield increasing, and then decreas­ing, returns-where we measure the marginal return of a dollar of advertising by the increase in receipts, holding output constant.

The return from a given advertisement will accrue gradually over t ime. Let us assume that the correct amount of advertising for a firm is $100,000 a year, and that it will reach 20 per cent of poten­tial customers, who number 200,000. Moreover, assume that each year 5 per cent of the customers die or move away (and are re­placed by births or immigrants), or forget the product once they have learned of it.

opoly Demand Curve The ;lf on 201

In the first year , 0.20 X 200,000, or 40,000 CU:Stomel"8 o-

}. '""' · formed· tD I the second year,

z. 0

9 _ v 40,000 old customers are st il1 informed 0 ;) ,... 0 = 38,000 ~ew customers are .05 X 200,000 = 10,000 previously uninfonned customers = 0.95 x 160,()()() - 152,000 ; 20 X 162,000 uninformed customers == 32,

400

Total infonned In the third year, 3

· 0_95 X 70,400 old cust~mers are stjll informed New customers are a .gam 10,000 Previously uninformed customers = 0.95 x (200,000 - 70,400), or 123,120 (or, more simply, t here are 200,000 - 66,880 = 133,120 uninformed customers) 0.20 X 133,120 uninformed customers

Total informed

-= 70,400

= 66,880

= 26,624

= 93,504

This process can be continued, to yield the set of numbers of in­formed customers given in Table 11-J.i' In eventual equilibrium, each year 10,000 new customers enter the market to replace those who leave, and 5 per cent of 166,667 informed customers ( = 8,333) leave or forget the product. The number of uninformed customers is 41,667, made up of:

10,000 new customers, who replace 8,333 previously informed customers, 1,667 ( = 0.05 X 33,333) previously uninformed customers

31,667 ( = 0.95 X 33,333) previously uninformed customers. '

The accumulated advertising capital consists of the value of being known by 166,667 customers, and depreciates at the rate of 5 per cent a year. Since this depreciation is exactly offset by new adver­tising costing $100,000, the capital value of the advertising is 20 X $100,000 or $2 million.

' See my "The Economics of Information," Journal of Political Economv (June 1961).

. ~ ; ,.

202 The Theory of 1\f on

opoly If customers turn over or forget quickly of course tl d . . ' 1e epr . t10n rate Will be higher and the capital value will be R

1 Ccta,

d th d·t· 1 .. ma ler 13 un er esc con 1 IO~s arger amounts of advertising will b · Ut sary to reach any g1ven number of customers--so hot

1 e nec_es,

to tourists will advertise more than apartment houses. e s catcnng The effect of advertising on the elasticity of demand f th

uct is still a matter of conjecture. The primary purpose ~rf . de Pro.()_ · · f h' h a vertts mg Is o course to ~' 1ft t e demand curve to the right and -It · ft 'd h h · Upward IS o en sat t at t e monopolist wishes a less clast'

1 · b } h . . . 1c c emand ecause 1e may t en ra1se the prtce w1thout a large reduction in

Table 11-1

Number of Cus tomers Informed by a Given Rnte o£ Ad 1

• • ver ll!lng

sales. This presumably means that he prefers D; to D2

(Figure 11-2); if so, it is false. Beyond output ·T (the monopolist may wis!h to operate beyond T to maximize profits) D2 is a more profitable demand curve because a given quantity can be sold for a higher price. For the statement to be valid, one must restate it: the mo­nopolist prefers a higher inelastic demand curve (Da) to a lower elastic demand curve (D2 ). This is indeed true, but it is also true if the words "elastic" and 11inelastic" are interchanged or deleted.

Future Effects of Present Prices

We noted that a firm in a competitive industry must ignore the effects of the induE!try's price on future sales because it could not influence the price. A monopolist cannot ignore such future influ­ences and as a result the distinction between the long run and the short'run loses much of its relevance in a regime of monopoly. .

Suppose, to be concrete, that the demand curve of a monopolist this year is given by

qt = 100- Pt,

Monopoly Demand Curve The

p

0 T

Figure ll-2

but that the demand curve next year is given by

qt+1 = 100 - Pt+t + -!(30 - p1

) .

203

0

This demand curve tells us that one more unit can be sold next year fot· every two dollars by which the price falls short of $30 this yea.r. If consumers have delayed responses to prices, as wear­gued above (Chapter 3, p. 26), this sort of demand function is highly plausible.

The marginal revenue of output in the present year will then have two components:

1. The current marginal revenue, which may be calculated:

p, = 100- q,, Revenue, = qt(IOO - qt),

MR1 = Revenue from (q 1 + 1) units minus reveuue from qt units,

= (q, + 1)(100 - [q1 + 1]) - q,(lOO - qt)

= 99- 2qt.

-204

2. The future marginal revenue discounting) :

The Theory of Monopoly

from current output (we ion ~uOte

Revenuec+l = 9t+d 100 - qc+l + t(30 - [100 - q1])}

MRt+ 1 = Revenue next period if (q, + 1} units sold now minu8 revenue next period if q, units sold now,

(q, + 1) q,

= qt+l 2 - q,+l 2'

ignoring terms which do not involve q,, or

Hence the full marginal revenue from the sale of an additional unit this year is 99- 2q, + q,tl/2. Hence marginal revenue in the present period will be larger, the larger output is in the next period.

The same sort of phenomenon may arise on the cost side. Suppose for example, a reduced output in the present period wil1 lead ~ laying off men, and there is a substantial cost in rehiring. Then the full reduction in costs from a decline in current output will be less than the saving in wages by the amount of prospective re­hiring costs.

These effects of the future will almost invariably be to increase the elasticity of current demand and cost curves. The rational mo­nopolist must recognize the fact that people learn from experience, and that present acts therefore have future consequences. Yet this is often implicitly denied. Thus it is said that large buyers some­times demand goods on unremunerative terms from small, competi­tive suppliers on threat of taking all their business elsewhere. As a single act t his is possible, and quite possibly profitable, because it will pay the supplier to sell at a price above variable costs in the short run. But in the long run such suppliers will disappear if they do not earn a competitive rate of return. A monopolist (called a monopsonist in this buying role) who plays this game will therefore end up paying more than the competitive price, since suppliers would demand the equivalent of an insurance premium against such capricious behavior.

~~ -"'"olist's Cost Curves: Monopsony ']'he lf~ O'""r 205

£ MONOPOLIST'S COST CURVES: ~NOPSONY

firrn which is the only buyer of a productive . The . t) has the same power to control price in seb rv~ce (a mo-

opsonlS 11. Th b uylng that o Jist has in se mg. e uyer will face a risin . a tnonoP~e) and this supply price represents the a g supply Pnce (as a verage cost of

p

Demand

0 R 0 Figure 11- 3

the productive service to him. The marginal cost will bear the usual relationship it has to an average, so MC = p(l + lf71) where now 71 is the elasticity of supply. If we postulate also a demand curve by the monopsonist (it is analyzed in Chapter 14), he will buy that quantity which equates marginal cost and demand price.

We illustrate this monopsony situation in Figure 11-3. The quan­tity purchased will be OR, and the price paid to the suppliers RS.

206 ~ The Theo111 of M

0 no-poly The t1·iangular shape, STC, will be a ~ensure of the social

1 arising because the resources are producmg more valuable pr d Oss here than in their a lternative uses. The analogy to monopoly ; . u.cts is complete, and it is true in general t hat the formnl analyr~ctng

. b . . . 1 . } SIS Of monopoly power m uymg IS symmctnca w1t 1 that of mon . . opoJv power m selhng. .

If a monopolist has any power on the buying side, he Will b Jed to combine resources in different proportions from those wh· ~ a competitive industry woul~. us~, and hence hi? c.ost curves :~II differ from those of a eompetJbve mdustry.1 He wlll1n fact comb· . dB. h . h lne mputs A an m sue proportiOns t at

Marginal Product of A _ Marginal Product of B Marginal Cost of A - Marginal Cost of B ·

This condition for minimum cost has the same meaning that it had under competition: the marginal product divided by marginal cost is the additional product obtained by spending one more dollar on an input, and clearly if one input yields more per doll ar at the margin than another, costs are not being minimized.

The monopsonist will substitute inputs whose prices rise slo\\•]y (whose supplies are elastic) for those whose prices rise more rapidly with quantity.8 The1·efore if his production function is the same as that which a competitive industry would have,0 his average cost.') for given outputs would be less than those of the competitive indus­t ry. But as F igure 11-3 suggests, this "economy" is actua lly a waste from the economy's viewpoint.

Care must be taken, hy both monopsonists and students, to know what supply curve they arc dealing with. If a monopsonist buys from a competitive industry, in the short run the industry's supply curve ( = sum of marginal costs) will have a positive slope because of diminishing returns. If a monopsonist should calcula~e a curve marginal to the firms' marginal costs, on average he Will buy at

1 Of course the comparison is with competiti\·c ~ost curvcs for inrlustry-widc

changes-the onlv kind of cost curve a. monopolist has. . . • The marginal ·cost of a productive service to a ;nonops~n!st IS p(l + n;.,, l),

where p is the price of the service and .,, is 1ts elnsttc1t.v. or supply. Tl~c monopsonist therefore uses relatively more of resources w1lh more elastiC

su~~~e=~ncral it will differ because of economics or diseconomies or compan~· size.

I

l l I I

I I

Bilatera l Monopoly

'll . I 207 ·ces as w1 Impose osses on suppliers a d . h pn · d n 1n th 1 snc . h fi rms wtll cpart to force remunerative ri e ong ~n

en.o ug he has only short run monopsonistic powe . P hc.es on hun. -rr nee . 1 ·r h r In t lss·t t· .('J.c 1 lid uc:c tt on Y I c plans to contract h' I ua Jon, d " tot ~ , < 1s own

1 an - petitive industry s long-run supply curv . ~ sea c. 1£ h com h . e r1,.cs beca t e . put prices, however, e Will take accou t f h' . use or • • JlO' IIi · n 0 IS 1 d'

r JSl o on input pnces by calculating a marginal t n lrect . fluence 1 . h . . 1 cos of the · 1n , product w 11c ts margmn to the indw"try•s

1. In-

dustrY 5 ~ · supp Y curve.

BILATERAL MONOPOLY

J3']ateral monopoly arises when a monopolistic seller deals .th 1

pc:onistic buyer. It would be pleasant to mention sc" 1~1 mono ~ h' 1 vera )ffi.

a t examples of t IS mar cet ~tructure, but its theory w' ll Portan . . 1 1 1 serve lain why 1t IS se com encountered (except in labor rn" k t ) to exp 1. 1 h . ...r e s .

Suppose a monopo tst. 1as t e margmal cost curve C (Figure 4) T hen at fixed pnces he would supply quantities indi "t d 11- · · b Cue t his curve so 1t may c termed the average cost curv t

by C' . t l . c o buyer, and then , 1s 1e margmal cost of the commodit the 1 · t' . Y to the buyer. T 10 monopsoms s marg1~~~ revenue ]1toduct curve . R and 8incc he would purchase quantities on thi~ curYe for fixed IS ric~s, it is tho average revenue curve to the seller, and R' is the P ·1nal revenue curve to tho seller. The monopolist would maxi mug . . -

. profi ts by operatmg a t output OA, and pr1ce AB, where his mJze I I' . I ginn) cost (C) cqua s us margma revenue (R•). The monop-mar . . fit b .

nist would max1m1ze pro s y operatmg at output OG and price ~D. for here his ma.rgi~al cost ~C') e~uals his m~rginal revenue product (R). The ob]ectbtv~sdare m?ons1stent, so prtce under bilat­

al monopoly is said to e m etermmate. er · 1 · th d' · Indeterminacy has a speeta meanmg : e con Itlons of cost and demand are not sufficient to determine the price and quantity. Ob­viously if we look back at any year, there will have been a definite uantity and a definite price, but they will have been determined ~y factors outside the traditio~al theo~y : skill in negotiatio~; p~b­lic opinion; coin flipping; a w1sc mamage .. To say t~a~ a s1tuatJon is indeterminate is a refined way of saymg that 1t ts not fully understood. · .

Joint profits of the two firms would be combined if they d1d n~t seek to exploit one another-that is, if they were content to explo1t

The Theory of M onop l 208 oy

. 1. d buyers. If R is the curve of marginal reven theJr supp JCrs an . 1 Ue

b d c is the curve of margma cost for the sen for the uyer, an . ld b 1 er, total profits of the two firms combmed wou e arger at output

OP than at any other. . . One method that might be used to reach this ~utput IS an all~or~

none contract: the quantity OF could be specified, although the

p

0 G A F 0

Figure 11-4

price would still be indetermi~ate . The objection _to this .solution is that cost and demand conditiOns fluctuat-e over tlme, so 1t would usually be undesirable for either firm to commit itself long in ad­vance to its rate of production or purchase. Since the profits of the two firms are larger if they can operate where marginal cost equals marginal revenue, there is a strong incentive for them to combine. The difficulty in naming interesting examples of bilateral monopoly arises because it is an unstable form of organization.

D . cri:mination price ~s 209

pJlJCE DISCRIMINATION

t atively defined price discrimination as the !l 1 ~re ten ~ t . .,a e of the " .-..odity a., wo or more pnces. On this ~trict d fi ..

coJilu• . · 1 · 1 ·~ e n1tJon satne d" criminatiOn IS a re atJve y uncommon phenomen Th,

. ce IS • t " . to t b . on. e prJ f discrirnma IOn 1s separa e uyers into tw nee o . . . f d d d"ff o or more

esse hose elasticitieS o eman t er appreciably and th' classes w

1·res that t he product sold to the various cl~E;<:es d"

1ff8 us~-

11 requ k ~ ~ 1 er m a Y 1 e or a ppearance to ·eep buyers from <:hifting Th . e p ac , . f d h ~ · e purest

tlfll ' £ discriminatiOn are oun w ere the commodity is int . . ses o l ( . l.k d" nnsJ-

ca 1 untransferab e a service, I e me teal care) or can be pre-ctll red from being transferred by con~ract (as when buyers of ,en . m for cable contracted not to use It other.,;se)

)urninu h b 1 . . e. The scope of the t eory may e. en. arged by defining discrimina-. the sale of two or more s1m1lar goods at prices whieh

tton as . . . l I f . are in different ratws to maJ gma ~ost. a book m hard covers sells

26 and in a paperback vers10n for $2, there is presumablv d" _ for ~ . h b" d" . J IS

. . at ion smce t e m mg costs are not sufficient to explain th crunm . . to . e difference m pnces. . . .

p ·ce differences do not necessarily mdJCate discrimination Ba:~s charge small bo~-rower~ a _ ~igher interest rate than large bor~ rowers of equ al financ1al rehablltty because the costs of the small loan are larger per dollar of loan. Wholesalers get lower prices than . tailers if on the average the wholesalers buy in larger lots pav

J C d C ' • Jore promptly, an so on. onversely, price equality does not ~emonstrate the absence of discrimination. If a college charges the same tuition for a large elementary class taught by an instructor, and a small advanced class taught by an expensive professor, it

,. Our definit ion of discrimination turns upon the inequality,

...E.!_ 'F ...1!::..... MCt MC,

Some economists prefer the slight.ly different definition: prices are discrimina­tory if the difference in price is not equal to thE' difference in marginal cost, or

PI - MCt ¢ P2 - l\fC2,

The proportionality definition has the merit of separating a monopolist's be­havior into two parts: (1) the simple restriction of output such that price is greater than marginal cost; and (2) the misallocation of given goods among buyers, which is zero if prices nre proportio11al to marginal costs.

210 The Theory of Mon 01Joly

is clearly discriminating. However, if it. charges the same tuition for two classes ,~h?se ~osts per stu?cnt chffer by say 85, we should not call it discr1mmntton because tt would undoubtedly cost more than SS to have separate fees for the two classes.

Conditions fo r Discrimina tion The basic requirement-s for price discrimination are that ther

nrc two or more identifiable classes of buyers whose elasticities ~ demand for the product differ appreciably, and that they can ~c sepnratcd at n reasonable cost.

The demands of different buyers will be governed by the factors discussed in Chapter 3. Their elasticities may vary with

1.. Income, as in the demand for medical care. 2. Availability of substitutes, as in the use of aluminum for cans

facing grcnt competition from tin plate and glass whereas aluminum in aircraft docs not have good substitutes.

3. As a special case of substitutes, there may be rivals in one market (say, foreign) but not in the other (domestic).

4. Tastes, as when some buyers are eager to get early access to the commodity (a first run movie) .

The form of discrimination is often more subtle tlian these exam­ples might suggest. It has been common, for example, to lease rather than sell certain kinds of machinery, although the practice is declin­ing somewhat due to antitrust convictions. When shoe machinery was leased, the basic charge was so many cents per pair of shoes processed-for example, 0.5¢ per pair for heel loading and altach­ing.n If use is not the chief cause of a machine's retirement, and it has more often been obsolescence, costs clearly are not twice as high for a machine which produces twice as many shoes, so dis­crimination iE< being practiced. T he use of output as a basis for pricing is then a simple method of measuring the urgencies of desire of different manufacturers for the machine.

The tie-in sale may offer a still more indirect method of dis­criminating among customers. If the use of a machine is correlated with some other commodity-salt tablets for a dispensing machine, cards for a tabulating machine-the machine may be leased on a

21 See Carl Kaysen, United Stales v. United S tales Shoe Machinery Com­pany (Cambridge, Mass.: H arvard Uni\'ersity Press, 1956), p. 322.

f) . crimination ]"ice

18 . 211

P . n.nd tht> user compelled to buy the related . tirne bnsJS • vho uses this mntcrinl ns n metering d . matena\ from

I o;:c:or, ' . CVlCe to m the e.- f demnnd. F or tlm cxplnnntion to hold f easure urgen~Y ~evice must be sold nt n non-competitive p;ic: course, the Jlletertn g ·

. . ntory Pricin g ·scr•nnn . . . .

O• nopolist wtll fntl to mnxmm:c the receipts fr th 'fhe rno £ 1 · 1 om e sale . quantity o 11s proc uct unless the marginal .

11 g1ven · . . ' revenue m of ' arable market tS equal. For example, suppose h II

Cb seP· •t . t k e se s a ea gregnte quanti y m wo mar ·cts at $10. H the d ·ven ag d 3 tl . . . emnnd

gt . ·t· s are -2 nn - te respectn c margmnl reve tJCI 1e . • nues are

elasand $6.67, a~d tl~c trnn~fcr of n umt from the former to the S5 "rl·et w11l rn.tse rece1pts by $1.67. In additlon the co tter tn<> " • ' mmon Ia . 1 revenue must equal mnrgma\ cost. mnrgtna . . f : b .

The determmntlOn o p11ces may. e 11\ustrated graphically {Fig-

11-5). Let the demand curves m two separable markets b n· tre d" · e 1

t nd D~, with co~-rcspon mg mnrgmul revenues Af R1 and MRz. ~hen if the n1nrgmnl revenue curves are ndded horizontally to get

[R we obtain the curve of aggregate quantities that can be c::old at ;1 1

' 0 t "l\ b ~ . marginal revenues. u put Wl e set where total marginal glVen\te equals marginnl cost, or OC. This output will be sold ·

1n reven . p ~

the two markets at pnccs t nnd P z, for at these prices marginal revenues are equal. .

This analysis holds only tf the markets are independent-that . if the demand curve in one market does not depend upon the ;;ice set in the other market. This is seldom the case. Often there is some direct movement of consumers between markets: if first run movies get more e>..'})Cnsivc relative to second runs, some people "';u shift from the former to the latter. Often the movement is indirect. For example, if a railroad has no competition at point A but other transportation rivals at point B, we should expect de­mand for railroad transportation to be less elastic at the former point. Yet if the firms at A and B are in the same industry and selling in the same markets, in the long run the branch of the indus­try at A will decline if high rates arc charged.

T he theory of discrimination is only a special case of the theory of monopolies selling multiple products, and when the markets are not independent it is t hen necessary to treat the products sold in the various markets as fair substitutes for one another and employ

212

p

0 c Figure ll-5

The Theory of Mo nopoly

0

~

the theory of multiple products. That theory says simply that the monopolist will maximize profits if he equates the marginal revenue and marginal cost of each product. If the products are related in demand, however, one must calculate a "corrected" marginal reve­nue that takes account of t he effect of the price of one product on the sales of others. For example, if product A has the demand schedule:

PRICE

$10 9

QUANTITY

100 200

RECEfPTS

Sl,OOO 1 ,800

the crude marginal revenue is $800/ 100 = $8. But if this reduction in the price of A decreases the sales of a substitute product B,

tw .. h ·~

. Discrimination pri,Ce .

I 1 by the monopohst., from 500 to 400 . 213 1-o so c · . . f . un1ts at .

!1 eo then the net gnm o rccctpts is only $"()() a Untt Profit of $3, ' of ;\ is only $5. o lind the marginal rc\·enue

• ...,.1• 1111tion as 11 Condition for Existen v·scrJ•... . ce 1 h ugh discrimjnatot·y prices are an incffi ·

A.l t o . . mcnt. mcth d . a commod1ty among mdividunls t.hey d . 0 of ol-

tocntlng , o Ytelcl n larger

p

0 A2

Figure ll-6 0

revenue than a single price system. Situations may therefore exist in which costs of production cannot be covered by receipts unless discrimination is practiced.

Consider, for example, tt community with two classes of consumers, with the respective demand curves for a commodity, D1

and D 2 (Figure 11-6) . Adding these demand curves, the total de­mand curve is RST. The average cost of producing the commodity is C. Without discrimination, there is no output at which price is

a as - " .o

214

4< )~

The TheonJ of M<mo 1 po,!J

so great as average cost. With discrimination, a quantity A t . A t . p ' can

be sold at price P ,, another quan tty 2 a pnce . 2, and the total quantity (A,+ A~ ~ ~3). sells .for .an average pnce of P3, which exceeds its cost. This Is, m a Simplified form , the defense of pr·

d. . b ') d I lee discrimination among comm~ 1bes Y rat roa s. n less extreme cases t he output may be considerably larger (and also considerabl smaller) with discrimination than without discrimination .1z y

D iscriminat ion is the~ said to be defensi~le o~ the ground that each consumer must gam because he has hts chotce of buying th commodity or not , and hence h e must gain if he buys it under dis~ crimination . This is not necessarily t rue: the production of one commodity that is priced discriminatingly will often affect the prices of other commodities. If a railroad will haul coal for 1 cent per ton-mile and diamonds for $100 per ton-mile, the shipper of diamonds may be compelled to use the railroad because it has driven out of existence the former (competitive) stagecoach indus­try that hauled both commodities for 5 cents per ton-mile. Still, discrimination may be defensible on this ground.

The dilemma posed by an industry whose existence depends upon discrimination is this : if price exceeds marginal cost , there are mar­ginal social gains from expand ing output; but if total revenue falls short of total costs, the resources as a whole may satisfy more im­portant demands elsewhere. Some economists accordingly propose a two-price system: a lump sum fee plus a price per unit equal to marginal cost. This method of pricing is in fact used when an initial installation charge plus a charge per unit is imposed. Another solu­t ion is to subsidize the loss resultin g from a price equal to marginal cost from the public treasury-a solu tion especially appealing to the buyers of the product. Almost all genuine solutions involve much more than the reaching of optimum output : the distribut ion of income, the in centives to economic progress, and related economic and political questions are inevitably introduced.

RECOMMENDED READINGS

Henderson, A. M., "The Pricing of Public Utility Undertakings," Man­chester School, 25 (1947), 223-50.

"There is no simple rule on the effect of discrimination on output:. see J . Robinson, The Economics of Imperfect. Competition (London: Macmillan, 1933)' pp. 188-95.

blerns 215 pro :R "The Theory of Monopoly," Econometrica 3 (1935) gickS, !· ·•. R eadings in Price Theory . ' • 1-20.

:ReP~~ted ~:rold, "~tabil~ty in .co~petit~on," Economic Journal. 39 JJotelbn.,, -57 . repnnted m Readmgs m Pnce Theory. (1929), 41 .

pROBLEMS

the marginal cost of a monopolist were, MC = 60 _ 3q(q < 21) }. ~£ d and curve were p = 50- q, where would he operate? Dedurt>

811d hiS . e~ for stable equilibrium. OnditiOD . th d d f the c discrimination e eman curve o 3 monopolist is tnadt> up

2. Under of two parts:

p = 160 - 8q and p = 80 - ~·

ese demand curves, and the marginal cost curve, .\I C = 4 + q. De­Plot ·the rices in the t':"o. ma.:kets and total profits; compare with price ternnn fip 'th nondiscnmiUatmg monopoly.

d pro t WI . l f an Calculate the short-run margma cost o a monopsonist, given the 3. . function of Table 7-1 and the supply curve of the \'ariable

pro~uc~lon = $6- q/10 (for q <50) . service · P r b · h r h I h

4. A monopolist has a set o U) ers, eac o w om 1:1s t e demand

function, p = 100- q

d the monopolist has constant marginal c~ts = SIO. Rt> charges a B1l d 1· ense fee which each buyer must pay m order to purchase the fixe IC .

duct and also charges for each umt. pro , ( ) What license fee will be set if there is no income effect upon the d:mand for the commodity? (Hint: the maximum fee is the consumer

surplus.) (b) What fee will be set if the quantity a consumer buys fn.lls 1 unit (at any price) for ea.ch SlO of t~e fixed fee? . . 5. The marginal reduction in pnce from rt>admg one mon> advertisement,

or seeing one more dealer, is (on average) a din.Unishing function of the number examined.

(a) Will rich people pay higher or lower prices than poor people? (b) Will people read more ads on kitchen stoves or on toasters? (c) Will a. store advertise each price? Each price change? If not, which?

c hapter twelve

Oligopoly and Barriers to Entry

The in~ustry consisting. of two fir~s is called duopoly; the in­dustry w1th u. few firms 1s ca lled ohgopoly. The theo1·y of pr· formation with oligopoly is, and for more than a century has be~:e one of the less successfu l areas of economic analysis, in spite of the fact that almost every major economist has thought about th problem, and a large number have written on it. The difficultiec of the theory will first be discussed, and then we shall pass 0~ to the perhaps more irnportant problem of why there are few fi tms in certain industries.

THE OLIGOPOLY PROBLEM

Suppose two firms ench own a mineral spring whose water is much esteemed by customet·s. There are no costs of production­the consumer comes to the well and fills a jug. This is the original formulation of the problem, as given by Cournot in 1838. If the firms combine, they will sell at the monopoly price (where marginal revenue equals marginal cost, here zero) and maximize their com­bined profits.

This could be viewed as a solution of the duopoly problem, with one proviso. How the profits of the monopoly are divided between the two owners of the springs is not explained, and indeed it is indeterminate. Either mRn can hold out for the 99.9 per cent of the profit, on threat of selling at marginal cost (here zero) or even less, if his demand is not met . But presumably some division will finally be agreed upon, because the two men together can do better by combining than by independent action.

216

Ol·gopoly Problem

The t . . . . 21 7

Ot Put this solution as1de, w1thout explaining ·h h . conrn . w y c did

I. ·h it Modern econom1sts hnvc usually followed C . t re IS · . 1 . . . . ournot m no. . g the monopoly so utton . The1r reJectiOn is balled reJecttn upon two grounds:

'fl1e collusive solution appears to have no natural t . 1 3 3

' s oppmg . · t,-WhY should not , o•· 0, or 300 firms collude on the same

potn logic? · b I' · z. Almost every economist c 1~ves that an mclustry with 2 ( anr\

. ly with 5) firms behaves chffcrently from a monoi'V'I\y ~~~ - . 'fhe basis for this belie f will be returner\ to shortly.

Colll·not proceeded to analys~ the problem on the assumption that

l fi rm Mts independently, m the sense that each firm assume;;: cnc l . . •· t,hat the riv1tl's output IS not affected by hts changes in output.

'fl analysis then proceeds as follows : let the demanrl curve he

lC • tl d' . ]00 _ q and retam 1e con 1t10n of no cost

p~ ) .

1. Let A set nny output, say 40, which fetches a price of 60. The fimtl solution will be independent of this output.

2. Then B will take A's output as given, and seek the output that maximizes B's profits. In panel A of Figure 12-l the output of B is found to be 30. The price in the market is 100- (30 + 40)

== 30. 3. Then A Rets his output to maximize profits, on the assumption

that B's output will be 30. A's output is found (panel B) to be 35, and the market pt·iee is 100- (30 + 35) = 35.

4. It is now B's turn. Panel C tells us that B's output will now be 32.5, and the price 32.5.

5. A in tum sets an output of 33.75, with a price of 33.75 (Panel

D ).

Since this is an infinite series, it would require an undue amount of time and space t.o follow the remaining steps, but it is fairly obvious that the final solut ion will be for each duopolist to produce 33i units, with a market price of 33-i. The monopoly price would of course be .50. I n this straight-line-demand-and-no-cost-case, t.he price will be 100/ (n + 1), if there are n firms.

The objections to Cournot's solution are two. First, neither duopolist seems to learn from experience, although even introspec-

\

218

p

( o)

p

(c)

Oliaopoly and Barriers t

p

0

p

100 0

Fig ure 12- 1

MR0

(b)

(d)

0 Entry

0

Oligopoly Problem 1'116 219 . «hould suffice to teach that his output changes aff .

tJOD ~ d1· d he would take these effects into a ~ct h1s rival. I f }le ' . ccount m fi · .

tput. Second, and m some ways much m . xmg h1s wn ou . ore Importn t o . ac: ~umption IS completely arbitrary. Why not n , the b_asi~ "~~~ match his output?• Or that the rival w~~~u~l~ that the rtVIl ftcr one week? In general there is no ratio l bo ?"' price cuts a . f . · na as1s to th

, conduct m the sense o selectmg a form of b h . e firtTIS •. . • fi . e llVIOt that . 1 ulated to maxumze p1 o ts--€xcept m the manop 1 1 . 1s ca c . h b .1 . o Y so uhon

. 1 economists ave een unw1 hng to accept. • wtuc I . h 'd h

J t how good IS t e ev1 cnce t at duopolists do not h' us . ? · ac 1eve the OpoJv solutiOn. The answer must be rather imprec·1~e b

IJlOD J d 1 . - ecause ne h as ever analyze t 1e evidence, which consists 1 no o . d' 'd 1 h' t . l . 'd a most

Jusively of m IV1 ua IS onca mc1 ents. One svstemat1·c t t' eXC h · • S .a IS~ . 1 study suggested t at m the case of radio commercials tl

tJCfl d t' . t . h 1 lC

1 tl. city of o. ver 1smg rn. es w1t respect to number of ~tat' e as . . . . ~ 1ons was - 0 .07- that IS, a 25 pel cent mcrcnse m the number of stations (from 4 to 5, or 12 to 15) reduced advertising rates by about

2 per cent.~ . A collustve system enc~unters two ~am problems. First, agree~ nt is difficult to reach 1f the transactions in which the firms deal

me '"' I . d re highly heterogeneous. n 1en an m ustry does custom work for :xample, each transaction may be unique, so " the" monopoly ~rice is difficult to determine. But heterogeneity is typical: buyers differ in the quantities they purchase (with Io.rge effects on costs), in the amount of service they demand, in their promptness of payment, and so on. If the firms standardize qualities, lot sizes, service terms, credit terms, and the like, these difficulties can be reduced-but it will reduce profits to standardize where buyers wish variety. Fur­thermore an intricate fot·mal classification becomes "cumbersome," meaning that it tends to hinder adaptation to the changes which shifting economic and technologica l conditions call for.

Second, an agreement must be policed. Even a whole-hearted col~ luder-and few are whole~hearted-cannot control all of his sales­men. Since there are many indirect ways of cutting prices, there will usually be some chiseling, as it is fondly termed- indeed the

'This market sharing assumption, it should be noted, leads to the monopoly price; see Problem 1 of this chapter.

• See my "A Theory of Oligopoly," Journal of Political Economy (February 1963).

.. 220 Oligopoly and Barriers to E

ntry difficulty of detecting chiseling makes it sensible for each 6 engage in some chiseling on the realistic assumption that his~ to are doing it. This chiseling will be harder to detect, the few nvals

er anct larger the buyers.

The costs of forming ngreements and especially of policing th are a major reason for departures from the monopolv sol t· em

. · u Jon These costs w11l he larger, ·

1. The more numerous the fir~s. The costs would probably b prohibitive for 20 firms of equal s1ze. e

2. The more complex the industry's product structure, includi in this term the differences among buyers in demand elasticitg (and hence possibilities of price discrimination), types and quan~~~ ties of product& bought, and so forth. Unfortunately there is objective criterion of _the complexity of. product structure, b~~ clearly a custom work mdustry (say, erectmg refineries) has much more complex structure than an industry producing a few well-de­fined major products (say, petroleum refining).

3. The more rapid the changes in demand and supply conditions. These changes call for new agreements, and complicate the t ask of policing since t hey add opportunities for chiseling (for example predating an order) . '

The number of rivals is clearly of great importance in determin­ing the extent of collusion. Not only does an increase in the number directly increase the difficulty of collusion but also it usually seems to increase the complexity of the price structure (especially if the new firm's location changes the geographical pattern of prices) and constitutes one important source of changes in supply conditions.

The very persistence of oligopoly (or monopoly) must be sought in barriers to entry if t he industry earns more than a competitive rate of return. We turn now to these barriers.

BARRIERS TO ENTRY

Barriers to entt-y arise because of economies of scale, or differ­ences in productive factors, or legal control of entry. We distinguish two types of economies of scale-those peculiar to the industry, and t hose due to absolute size.

. rs to En try J3orrte 221

·cs of Scale Within an Industry £conoJlll

I r e are economies of scale throughout the reg1• f . If t te on o poss1ble " outputs, only one or a few firms may be abl .

· dustr J 1 1 e to ex1st 111 'ndustry. For examp e, et the (long-run ) indust d · the l h · ry emand 1Il b D and half t e mdustry demand curve be D · p· urve e 1 · ~. m 1gure c With homogeneous products a_ monopolist can sell at . 12-2· . . . . d. d b D - ____ Y.ru'Jous

. the quant1t1es m 1cate y ,, and each of two d 1. -Pr1ces . . . d. d b uopo 1sts

11 tlle quantities m 1cate Y D ... If the average alte · can se - rnatJ\'e

p

0 M Q

Fig ure 12-2

cost curve is C, a monopolist can operate at output OM and make profits of 1YT per unit, but if a second firm with identical costB enters, neither can sell any quantity at a price equal to or greater than the average cost of production. If the average cost curve is C', two firms may exist in the industry, but not three. 'Coder these conditions, monopoly or ol igopoly will not be eliminated by the entrance of rival s, and monopoly profits will persist unt.i l technol­ogy or demand changes.

But if the demand is iarger, or much less elastic than average cost, the economies of scale may not prevent the entrance of a con-

222 Oligopoly and BarrU:ra to E . . 'llry

.!- idernble numl.wr of n val«. Aga tn let the demand curve or the ind try be D, a.nd ha lf t he d mand curve 1>-r.. and one-qlUlner oi u • demrmd curve D., a.s in ~igure 12-3. l,..,et the :s\·erage co" cu~~" of on finn he r. Then wah lWO or four finru ther'e are OUt .

for c:irh firm tH which price exceed a\·era.ge cost, and Lhe nur::U!Je-r

p

0 T M 0 Fi~fure 12-il

of fi n n · may inrrt:u&:-. 3 T his ..,:iiuation j,. ill u,.lratcd in the rN niling of food. Ther<' Hrt • no b'T~:l t economies from operating a large store mtlwr th an u ~> lllHII on(', and cont:uuwr ' nttach ome value to a conv<•n i(:'ntl~' loNit l'd stor<'. H('ncc in spa r~eJy ett iE'd sections the 1-t<lrc:< wil l II(' :- llHd iL"r and more numerous relntive to con umers. ~o Hppr(•ri:th!t> lllonopoly pro fits are to be <.>XJH:•<:ted in this case,

' In nei ther t his <'IJ.Se nor that described in F1~ure 12-2 must additional firm:! ent€'t : a ::.ugll' fi.rm can set s suffitieutl~· low price to rna.ke any output of 11 ri\•lll unvrofitable, wbJll' still making some monopol.y pro1il8.

- to E ntry '>') ... 8 ,-ncr<> • LO 41 .(. , tx- murh nt)(n •,• thl' frornJO(llJtin>l lf'v(' l · 1 .. \,;11 pn . • tn rtt"nwly

110f i -('CtlOO" uloH'( ~ f I · poP l('lrt flD<'l' 0 1 (•ronomr , o ... ra t' m <'rt'n in!{ ronr

'fhe unt ucturt>:l \·nrir:~ widrly from fir•ld 10 h<·ld In 1 tr~n trlatl><il

d .:lr" ;:- tr . . nr ()('n iJl U- · ··J' ti£' IWHI r gn~ nod Ph•rtrtrlt\' , l~> lrphonf' l it is de · ·

'-lie utr I "' . h · . Cl•r vp, r~u· · tu fllt'tu nn~ ~' ctor t er{' nre f w mclu.:tril' in whidJ th

th" '1161

• r fi · h In . . tUOI e tfir i£'nt ::- ll.C' o l r.m ~~ u" lllU(' us S J)('r cent of the i:ndu • u1rnlll t nnd ('onc·entrt\llOn mu~t })(' t•xplaincd on othpr cn-ounrl

. · ~ 0 utpu ll!o' ~. tr) :-

. "' or Scalr for Capital £coOOI1llta . .

I 1 hr r<'riod lwfor<> c-orpo rut1on.-. w(.'r(• the lypt~·nl form of bu-i-

ll . • niza tion ( rou!UJiy . fro1n 2000 ll.C'. to 18R1 ,. o l, thl' !\mount ;;::; org<l . I . . ne- uib· fund~ n n <·ntNprl:>(' Pf1 :-«- ~ ·~ . '~'Ill-' ~~\'L· n . hy thl' f)('r;:;ontll o~ ~b · ·0 11 of wl.':d t h t111d th(• po~~ 1btl1trcs or u-.1ng partnel"'hi"~. d · t rJ uti . ,, 1

" . ('r .. ncconi in L! Iy. fr w <•nt<"rprl~l'" that could haw cn uitv in -'f}le rE' w '. . - . ,, -ts of the IIW~II tudc of 100 or tiOO tunr:; th{' U \'era~c- iu: ,·estruen

er:-<>ntll wealt h . of fquH ,. funds cnn of l'Our:<<' lw fiU~IIWn lPd hy borrow(•d funrl -;.

' . c.e the cqu i ty funds providr t lw ~uurflntel' of rr pnyrnent of but !:-10 . · b lcndc>rs will rhar~c t11~ l ll'r rnll'R Uw lnr~rr the proportion of de t, · I I Tl I . . r ~1 ' o f an pntc•q )rr ·c t acy ~<upp y. l<' 10rrow1n~ c·apae1ty of the un~ 1l •

f:i tit a gh ·tm interc;;t rul e , W i ll (kp<·rHI ui:'O upon thr nnlurc a rm. · I I · I b · of it.s })ul" inc<:s: till infiUhll')' Will I'(• Ult\'C' y Sla l c.earn ~ng' ((•lectric

·r·t' ,., for cxamp!P) C"un borrow much more at gtven tntf'r •Ql rates ut1 1 ' ~"' h one with urw£'rtain curninp;l' (pro:.pcctinA for crude oil) .

t an . . 'fhr <·orporation ht1~ wr-akcned the r·onnl'rt1on between firm Hlt'

1\nd per omd wcn lth h<•(·.au~c. it C' liminat.cs the rnt\jor hnndicup of lar)!C' purtJWr:< hips. the ltu lnlrty or ('f\c·h for the dPht!l or all. But nn with limitNI li abili ty in,·e ·tors Pcldon1 fl oc·k to m·w ''••ntun'"

~n large nUtll iWr : !lll t?nt C' rpri!IC' ll111S t have Q hi tory or i'W>luined f Ur<" C• .:' be fore it 1·un ruiM· la1·~t· !-lllllS by tire• l'& lc oi cotnrno.n ~tock .

There· wil l therefore· Of' only a .,lrlull numhc·r of entcrprtsc:; that ran r n tN indu ... t riC''i in whic·lr rr-latively vt ~ arnou.nts of rapita l are nece~ ary to •·ffi <"i('nt opNatioll. H the nu111ber is ~<mall rclutin • to the profituhl r- opportunities for :-:uch lnrgc ventures, the mtc ~f rl'turn on h1rgc· equity funds will cxre<'d that on small fun~. 'fhrs i · ro1nmonly a ll rgcd , at lca,.; t im pli citly : it hus often ~en stltd. that high ra te of ret urn in autornohilc_, c·igH rcttes, ccrtarn chemtMis. and other· ind u,;tl'ie. h tw e r ('rsisted 0\'('r long periods berau.se no

224 Oligopoly and Barriers to E ntry

new firms could raise the capital necessary to enter on an ffi . · scale. The evidence, however, is not persuasive.• e Clent

In addition to this problem of scarcity of large amounts of . funds, there is a popular belief that smaller amounts of eq~Ity ( eithe1· borrowed or equity) frequently cannot be obtained bv capital prises which could use them to earn much more than mark~t enter. taking risks into account. A variety of industrial practice r~tes, been attributed to this 11imperfection of the capital market."~ ave

The most famous is the predatory price war. It is part of A . can folklore that the old Standard Oil Company cut prices :~ri­costs in selected markets and forced its rivals into selling etow b · · If th' b t · ou at argam pr1ces. 1s e rue, It would be an effective techn' only if the small rivals could not raise capital to finance th

1~ue · h h e price

'~ar: If t ey _coul?, t er~ would be no sense in even trying the tech-mque. The histoncal ev1dence does not support this folklore. St dard Oil usually bought out rivals at attractive prices.s ' an-

There is no poverty of instances of able men who could not · th · t 1 f · · . . raise e capi a or a w1se mvestment--W1lham C. Durant could not

• .In the period 1954-57, for exam ole, we may take the 200 largest m J ~urmg ~rms (F~rtune, _19~) an~ classify them roughly into so-called a~t?t mdustr1es. The mdustnes m whiCh t he large firms have the largest f t ' gt r . d t t • b I . rae IOUS o m us ry asse s are g1ven e ow, together w1th the average rates of t in these industries during the period. re urn

INDUSTRY

Tirea and tubes Petroleum refining Motor vehieles Miscellaneous tobacco (elgaretteA) lnduatrial ebemicals Tin cane Iron and eteel Glau Communications equipment Pottery, cut stone, etc. Office and store machinery Soap, perfumes Generating e.pparatua, lampa, and so on Pulp and paper

NUMBER OF

GIANT FIRMS

SHARE OJ' INDU8TBT ASSETS

(%)

INDtiSTRY RA.'l'e OP RETt18N,

1954-57 (%)

5 wo 5 23 99 •47 12 6.53

5 86 9.48

17 86 7.60

2 81 8.07

16 75 6.20 75 7.11

4 73 10.39 ~ 61 S.H

S8 5.81 3 55 6.96 2 64 8.16 4 53 7.10

12 50 7.79

The matching of industri.es. with companies poses numerous minor problems. The general lack ?f assoc1atton ~f rates of return (taken from my Ca.pital and Ra~es of R~tum z~ Manu/actwnng Industries) and the share of the giants in an mdustry IS obv10us.

• The most important example comes later: the inability of men to Lorrow fu~ds for academic train in~~; that would be highly remuner~tive; see p. 265.

S~e John S. McGee, "Predatory Price Cutting," Journal of Law and Eco­nomzcs, 1 (1958).

·e~~~~ 225 ~~ , .

. e $2 million to buy Fords company J.n 1909; it could have been rals

1 ·nvestment. But the demonstratiOn of important· rf

Jove y I . I k t t b lmpe ee-n . the cap1ta mar e canno . e made by selective h' d . h · ns JO f t . m Big t

tJO pected rates o re urn on mvestment, given the probabTt' · If the e:xss as thev appear ex ante do not differ among indu

1 t1 ~es

f 5ucce · . . . s r1es o the market IS not 1mperfect-1t simply has imp 1 t

d areas, Th ffi . er ec an 1 dge of the future. e e Clency of the capital markets . knoW e I . d b' t . . . IS

. a relatively unexp 01 e. su JCC . m economics, and we leave its stJII a barrier to entry m doubt. status as

• or Resources supen . l't' f

0 sionally super1or qua 1 1es o natural resources occur in such

cca . b . h 11 quantities that a maJor amer to t e expansion of the indus-

srns.. provided by the unavailability of other good sources. Among trY IS d' d .

Ost famous cases are 1amon s, mtrates, potash radium baux the m . . . ' ' -ite, nickel, and sulfur. The ~ItuatJ~n Js an unusual one, however:

1 ost always subsequent d1scovenes have been made of deposit-s a rr:omparable or even higher quality-in fact this is true of each ?tem in the above list. 1

But a rising supply price of a resource, even a steeply rising supply price, will not lead to an oligopolistic organization of the industry unless the individual firms have economies, or at least no appreciable diseconomies, of scale. The extractive industries have been organized as compulsory cartels more often than as small number oligopolies.

One unnatural resou1·ce, the entt·epreneur, occasionally reaches such heights of ability as to become the dominant producer even in a major industry. H enry Ford is, of course, the premier American example of such a man: without any advantages other than ability he lifted his company to where it produced over half the output of a great industry. A considerable number of less famous men have achieved comparable positions in smaller industries. The resulting concentration of control is intrinsically unstable: captains of indus­try have been no more successful than kings or dictators in dis­covering a method of breeding heirs of outstanding ability.

Franchises and Patents

In some industries entry is controlled by franchise. A certificate of convenience and necessity, or its equivalent, is necessary to open

226 Oligopoly and Barrier8 t :r;. 0 ~n.try

a bank, build a pipeline, start an airline, broadcast radio vision, or produce gas and electricity. Often these fields wou~~ ~le. few firms in any market because of economies of scale, and a~e utilities were once defined as ~<natural" monopolies (indust . PUbhc could not be competitive). But franchises have been gran~~s that

"'1'estrictively not only in fi elds where there was obv iously r Very more firms (banking, pipelines, radio) but also in fields wheoorn for petition was highly effective (~otor trucking, taxis). The e~:c~~:­ness of these entry controls wtll be greater if they are ap 1i d e­the individual plant (as New York City taxis where a fp eh.to . . , ranc Ise 1s worth more than $20,000) than 1f they are applied only to firm (a regulated motor carrier can have as many trucks t~e

· h ) Th · · 1 b as 1t w1s es . ere 1s no spec1a pro lem of explanation for th t · t. · s . ese re-~ n~ tons: as adn an~11ent cottish philosopher almost remarked

usmessmen an legts ators seldom have a picnic except at th ' consumer's expense. e

The patent is a grant for a period of 17 years to the excl · ' h . Qft

ng t to a process or. product. The basis for the grant lies in the fact that the production and testing of new knowledge is exp · b t . 't . h w· h ensJVe u copymg 1 IS c eap. 1t out patent protection an ente · . . • rpr1se would mvest m research only on such a scale that the expected returns to the firm because of a head start or secrecy would e 1 c~st at the margin, whereas from the economy's viewpoint the~~:­gma~ cost ~f research should equal its marginal social product (in­clu?mg gams to all o~her fir~s) . This. ~asis is obviously formally vahd, but does not gu1de us m determmmg the types and amounts of rewards necessary to bring marginal private and social products together. All one can say for the 17-year period is that it was not inconsistent with the amount of invention we have had in the past.

An inventor will normally license everyone in a comp~titive in­dustry to use the patent simply because this is the most profitable way to exploit it. If the patent holder did not license and instead sought to displace the competitive industry, diseconomies of scale would usually thwart the desire or lead to much smaller net returns.

When the patent covers a new product it is more likely to lead to monopoly or oligopoly. Among one-time American monopolies based upon patents one may mention aluminum, ethyl gasoline, rayon, cellophane, scotch tape, and sulphur extraction (F rasch pro-

.-iers to Entry ~n · . m

Even when an mventor devises a new prod t cess)· l(y been possible for others to find alt uc .' however, it }las usu~ end and patents have not played a maJ·eornatlJv~ routes to he sattl< , . r ro e Ln bri . t . dustrial concentration. ng~ng

about tn .

Tbe Pace of E~try .

I f the discussiOn of entry bamers suggests that there a ff . cl ~~ t · . re e ecbve

JJ)..8lle.nt obsta es .1&1 en ry _m mag mdustries Jt is mi"'l d-:-~ reallY profi table monopoly or oligopoly has e~er laste·d~ ea Jng. l"o . fi d th · · a mere tOO years: nvals n etr way mto the field or devise an alterna-. product to attract away the customers. Of course th' d

ttVe . h f IS oes t Call for exce~stve E>ympat y or the monopolist: if he can ta' no . . . . re m

his position for mne years, earn.mg $1 ~mlhon of monopoly profits a year, the present value of thts. annUity (at 8 per cent) is half

f the value of a perpetual annmty of equal amount. Nine y o . h d d . I' ears in hand are worth nme un re m a c 1stant bush.

Once we take explich account of the fact that entry is basically a question of rate, .we should t~ke account of two other devices to retard entry. One 1s sec~ecy: 1f one can conceal the profitability of his situation, entry w11l be slower. The second is related: if one does not seize the entire profits that could be obtained in the ab­sence of entry, entry itself may be retarded, because the prospective entrant is better able to judge existing profits than maximum possible profits. This is the rationale of the traditional belief that potential competition is a significant limitation on the power of a monopolist or group of oligopolists. Whether potential competition serves this function to any important degree depends upon how the potential entrants are affected by changes in current profits.

The intelligent prospective entrant will rank industries, let. us as­sume, by their curr ent rates of return and the probable rates of growth of demand over time. The monopolist can reduce the attrac­tiveness of his field by selling at lower prices, but in general he cannot or will not retard t he rate of growth of demand. If the rate of growth of demand is large (say equal to one-half or more of the interest rate) , it will dominate the rate of entry ; in the converse case the current profit rate will be dominant and there is more room for the policy of moderate pricing to discourage entry.'

' See mathematical note 11 in Appendix B.

228 Oligopoly and Barrie1·8 to Entry

RECOMMENDED READINGS

Buin, .r. S., Barriers to New Competition, Cambridge, Ma...,8 .: F:Tnrvttrd Univcrsit v PrrS'l , 19.'i6.

Fr llncr W.- Competition Among the Few, New York: Knopf, 1950. Hurwidz, L·., "The Theory of Economic Behavior." Reprinted in Readings

in Price TheO'if· Modiglinni, F ., "New Development.~ on the Oligopoly Front," Journal of

Political Economy (June 1958).

Stiglc•r, G ., "A Theory of Delivered Price Systems," American Economic Revie11J, 39 (1949). 1143-59.

Sti~ler, G., "The Kinky Oligopoly Demand Curve and Rigid Prices." Reprinted in Reading.y in Price Them·y.

Sweezy, P., "Dcmnnd under Conditions of Oligopoly.'' Reprinted in Readings in Price Theory .

PROBLEMS

1. Each duopolist expects to have 50 per cent of the sales at any price (markel-sharing). Determine price and output for the Coumot case of a demand curve, p = 100 - q, and no production costs. What will happen if the duopolist's expectations arc for shares adding up to 110 per cent of the total?

2. (The Dominant Firm) Suppose a firm with a large share of the in­dustry's output decides to act monopolistically on the assumption that numerous small competitors act competi tively. Then at any price these competitors wiiJ sell quantities such that marginal cost equals price, and the remainder will be the quantity demanded of the domjnant firm. rSee my "Notes on the Theory of Duopoly," Journal of Political Economy, 48 (1940), 521- 541.] Now an example :

p = 200 - q is market demand,

MC = ~ + 1 is sum of the marginal cost curves of the minor firms,

MC = q - 15 is the marginal cost curve of the dominant firm.

Determjne price, output, and profits of the dominant firm. 3. The following are famous solutions in the theory of duopoly. Solve

and appraise their s ignificance.

(a) The two .firms ha.ve constant marginal costs of $10; market demand is p = 100 - q. A is first a monopolist; then B ent-ers ar.d sella an amount

~~ . . pr . .,·1tcs his profits on the assumption that A ... ·

1tl

. 1 maxi .. · . . " . not chang whJC I t· tbcn A docs hkCWISe; and so on. rc ournot] . e · outpu • . .

hiS •trnc cost~ ond demand. A Ill agaiu a mononoJilst · th ) The s. . . h . •· . en B

(b d sets u pncc on I c assumptiOn that A will not b . h' t rs an . d rB c angc 111 ell e h . A dONi Jikewtsc ; IUJ · so on. crtmnd] ·cc. t en .

pn ' 5 (b) except that the maximum output of each fi ....... · 40 ) same n • ,. . . . .... ts .

(c k into account the possJbtht.y of one firm mcrl'asing ·1ts fi

tl' ce ta e · h . . pro tB p.en . . its price when the ot er firm IS sold out. [E<lgeworth]• by raJSIDg

I. opoly theory tha t reappears frorn tirnc to t ime emph""iz 4 An o Jg . A I . . ""' cs

. f )Jotcn tu:ll en t ry. s a resu t, the ohgopoiJs ts ( presurnabl threat

0 · h b ·r Y

the . ollusion) set a pnce sue t at 1 an entrant appea red there . g tn c . . I . I h ' actlfl be no rate of output at w u c 1 e could make more than a com-would te of retunL Illustrate the argument graphically. pet.itive ra . .

thema.tical note 12 m Append1x B. • See mo.

5

chapter thirteen

~artels and Mergers

If a large number of producers wish to escape the rigors of t ·t· th d b . COzn-pe 1 10n, ey must o so · y formmg an agreement to act tog th

(called a cartel, after their German name) or by actually mee . er · fi , rgmg mto one rm.

The distinction between a cartel and an outright merger is only one of degree. There are all degrees of scope and duration in the agreements firms may make. The loosest form-a set of verbal promises to abide by a price or market division-is called a gentle­man's agreement, although the participants seldom are, or long do. More formal armngements are customary, and two examples may be mPntioned.

The first cartel successfully convicted under the Sherman Anti­trust Act (1890) is our first example. Six firms making cast-iron pipe dominated this industry in 35 Southern and Western states and in Indian Territory. They founded a combination in late 1894, which later took the following form. Certain cities were reserved for each company, and in these cities the other companies entered higher bids on all contracts to give an appearance of rivalry. In nonreserved cit ies, pri<.'es were fixed by a central committee and each company offered a "bonus," say of $2 to $9 a ton, to the com­mittee for the contract. The highest bidder received the right to make the official bid (the 1'ivals again quoting higher prices) and the "bonuses" were periodically divided among the firms in propor­tion to assigned capacities.

·w e may note that although this method of allocation of contracts was ingenious, it made for friction among the collud~rs. Bo~uses could be bid up by firms which were not interested m gettmg a

230

of Cartels and Mergers for Monopoly 231

fhe 'fheOrY ract simply to increase the bonus distributions, so t·cular cont. d stry profits could be altered continuously. Less

par 1

· of m u d" · · f · · d' · division . tions of t he lVlSJOn o gams IS expe Ient, If the tile uent detefl1lbllla table. Aside from this objection , the plan had {reQ · to e s fi h ·

)Jusion JS . . each contract to the rm w ose cost plus fre1ght CO • { g1V!Og th d' . . f b ' h Jl1ent

0 the given contract, so e lVJSion o usmess t e aJlest for .

was srn s was efficient. 00g the firm tels in industries such as cement and steel dis-am G man car . . . E h fi .

The er f mal orgamzatwn.l. ac rm was ass1gned a more or . 1 d . (. ) . ]11yed a t'mes on histonca pro uctwn non , sometimes

p b ed some l . ( ) F ' quota, a~ , estimates by impartial experts cement . Irms ex-on

11CllpacJtY ( hich included use within the company, in the in-

uotas w · 'd 1 • ceeding q . tical integration) somet1mes pal pena t1es and · w1th ver · d b · th · d · dustr1es . h t of quotas rece1ve grants, ut m o er m ustnes

firms falling 5 ~:s could be sold. A joint selling agency was used

(steen t~edquto 'es and in others customers were assigned to each Jl1e m us rJ , I .b. . . . in so There were usually pro 11 ttions on ass1stmg new entrants producer. r Prices were set by the cartel. These cartels were . ny rna nne . . ts d d. I d ID a . II , free of legal restram an 1sp aye a greater dura-bstantJa ) . · · s~. than the illegal Amencan consp1rac1es. b!lltY the cartel agreement is legally enforceable, and provides

When . d'ff . 1 • t f . · t sales agency, 1t 1 ers m on y mmor respec s rom a for

8 JOIDer The chief economic differences, in fact, ttre only two: full rnerg · . ( . . tel contract ts not perpetual as a merger IS) ; and 1f the car . .

. d ndent firms contmue to operate the plants m a cartel, any 10 epe · f 1 · d d E · I Om]·es or diseconomies o sea e are avo1 e . ssentla ly the econ .

same economic theory therefore apphes to both cartels and mergers for monopoly. There are, of course, many mergers wholly irrelevant to monopoly, and t hey will be discussed subsequently.

THE THEORY OF CARTELS AND MERGERS FOR MONOPOLY

Assume that there are n competitive firms in an industry, in short- (and long-) run equilibrium. The situation of a typical firm and the industry are portrayed in Figure 13-1. The price is p

0, the

'See the. numerous reports of the Commission to Investigate Canditiom oj Product10n and D~·stribution in the German Economy (in German 1930) The present legal situation of cartels varies greatly among European n~tions ..

232 Cartels and M ern vera

output of a firm Om, and the output of the industry OM ( == 11

t" Om.). A cartel is now formed, and each firm is assigned a unes

· ff ~~a of 1/ n tunes total output. In e ect, then, each firm faces a dein. curve equa l to 1/ n of the industry demand curve. Provided ~~d quotas arc obeyed by all firms, they will each produce the e

fi . same output. Therefore when a rm mcreases output by one unit t ta output is rising by n units. Price now depends upon the ~uto u! of the firm, so we may draw a demand curve, d ( = 1/n times b),

p

0 c mb (a)

p

q 0

Figure 13-l

C M {b)

Q

and a corresponding marginal revenue curve, mr. Profits are maxi­mized by the price, P1·

The merger analysis is strictly equivalent. Draw the marginal curve MR for t he industry, and treat the supply curve (which is the sum of the marginal cost curves) as the marginal cost curve of the combined enterprise. Again a price of Pt is set. If there are diseconomies of scale, the supply curve will shift upward and the analysis differs in details from the cartel case.

It is evident that since d must go through point s, the short-run result is a rise in profits. (A corresponding statement holds for mct·gers unless there are large diseconomies of scale.) At least four problems are encountered, however, which destroy t his idyllic extortion.

The Theory of Cartels and M ergeTs for Monopoly 233

Recalcitrant Firm The fi . . h

pose (n- 1) rms JOIO t e cartel, but one firm r . sup b f h ema1ns out-s far as the mem ers o t e cartel are concerned th . .

~·de. 0 E h ' e situation ~~ t very different. ac gets a quota of 1/ (n _ 1) oft t 1 1

· 5 no fi . . . o a sa es ' th cartel. The rm remammg out..s1de the cartel i t

1 bY e h . fl . s no arge h to have muc m uence on pnce, so it \\~ll sell appro ·

1 enoug . n.... H XJmate y b if the price .Is a?out vp 1. ence the output of each member of

0 rtel at this pnce would be (OC- Ob)/(n -1) which 1•

1 the ca . f h b ' s on y ~lightly less than Oc 1 t e num er .of firms is fairly large. If w~ ~ere inclined to get the exact new prtce we could do 50 by an exten­sion of these remar~s: subtract the amount supplied by the outsider

. by his marginal cost curve) at every price from the market (gtven d d n· . d and to get the cartel eman . !VIde this by (n _ 1) to get

hem cartel member's demand curve. Then find the output (and t e · 1 l · 1 . e) at which margma revenue equa s margina cost p~ h' .

If the cartel members are not muc mfluenced by the recalcitrant firm, its owner is much altered in circumstances. He obt.ains a profit of hkt in excess of that of a cartel member, per unit of time. After all he is getting the full benefit of the higher price without paying any of the cost by way of reduced output. In labor union language he is a free rider.

And this is the first difficulty in forming a cartel. Every finn would prefer to be the outsider, and yet if enough stay outside the cartel becomes futile: a large group of free riders will find that the streetcar won't run. In general the cartel becomes feasible only if the number of firms is not very large, and (what is then usually the case) a few firms are so large relative to the industry that they cannot inclividually abstain from the cartel or it will not be formed.

Different Costs

If two cartel members with different marginal cost curves receive equal quotas, a second set of problems arise. We illustrate them with Figure 13-2. Firm B would pt~efer a lower price than firm A would <Pa > Pb). Moreover, profits of the cartel are not being max­imized at any price: minimum costs require that marginal. costs be equal for each company. This condition will be met only If the quotas of A and B are in the proportion Or/ Os.

,. I r

Cartels and M erg 234 e~

This problem is customarily solved by ~llowin~ the sale of quotas

t I member to another. But m pubhc cartels (such a by one car e h T s h A · 0 tobacco allotment scheme or t e exas Railroad t e • menca .

C · · n's )Jroraling of output of 011 wells) the quotas are not

Otni111SSIO • . .• fully transferable, and an meffie1ency addttional to monopoly itself

is introduced.

p

0 r s 0

Figure 13-2

Investment Rivalry

T he cartel system described through Figure 13-1 is a short run solution. There are incentives to individual firms t<> engage in rivalry by way of investment. Suppose the quota of a firm is based upon some sort of "capacity" measure--say, barrels of oil that a plant can refine, or tons of iron a blast furnace can produce (in each case under "no!·mal" operations). The individual firm may then find that revenue is approximately proportional to its quota, but long run marginal costr-; are Jess than price. It will then have an incentiw to enla1·ge its plant and add to its quota.

We illustrate this temptation by Figure 13-3. The firm was origi­nally at Oc, with a plant whose costs are given by SMC. If the

f Cartels and Mergers for Monopoly 235 TheorY 0

1'he its ~~capacity" by 1/ 3, it will be allowed to sell Ot . creases . I t (C

firtll tO The long-run rnargma cos curve ) for a finn which t :::::: 4/ 3 Oc ' · oYersize p lant to justify its quota will lie above the

111ust have an gina! cost curve (LMC), which in turn lies above

100g-run roa~t Oc.~ Nevertheless, the firm 's profits rise by the cross­sftfC at outp hatched a rea.

p

mr

0 c t m

Figure 13-3

4d 3

0

And this is the story of cartels' lives. When this rivalry does not take the form of investment, some other form achieves the same result. Thus some states have had Jaws that no one could sell liquor, or gasoline, or some other commodity at Jess than a designated price (or mark-up). A firm will then seek additional patronage by adver­tising more, giving better service, or some such device. As a result,

'LMC is above SMC if (as postulated in Figure 13-1) the original competi­th·e position was on£' of long-run equilibrium, because then long- and short-run marginal costs were equal at output Om.

9 · X' wart n ·e

236 Cartels and Mer gers the cost cun·cs shift upward. and in l~ng-run equilibrium, the lon • run marginal cost cwntually equals pnce. g

Thl' throry of cartels. we ha,·e said. is closely related to ih of mcrgl'rs. The merger will certainly have the problem of the fi at that refuses to join. The merger will escape our latter two probl l1n howeYcr : each plant can be run at the output such that mar~msj rosts are equal for all plants, and total investment will not bee na

· 1 xces. ~i,·l', n:< w1th <'arte s.

The Interloper The new entrant into the industry , eager to share the monopol ,

profit s. i~ a pro~le_m common to b?th merger. and cartel. This inte;. Ioper. Hi' the extstmg firms caressmgly descnbe him, is in the p ·­tion of the recnlritrant firm: he will no~ join un~ess given unusu~:l~· ftn-ornblc terms (quota. or purchase pnce). It 1s, therefore cruc· 1 to the stability and long-run profitability of either a cartel or

1

~ m<'rger that. new entrants do not app£>ar too oft.en or too quickly.

At thi~ point, tht-n, we nre back to the conditions of entry I be . d. . I . ' as

~e mu~t n ways_ m_ JE:cussmg_ ong run de~artures from competi-~lon . S1~c£' the d1scuss1on of barners to entry. m the previous chapter IS n~phcable . we ~~1all merely re~eat that m the absence of large bamcrs. the firm~ m the cartel w11l eventually earn only competi­tive rates of !'('turn on inve~tment.

If the rate of l"ntry depends upon the rate of profi~ in an industry. tht? merger or the cartel may find it profitable to charge less th~n th(' price dictated by short-run demand conditions ";th a view to retarding entry. :\ reduction in the cartel's price below the mo­nopoly len•) in th£> present pt'riod will (1 ) reduce current profits and (2 ) increase future profits because larger quantities can be sold by the cartel at eal'h price. Hence a "corrected' ' marginal rev£>nue rurn- for th£> present period will be more elastic than the un<'or­rt'Ctl'd run-t>. Industrie:;; fonning cartels or monopolistic mergers almost invariably ~mffer declining market shares OYer time, and presumably t he rate of decline is dependent upon the priring policy.

~lERGERS FOR OTHER PURPOSES

A comprehensi,·e census of mergers would reveal a ,·ast number that have no real relevance to the question of monopoly. When

1 Other Pu.rposes

Mergers or . . 237 bU"-'S (or leases) add1tional land this is b .

I rnJer J f ' o Vlously a 3 n \\"hen two lawyers orm a partnership this is

ger. d 1 b . ' a merger so:r t]le !oral lumber en er uys a service station this is a mer . \\}len . one of these tn('rgers mny have the slightest relev ger. cJearl) n ance to

lY . JllonopO · t he largest part of these mergers-and an equallv

perhaps . ( . . numer-" .. txetun of dissolutiOns£ _ord_n:gdatt

1ve mergers)-are incidents of

ou~ .~ -tnlent programs o m 1\'1 ua s. As such they are not d.ff the Jn\'e::> f h' 1 er-

f rn the merging o owners 1p of two stock certificates each

ent ro . t' ' 00

hares of a g1ven corpora 10n. for 1 5 · h. h fi · Th yertimll merger, m w lC a rm acqmres a supplier or a custo~ner, h as ~heady _been dis~ussed implicitly (p. 169) .as a phe­

n assoc1ated w1th the s1ze of the market. There 1s a deep-notueno . 1 . A .

i -usnicion of vert1cn mergers m mertcan antitrust Jaw on -~:::> r . ' • cr ·ound t hnt such a merger forecloses part of the market for the ,I I . f l f . t . rivnls-for examp e, 1 a s 10e mnnu nc m er acqmres a chain of shoe . ., rivnls will no lon~er be nble to sell to them. This suspicion :otore~ , . . I . I b·t· . . . creneral tllogtcn , smcc t 1e n 1 tty of nvals to sell shoes will I~ lD "' . h .I 1 . I be impaired only 1 f t e retlu c uun 1ad monopolistic powers in

the retail market.s T here arc, in fa<'t , only three rensons associated "';th imperfect

0111petition fo1· Yertical int<'gration. The first is to pr:lctice price (' l. . 1 discriminRtion: a monopo 1st m t 1e production of aluminum. for example, usually could not discriminate in the price 'Of a luminum ingots for different products emerging from fabrication unless he was also the fabricator. The second reason for Yertical integration. more difficult to document , is th<' desire to put an obstacle in the way of prosp<'dive entr:1nts: if a new steel company had to enter the iron or<' ns well as the steel industry. presumably entry would be retarded:' The third noncompetitive reason for vertical integra­tion is to elitninnte monopoly: if a cartel s£>t noncompetitiYe prices on supplies, backward intcgrntion by buyers would be a suitable way to get t ht> supplies cheaper. Such integration would of course be unnecessary if t he cartel WNe intelligent enough to recognize that it could not exclude entry by large customers, for then it would

1 0£ COUrse ODE' <'1\ll buy a monopolistic seller Or buyer. but Onlv at 11

price which inrludes the capitnlizrd vnlue of tlll.Y monopol~r g&ins. 'The European cart E-ls frequent!~· had exclusive dealing ron tracts with sup­

pliers and distributors, or grmltcd " loyalty discounts·• (based on aggregate purchases from the cartel) to this end.

238 Cartels and M erg era

not attempt to get non competitive prices from such custom pie without monopolistic power should not exercise it. ers. Peo.

R ECOMMEN DED REA DINGS

Pat inkin, D ., "Multiple-Plant Firms, Cartels, and Imperfect Com .. Quarterly Journal of Economics, 66 (February 1947), 173-205 Petition,"

Stigler, G. J ., "Monopoly and Oligopoly by Merger" p · . American Economic Association (May 1950) . ' roceedmga,

PROBLEMS

1. F..arh firm in an industry has the cost curves given in Probl 1 Chapter 10 (p. 191). The industry demand curve is p = 25 _ q/l 7~m'M of

gina! costs of a finn arE> MC = q - 2 and total costs are · ar-

C = (q - l~(q - 2) + 135.

(These equations reproduce the table on page 191 for q ~ 7; note that MO is not a derivative of C because finite changes are employed.)

(a) Verify that the industry is in competitive equilibrium with 100 firms. (b) If all the firms join in a cartel, what. price will be set? Wbat will profits per firm be?

(c) If all the firms except one join a cartel, what will the price be? What will be the profits per member firm, and per outsider firm? (d) What will price be after 10 additional firms enter the industry and join the cartel with equal quotas?

(e) How many firms must enter before profits are eliminated?

(f) What will happen to price and profits if now the cartel is abolished ?

2. The same basic problem applies to mergers. Now let there be 20 firms and the industry demand curve, p = 25 - Q/ 34. Will it be profitable to form a mergPr of the firms if (fixed) co~ts of each plant rise 10 per cent because of internal diseconomies of s.::tle?

?'G

chapter fourteen

The Demand for Produettve Services

; .

The apparatus o~ price t heory we have been discussing is for-

11 l. ust as applicable to markets for productive services as ' t J)1fl y . d' t fi . h I is to markets for mterme 1a e or ms ed goods: After we establish the determinants of the demand for productive. services in the present chapter, we sha ll not be much concerned w.1th manipulating

Plv and demand curves, for there are no new principles involved.

sup ~ · · I d t · Instead we sha ll ~xamme t 1~ e ermmants. or ~he supply curves of labor and spec1fic procluctlve goods. Cap1tal 1n general will be treated in Ch apter 17.

DEMAND UNDER COMPETITION

The firm will hire each productive service in such quantity as to maximize its profi t s . P rofit s will be maximized when the amount added to the revenue of t he firm by an additional unit or the pro­ductive service equals the amount it adds to costs. Under competi­tion a firm does not exert an appreciable effect on the prices of the productive services it buys, so the amount a unit of the pro­ductive service adds to costs is equf\l to its price. The amount added to receipts is the mnrgina.l physical product multiplied b~ the .price of the product (since the output of the firm also exerts httle mftu­encc on the price of the product). These relationships are illustr~ted numerically in Table 14-1. The marginal physical product t1mes price (called the value of the marginal product) diminishes as .the quantity of the productive service increases because th~ margmal physical product diminishes and the price of the product IS constant.

239

240

QUANTITY QUA NTITY OF

OF A PRODU<."T

20 6810 21 6865 22 6915 23 6960 24 7000

The Demand for Productive .S . ervtcea

T a b le 14- 1

PRICE OF

PRODUCT

$0 .60 0 .60 0 .60 0.60 0.60

RECEI PTS

OF F lltM

$4086 4119 4149 4176 4200

55 50 45 40

sa a 30 27 24

The value of the marginal product is the demand pric f productive service if tbe quant1:ties of the other productive se 0.r a

erv1ces are held constant. Demand curves, however, usually refer t d mand prices when the prices of other productive services ar

0 h ~­

constant. We shall show the difference between these two d: e d prices graphically (Figure 14-1). Let MP1 be the cu rve of the ~~nd of the marginal product of a productive service A when the quan~~ of the other productive service B is 100. If now the price of A falls from OR to OS, the quantity of A demanded will rise fr RC to SD if 8 is held nt 100. But the entrepreneur will not h~~ B at this level for, if the price of B has not changed, the minimum cost condition,

ma rginal physical product of A _ marginal physical product of B price of A - price of B

no longer holds. Tbc increase in the quantity of A (from RC to SD) will inc•·cnse the marginal product of given quantities of B :;o the quantity o f H will be increased to (say) 125 to minimiz~ costs.1 T h is larger quantity of B will raise the mm·ginal value prod­uct of A , and n new marginal product curve, M P2 results. Hence at price OS, the quantity of ..-1 demanded rises to SF. If we join point:; such nl' C and F, we trace out the demand cur·ve of the firm for A. tll(' price of B (nnd that of the product) being held const.nnt. The demn11d curve will be more clastic than the curve of the value of the marginnl product.2

'It. is possible with A and B suhstilut C'S, for th<' mnrl!innl pi'Orlurt. of B to be reduced if t.he quantity of A rises. ThNt the cnlreprC'neur will reduce the quantity of B and U1is will in turn inrrcaac th<' ma~iunl product of A.

• See mntbemntical note 13 in Appendix B.

d V1lder Ccm~.petition J)e11~11 . 241

d and curve of tho mclu1ltry is the sum f 'fhe ern , fi 1 . 0 the dem d

{ the industry s rms, )Ut, as w1th supply . an e" o . curves we m cut·V • 1 t things com,tant to one firm need not b ' ust

. e t 1a . . e constant t noll~ d trY. If the pnce of a productrve service fa lls d o

111 tl!' • . f tl . 1 ' an all fi l'lns the tput the pncc o le me ustry's product must . e-xpand ou ' necessarily

R

s

0 A

Figure 14-1

fall. We thet·efot'<' di:.;tingui:;h bctwt>en the demand curve of a firm when the price of the productiYc SNvice varies only for this firm, nnd the demand curve when tlw price varies for all firms. Thus, let D 1u be t he demand cut've of n firm for u productiYc &'rvicc when tho price of lh<' product i~ $10 (Figure 14-2). If the price of t.hc productin• :-<crv ic<' fnlls from OR to OS for nil firms, out~ut of the indu~lry will 1·isc t>nough to reduce the price to (say) $9.

1

242 The Demand for Productiv " e A.Jervice

Then the demand curve of the firm will fall to D9

and . 8

take ST of the productive service at this price. If we c~nnect lt ~Viii like M and T, we trace out the demand curve (D) of thPOints for industry-wide price changes, and it is t his type of dema de firlll that we may add to get the industry demand curve. n curve

p

0 ()

Fig ure 14-2

The RuJes of Derived Demand

Since the demand for productive services is created by the need to produce a product for sale, the demand for the services is said to be a derived demand. The elasticity of this derived demand for a productive service is govemed by four conditions, and three rules of derived demand have accordingly been proposed.3

• See A. Marsha ll, Principles of E conomics, (London: Macmillan, 1922), Book V, Ch. 6; also the papers by Bronfenbrenner and Hicks, Oxford Eco­nomic Papers (October 1961). See mathemaLical note 14 in Appendix B.

Under Competition vemand ~3

. The demand for a service is more elastic h R.tJLl> 1 · other services may be substituted for it. ' t e more readily

sure of substitutability commonlv used · th T) e mea · h · Is e relati 1

. the ratio of t e quantity of the producti . ve ge tn . f · ve serv1ce i

chnn . to t he quantity o some other productive serv· d. . n ttOD • th . . ICe, lVIded

ques lative change m en pnce ratio.• It is self-evid t 1 the re . . .1 1 b . . en t 1at

bY b titutabthty entat s a arge su stJtutJon of other . . h su s . . h . s· services htg }Jose relative price as nsen. mce aluminum and

. 0ne w . d . . . copper fot both effiment for con uctmg electnClty each will h

· are . b ' ave an w1re . d nland in the neigh orhood of the ratio of the p · f 1 st1c e nee o

e a . 1 to that of copper of 2 to 1 (taking account of th . Junnnun . . ) e1r a . ht and conductiVIty . ~reJg S

2 . The elasticity of demand for a productive service will be RuLE · 1 th J. t ' ' t f d larger, the arger e e as .1c1 yo emand for the final product.

h logic of this rule is also direct : the more elastic the demand 'fthe product, the more output wil1 fall for a given rise in cost

for e · · th · f d · (and price) due to a nse m e pnce o one pro uctlve service.

R E 3. The demand for a productive service will be more elastic the UL . • I

more elastic is the supply of the other productive services.

When the price of one productive service rises, the increase can b bome either by buyers of the final product (who pay more) e by suppliers of other productive services (who receive less) . The ~ore elastic the supply of these other services, the less possible 't is to reduce their price with a given reduction in their quantities. ~ence the greater must be the reduction in the use of the productive service whose price has risen, if price is to equal marginal cost.

There is a fourth rule, which will appear more obvious to most people than any of the fo1·egoing: the s.maller the fraction o~ t(lt~l cost the pay ments to a productive serv1ce are, the less elast1c Will

• This is the elasticity of substitution, formally defined as 6(a/b)

alb tlp&/p.'

P&/p.

where changes in (a/b) are compared with changes in ('fh/p.) to keep the elasticity positive.

-_,"" The Demand for Productive Serv·

244 tees

be it demand. If doorbells do.uble in ~rice (say from $1 to $2) 'h t of building a house will also nse by $1 , or say 0.005 ""• • e cos b d' d f b . ... ... r

t S. e few people will e 1scourage rom uymg a ho

ccn . Jnc be l '11 b . . use by this rise, the demand for d~or b I ~ w1~ 'tet~mte melastic. 'I'here is some truth in the rule,S but Its asiC lml a wn may be suggested I ns fo llows. Suppose we classify the car~enters who build a house into Polish, German, Irish, and so on. Smce t~e wages of any one group of national origin w~ll be a small fract~on of total cost-i£ it is not, we shall subclass1f! carpenters by v1lla~e of origin-can we not say that the elasticity of demand for Insh carpenters is smaller than the elasticity of demand for all carpenters? Indeed we can say this, since freedom of speech includes freedom to speak error. The substitutes of_ co~rse become better as .we subclassify carpenters and the subst1tut10n effect leads to an mcrease in the elasticity of demand. This is usually the case, or we would be able by mere subclassification to make all derived demands inelastic.

It follows from the theory of cost curves that the elasticity of demand for an input will be greater in the long run than in the short run. In the short run the quantities of all resources are not freely variable, so the full effect of a price change on the propor­tions in which inputs are combined will not be achieved. There are really at least two long runs to take into account for a complete analysis: the inclustry purchasing the input whose price changes will require time to make a full substitution in favor of or against the input, and the buyers of the commodity in turn require time to make a full adjustment to the resulting change in the price of

the industry's product.

DEMAND UNDER MONOPOLY

The demand price for a productive service will be equal to the increment of revenue that the firm derives from the use of one more unit of the service. Under competition this increment of revenue is called the value of the marginal product, for it equals the mar­ginal physic11l product of the service times the price of the product.

• It is not generally valid, however, unless the elasticity of demand is larg~r than lhc elasticity of substitution; see footnote 3 for details.

d Under Monopoly 245 peman adds 20 units of product per day and the p d

1 bOrer ' 1 1 f h' . ' ro uct lf n a 50 per unit, t 1e va ue o IS margmal product is $lO ~en: {orr $~;onopoly the firm must ~ake nccoun~ of the fact that the

unde r product lowers the pncc of all umts of output so 0 l ent- o h . , n Y

increil1 . 1 revenue of t e mcremcnt of output is received Th argtna · h · ll I th · · e the 111 f value, whtc ts ca ec c margmal revenue product

incren1ent 0

the marginal physical product times the marginal therefore

is 6

revenue. t that the demand price of a monopolist equals the margi-'fhe fac product of a product ive service is the reason monopoly l revenue · f S h' · ns a misallocatwn o resources. uppose t IS marg~nal revenue

leads to . e~tO which will also be the value of the marginal product duct IS ~ , . 1 1 l pro t ' tive industnes. T 1en t \e va ue of the marginal product

. cornPe 1 . ' 11 b ~n the monopolistic industry ~d~lb e1 ~fr~ater than $10 ,~ and aggre-

10 t ut would be increase y s n tmg resources from competi-gate ou P }' · · d t . . d stries to the monopo tStiC m us ry. tJVe JD u . d d d

'f f the rules of denve e. man carry over from the competi-

wo 0 . . 1 l't l 1 . t the monopolistic case wtl 1 1 t e c 1ange. The demand for uve 0 '11 b I . 1 \ a productive service w1 .

11ebmore c n1sti~ t \Ch >etter the substitutes

for it, and the demand WI c m~~ e as~1c,t\t e ghreatcr t~e.elasticity £ the marginal revenue curve. · e ru c 1at t e elastiCity of de-

~nand for a productive !.'ervice will b<' greater, the ~realer the elas­ticity of supply of the ~th~r fac~ors, .however, _ra1ses a problem: ·r the supply of any service 1s not mfimtely elasllc to a monopolist. ~hen he can also exert infh1ence on its price and becomes a monop­sonist (see p. 206). H e will accordingly t ake account of this infiu­ence, and hire such services only up to the quantity where their marginal cost equals their marginal revenue product, so the rule must be restated: the demand for a. productive service will be more elastic, the more elastic the m at'ginnl costs of the other services.

'When the quantity of the productive service rises by c.a, revenue rises by

AR = (p + Ap)(q + Aq) - pq = pAq + qAp, approximately.

AR Aq ( Ap) Aa =Aa p+qAq

Aq ( l) · l = - p 1 + - - Marginal physical product X Margma revenue. Aa 'I D

'It will be equal to SlO divided by (1 + 1/1)) , or $12.50 if 11-= -5.

246 The Demand for Produ.cti ve Sei"Vicea

RECOMMENDED READINGS

Bronfcnbrenner, M., and J. R. Hicks, Oxford Economic p 1961). o.pers (October

Marsha]), A., Principles of Economics, London: MacmiUa 19 Ch. 6. n, 22, Bk. v '

PROBLEMS

1. If there are fixed coefficients of production so a unit of d requires n units of productive service A, and the supplies fprothuct always · · · fi · I Ia · 0 0 er Prod tJve serv1ces are m ntte y e stJC, prove that the elasticit f d uc.

A is K times the elasticity of demand for the product (KY ~ hemand for A f . · 1s t e amo spc.nt on as a ract10n of total value of the product.) · unt

2. Explain how the demand for gasoline would be affe t d b the following: c e Y each of

(a) A tax on bus t ickets. (b) Growing traffic congestion in a city. (c) A tax on horsepower of automobile engines.

(d) A subsidy on lubricat ing oil produced in fixed proportion with gasoline.

3. Let each of 60 firms have the marginal product for a fa to M.P. = 30 - Q. /10. Let the quantities of the other factors be fixe~· r t~' short run and derive the industry demand curve for the factor, giv~~ th: demand curve for the product, p = 20 - q/1000. (Note thnt the prices of the other factors are not held constant, as in the usual demand curve.)

c hapte r fifteen

R e nts and flnnsi-Rents

As recentlY as a century ago, the t~eatises on political economy .11 devoted much space to land-to 1ts unusual properties to th

st1 f h' 1 . • c . s forms o tenure w 1c 1 were used m various plac d var1ou . . es, an to the forrnid~ble ha mer to econom1c .growth tha~ .a fixed supply

f l"nd constitutes . Thereafter, as ugnculture rap1dly declined · 0 .., . d 1' d I . 10 relative importance, 1t ec me a so 1n the attention it received in

economics. The interest of ren t theory for general economics is nevertheless

substantial. Any pr~ductive factor in inelastic supply receives a re­turn that partakes m ~o~e measure ?f a rent. Almost every piece of capital goods-a bUlldmg, a machmc, a tool-may have an in­elastic supply in the short run, and then its return is called a quasi­rent because o f this similarity to the rent of land in the classical

theory.

THE CLASSICAL THEORY

Let us assume, with David R icardo, that the supply of land is absolutely fixed in supply, and that the country is a closed economy (no international trade). Then clearly the supply curve of land (or or lands, if they differ in significant respects, including locations) is a vertical line to the industry using land, and rent will be equal to the value of the marginal product of land. If the d.emand de­clines, rents will decline; if the demand rises, rents will rise. We may therefore say that rent is not a cost, but is determined by price-which is obvious enough when one reflects that we have lumped all uses of land together: then naturally land has no alter­

native uses.

247

~ 248 Rents and Qu .

.Q.~~Re

The classical economists (who get t his n ame from of II 1lts

K arl Marx ) reached this . result wit~ another appar~tus ~h~e?Ple, some in terest. T hey combmcd other mputs into a dose of " ~s of and-labor'' and postula ted a schedule of diminishing mar . cap1taJ~

. . gina} p ucts of cap1ta l-and- labor on each quahty of land A. t . rod.

· • YPlc I of schedules woul d look like Table 15-1. a set

Table 15-1

Marginal Product from Various Agricultural Lauds

OOS E S OF

CAP ITA Jr. AN D-LA:SOR

2 3

4 5 6

7 8 9

A

140 150 160

150 140 125

110 100 96

B

135 140 135

125 110 105

100 95

--=::::::::: Q UALITY OF LAND

c D ---E fi' 120 110 100 120 100 95

90 115 90

110 105 100

95

The land of t he lowe:st qual~ty that will yield a product equal to t.hf' cost, of a fi r:"t dose of ca p1 tal-a nd- la bor is called t he ext ·

· 1'h" 1 b . ens1ve margm . . 1s _wou d c lnnd '! 1f t he cost of cap ita l-and-labor were 100 bushels ; 1t would be n 1f the cos t were 110 bushels. Th 1 t ci h. t . . e as . ose ~ 1c 1 IS ~ ust remunerative on any type of land is called t he mtens1v~ Jllargm ; at a cost o f 100 bushels , on C land this would be t he Sixth dose, on A land, the eighth dose.

R ent is he re t he surplus over what the capi tal-and-labor costs. ~Vi th competition t he v aria ble inpu t receives its marginal product; 111 other words, the fa n ner will use va r iable inputs unti l t heir cost equals t he value of t heir margina l product. If a dose of capital­and-labor costs 100 bushels , the A fa nner will hire 8 units H is rent, which equa ls the sum of t he ma •·ginal product~ rHo+ 150 + · · · + 110 + 100 = 1075] minus t he input bill [8 X 100 = 800], is 275, the maximum obtainable. W e could also mea~ure rent d iJ't>ct ly by t he m arginal productivity technique :

I 'n"sical Theory ~~ m

. the amount of lnnd, hold the number of doses of c . ~tll1· 1ng ons ta n t. The result would be t he same., 8P1tal ~

d lllbor c . . all - ct of t hts proof that rent 1s not a cost 1·

0 e aspe s a source f n . , . we Jumped together a ll the uses of land ~0 b . d fi .. 0

. ·,.,og:-. . f '' ·Y e n1hon .,,, s~P . 10 al terna tive uses or land. Would not t he 8 d . I re at e t . t t ? R. ' a me efint~ p e . k turn wages m o noncos s. tca rrlo ~answer . . • 1 trJC . ~ , prev1ously

tt011<1

. 1 ed is : but m en must. b(' pa1d enough to Jive and d ubhS 1 • . . repro . uce unP I , s whereas t ht> land wtll remam no matter how 11 b

n"e ' e- . d 1en e-thel ~

0 ly if we could ad to the demand for labor the d d

h ve n • . ld eman a ~ be born and hve cou we say t h('re a re no alternatives A

not 0 d reply but. not wholly satis factory. Some land al~ h.

rJ goo ' . . ..,o as ve lte native of dea th : one may cul tivate m such a manner th t the 8 r · · · d t d I · n h~ fertility of a sotl IS es roye . t IS not so e~sy , however, to de-t 1 cation (for exa mple, n cen t ral metropolitan location) . stroY 0 d · ( · )

h . are nonpro uc t10n consumptiOn uses for a ll rcso•lrC"" T e1e •· ' , .• , el. a nd these compete for J'('Sources . .lust as the alternat1·,,e howev , .

to labor is leisure, so thr al ternntn •c to a com~11ercin l use of land ._ ersonnl use-n flower ga rden , n large parkmg lot for the wife 1:; 8 p } · t · · I ' . tting g 1·een. v.,r \1'\ t IS rut', agnm , IS t 1at the consumption Ui!es ~f ~~nd tak e o~1ly. a t iny fraction of land, whenn~s the consumption

• of a ntmYs tnn<' a re large. A lnr11:e change m the denutnd for uses . . ' fi d )and could not b e m et m any s1gm can t egree by decreasing these onprodurtive uses of lan d .

n So it seems, a ga in , t hat lnnd is a little different : its aggregat(' supply is not highl y e lasti c t'vcn in the long 1:un. It is different , however , only in respects t hat do not mat ter much. Almo::;t all real economic q uestions involve n pnr'ticulnr use of lund- growing wheat or t rees, res iden t i a l subdivisions, nation nl pa rks, superhighways . tlnd so on . Then the a ltcrntlt.ivc uses of the land are :::ignificant, nnd one must reco gnize these costs (and, from another viewpoint, the suhstnntinl e lastic it y of supply of lnnd) .

Tobacco Quotas and Pure Rents The tobacco ncrcage restriction progmm provides an interesting

example of a pu re classical ren t problem. Some 500,000 fa rms have

'This is intui t ive ly plausible. If we wi thdrt\W o unit of (~\>' ) D land, thr product declines bv 210 bushels. The 2 units of cnpital-and-lnbor can produce 200 elsewhere, so. the net decline of output is 10-which is the rent ol D land. More genera lly, look at the discussion of Euler's Theorem, P· 151.

250 Rents and Qu . aSt-~e

allotmrnts of acrenge to grow tobacco, ranging from a fracr ~~~ an aere to hundreds of acres. These allotments are b"""d . 10

ll of • . · "~" Pruu · upon prcYIOU:S acrenge m _tobacco, nnd ne"· allotments are

1 811ly

unobtninnble. If tobacco IS grown on land without an all ~ lllost the fnnner must pay a tax. of 75 per cent of the gross valu~ lllent., put times pre\'ious year's pnce). (out-

The supply cun·e of tobacco land thus has three branches·

1. If the price of tobacco fnlls below the price nt which can be earned in other crops, the supply of tobacco land va ·~hlllore

I I . t" I . . I d. m, e~ 2. T 1e supp y 1s Yer 1cn m t 1e or mary range of prices. -· 3. If the price of tobacco rose to where 25 per cent of the r . .

1 1 ece1pb y1elded n larger return t 1an ot 1er uses of ]and, the supplv of Ia ~ would become immense. • nd

1\e illustrnte this cun·e in Figure 15-1. Since allotments are in fixed supply, their annual value 1• s set ?Y the extra profit that m~y be earned by the cartel price implicit

m the Depart~ent of Agriculture allot~ents. The capital value of an allotroe~t 1s tl~e present, value of Its expected flow of future profit~whtch obnously depends on tobacco prices, changes in al­lot~ent:;,. and changes in taxes on tobacco not grown on allotment. This cap1tai Yalue was $1,600 to $2,500 per acre in 195i.2

"\\here tobacco farms are rented to tenants, the extra income due to the allotment goes to the Jando"-ner: tenants can earn no more in this line than in others under competition. When allotments are sold, the buyer pays such a price that he earns only the current rate of return on his inYestment: buyers of tobacco a11otments can get no larger returns than buyers of other assets, under competition.

QUASI-RENTS

A quasi-rent is the return to a durable specific productiYe instru­ment. If the producti\·e factor is durable, it will be used throughout its Jife provided it yields more than its scrap value. Since it is a

• See F. H. Maier, J. L. Hedrick, and W. L. Gibson, Jr., The Sale Value of Flue-Ct:red Tobacco Allotmenu, Agricultural Experiment Station, Virginia PolytechniC Institute, Technical Bulletin No. 148 (Apri11960).

· ]lents 251 Qu~~ . . h .

ductive mstrument, say a ouse or macbme tool it is te pro . ,

concre: d to 50111e degree, and cannot change mto another form speciuhze d for its services falls.3

if the delllnn 1•011-in a period long enough to build new instruments

t l c long . In '. t old ones-the return to the mstrument must equal the or weat ou

0

~ (l) 0 t-

u.. 0

uJ <..)

a: 0-

0

~-------5

LAND

Figure 15-1

current rate of return on capital (";th appropriate allowance for risk) . If the machine's quasi-rents are le.~ than interest plus de­preciation it will not be replaced; if the quasi-rents e.xceed interest plus depr;ciation more will be built until equilibrium is restored.

'If the future life of the instrument is shortened by u..~g. it in the present short run, this shortened life is a cost of current use, and IS ~ed th_e ::; co$l of the instrument. The u.."Cr cost must be covered by reeetpt_s 1

1° ~~ 1

of present use, but if it is covered, we reckon the gross returns me usn e u..<:er cost as the quasi-rent.

252 Rents and Q .

1~1 1 . uast-n 1c on~-rnn net t·eturn on capttal goods must . 1 '1ellt3

· · ' YIC d tit mlcrcst rate; thetr l'horl-run gross rctum is a . e approprj Tl I

· 1

· . qunst-rent ate l<' ~r·:\p ll<'a lllu~t rHlJOn of qua~i-r·entR re t ·

h t · s on the t . R or -run cost curves of th~ firm (Figure 15_2). The radttional nt outpu t OA under competition (with demand firm OPera•-

curve D ) l\'

p ' ' and thl'

MR

0~---------------------------A+---------------------------------------­O

Figure 15-2

n~grcgatt.: returns to nonvarinble producti,·e sen·ices are OA X BC. t:nd~r monopoly conditions (with demand curve D~) the aggregate qua,t-rcnb an: OA X BO. These are quasi-t·ents inclusive of de­prcri_ution . If th~ r<' arc :seYeral capital goods involved, their separate qua:-1-rents would be determined by usual marginal productivity ::ma ly~i :>.

lication of Re11t Theory .411 APP . . 253

CaJlital val ue of nn ext tmg capil:d good ,, .11 b

The • · , . .vr e eq 1 l lt \"li tH' of 1t~ futur(' qun:sH·cul o I f tl ua to Hr"e ' .,. 1C expect d

the I . - vear t are R,, and the intere t rate i i n . e quasi­rents tn J ' te \' alue of tht "ood is " R2 + R3

V =" R. + (1 + t) (1 + t) 2 + ... + R. S (1 + t)•-• + {1 + 1)•'

. ' t bas an expected life of n years nnd a ~alvage val f S If 1 h . t 1 . ue o . If we ask why t e quas1-ren s c ertvcd from a particular d

. t' l' f f . pro uc-. .1nstrumcnt o,·er 1ts en 1rc 1 c mlcd to return the or1·g1·n 1 t1ve . . a cost

of the instru~ent. pl.us the ~PPI'Opr·l,ate mle~cst on thi:s investment, the answer wtll nh\ ays be. because of mlstakcn expectations at ~he time the investment was made. The entrepreneur must predict

I , fu ture course of the l:iUpply and demand for the services of th t 1c . . . b .1 1 e instrument, a.t the tun~ It IS ttl t . f the pace of technical advance is greater than he predicts, or the demand for the industry's output. less, the quasi-rents will _ not return the in vestment plus the expected rate of return. There wtll probably be nn asymmetry on the other side: if quasi-rents are larger than were expected, new instruments will be added until these extra qua i-rents ure <'lirninated, _0 the e,_-tra gains will have a shorter duration than the unexpected losses. The asymmetry arises, of course, becau e one can build a machine or plant much more quickly than he can sensibly wear them out.

Since errors in prediction arc inevitable, the entrepreneur must take account of them in his investment decisions. The more special­ized he makes a machine, the more likely it is that its quasi-rents \\;ll not be what he expected, because the demand for a les spe­cialized machine will be more stable than that for a specialized rnacbine. Similarly , the less durable the machine, the sooner the invest-ment can be disentangled if it proves to be unwise. \\e therefore expect to find the mo t specinlizcrl und durable inst ruments in the indul!tries with the most stable demands and technologies.

AN APPLICATION OF RENT THEORY

The superhighway,.: th:at are bt?ing built from the periphery t~ the center of American cities oiTer u variety of interesting problems

'

.... .

254 Rents and Quas. b

t~~ent

for rent theory. !-ct .us consider only the question: what is the rna ~ nitude nnd di~trlbutwn of benefits? . g

T o keep the problem concrete and s1mple, we shall study . ·n a plane with all laborers working daily in the central bua. Cit)· t ' ' . b 'I SJness di trict. A ~uper highway JS now u1 t out to the periphery .

. . d t d . Jn one direction. 1~ redu~es the b~te redqmre o. tr1

1ve

1 to work by half

for those livmg adJacent to 1 , an 1~ppropbna .e y ess for those Who Jive near it. We can draw contour mes s owmg equal travel f to the central. city .before (wit~ concentric circles) and after1~: highway is bmlt (F1gure 15-3).

The cost of tra.veling ~o. work is the sum ~f . automobile costs and time and stram of dnvmg. One hour ?f drlVIng has been esti~ mated to be worth perhaps $1.50 to the dnver, and the automob'l costs a re perhaps 82.00 per hour. If the driver makes 240 rou~; trips a year, the travel costs become $840 a year. As between two Jots previously one hour from the city, t ha t on the highway will have about $300 or $400 lower commuting costs per year,G and the value of that lot will be greater by the capitalized value of this sum, or perhaps $5,000.

If the population's demand for residential land was inelastic the highway would lead to a reduction in aggregate residen~ tial land values, for the effective supply of residential land has risen (by almost half the diamond shape in Figure 15-3 ). But what­ever the elasticity of demand for residential land, a new pattern of land values would emerge, and it would be governed (exclu­sively, in our simplified model) by the structure of transportation costs.

Since land becomes cheaper, the more distant it is from the city

'For those people living off the highway, the driving time from distance d (mellSurcd along a radius) will be one-half t.he former time plus the time necessary to cross over to the highway on an urc. If the angle between the radius on which they are located and the highway is e, this circular distance to the highway is do, so tbe boundary of the a rea benefitted b.v the highway is given by do+ d/2 = d, or o = 1 (about 28°). Within the benefitted area (8 < ~), the equal driving time con tours (d') are gh•en by solving d'e + d'/2 ~ d, or d'!d = 2!(28 +I). The area of the new territory within the 00-rninulc zone is found (by integration) to be about one-sixth of the init ial largest ci rcle.

• The S840 figure, und any based upon it, must be scaled down because there are on aYernge perhaps 1.8 persons in each commuting car.

Highway

Figure 15-3

255

te but building costs decline much less, if at all, as one moves cen r, ·t· l · t b '!din t 1 nd will be used in large1' quanti 1es re at1ve o u1 gs. ~e~c: the density of population will also decrease as the distance

from the city center increases.

RECOMMENDED READINGS

Barnett, H. J., and 0 . C. Morse, Scarcity and Growth, Baltimore: Johns Hopkins University Press, 1963.

LOsch, August, The Economics of Location, New Haven, Conn. : Yale

University Press, 1954. Marshall, A., Principles of Economics, London : Macmillan, 1922, Bk. IV,

Chs. 2, 3; Bk. V, Chs. 9-11. & Turvey, R., The Economics of Real Property. London: George Allen

Unwin, 1957.

256

PROBLEMS

1. Let there be 1,000 t>ach of three types of farm, the marginal pr schedules of which a re as follows: oduct

LABORERS

1 2 3 4

etc.

TYPE OF FARM

A B C

100 96 92 88

etc.

92 90 88 86 etc.

80 74 68 62

etc.

(a) lf there are 7,000 laborers, determine the rent of each tyPe of farm and the w11ge rate.

(b) Do the same when there are 14,000 laborers.

(c) Destroy one farm under condition (a), allocate its laborers to other farms, and measure the decrease in produce. The decrease (the marginal product of t.hat type of farm) bears what relationship to the rent of that type of farm?

(d) A minimum-rent law is passed, under which no farm can be worked at. a rent of less than 50. With 14,000 laborers, find the effect on aggregate product and aggregate rent and wages.

2. The marginal product of labor diminishes on a given farm as the number of laborers increases. Suppose that the total output of the farm is fi.xed, and that an improvement takes place in the methods of produc­tion. It may be of either type:

(a) The marginal product curve of labor is raised by a constant amount. (b) The marginal product curve of labor is raised by a constant per­centage. 'Vhat. will be the effect on rent in the two cases? Compare your answer with Marshall's (Principles of Economics, Appendix L).

3. Let the production function of tobacco be Q = P:"L"' where P is labor and L is land. The demand for tobacco is p = 100 - Q/100. The price of labor is S2 per unit; the rent of l:md in other crops is S5 per unit.

(a) What will the price of tobacco be under competition? What will the quantities of labor and Jand be?

(b) Now reduce the land allotments by 10 per cent. What will happen to the price of tobacco? The ' 'alue of a11 allotment of R unit of land?

chapter sixteen

Wage Theory

b . ·8 much the most important productive service-it receives La 01 1 I . . fift} s or more of tota m come even m an economy ns well

fourk- d ~ith capital as t he United States. Adam Smith said that stoc e · · d b · . )OSe of productiOn was consumptiOn; an ecause he said the pul) . . . . . · true. But it is almost as true that the cond1tions and nature It, It IS . f I . I' f of a man's work are a maJor partbo 11s tke. . ...

Th. special s ignificance of Ia or mar ·ets to 1ts participants has IS . l h I .

led to many social co~tr~ls, of whiC ~ ~H.IC t 1e most Important from the economic viewpomt 1s the prolubJt.lon of slavery. Even YO]un­ta slavery-the making of enforceable cont racts for the long term

ryf 1•01ance of labor services-is prohibited. The moral basis for per o . . . h . . h t this prohibition is beyond q~estwn,. b.u~ 1t. IS ":ort nohc~g t a like most desirable things, this prolnb1t10n has Its costs. Smce the

orker cannot make enforceable long term contracts, he cannot :~1ift the risks of unemployment to the employer. Since the worker cannot sell 10 vears' services he may find it more difficult to bor­row against future earnings, and therefore to equalize his income stream over ti me.

We shall concentrate attention chiefly upon relat.ive wages in various occupations, but a few notes are added on population theory.

COMPETITIVE WAGE STRUCTURE

Competition tends to eliminate differences in rates of wage~ for similar workers in different occupations and geographical l~catJOns, for the worker who is in the job where wages a re low will move

257

258 Wage Th

to the higher paying job. This movement will raise eory . Wages .

mnrket the workers arc lcavmg, and lower them in th 1n the · e mark t workers nrc cn termg. e the

Equilibrium will be reached in the occupational and wage structure when the n et advantages of all occupge~graphicat to the worker arc equal. "Net advantages" embrace an\~ons open which attract or repel a worker, and the main content of the factors of competitive wage structure consists of the analysis of the theory tors. Aside from t he wage rate itself, these components of ,;se fac, vantages" are as follows. net ad.

Direct Occupationa l Expense

If a carpent er must provide his own tools but an empl ' oyee · a sash nnd door plant does not, the former must be comp 10

f 1 t f h. 1 . . . 1

ensated or t 1e cos o 1s too s, m arnvmg at t 1e comparative net d

f 1 t o F . a Van-tages o t 1e two occupa Ions. ew questwns are raised by th' .

1 . • lS Sim-ple example, but a host of subtle d1fficulttes are raised by th

. 11 . h . o er cases-cspecm y smce t e mcome tax allows one to deduct occ . 1 L . . t upa-bona expenses. et us g1ve JUS one e.'<ample.

A pr~fessor buys books on_ the subject he teaches. Are they an occupatiOnal expense? Yes, smce they are necessary to the work he does. P erhaps-but why doesn't he borrow them from the li­brary? No, because he likes the subject and would buy at least some of them even if he were not a professor, say merely a college president. And what if he doesn't get around to reading the book? Should it then be charged to furnishings? These complications can in turn be made more complicated, but they should serve to suggest the shadowy boundaries separating occupational expenses from con­sumption expenditures.

Costs of Training Suppose a young man of 17 just finishing high school is attracted

by two occupations. In one (A) he will earn $3000 per year until age 65; in the othct· (B) he must first go to coll ege for four years. How much should occupation B pay to offset the additional costs

1 One is: why docs not the employer pn.y directly for the carpenters' tools? The obvious answer is that a carpenter mn:v work for many employers, _but the provi~:ion of tools by workers is sometimes encountered in occup_attons in which workers do not change employers frequently. If a worker \nil use others' tools carelessly it is to the benefit of both worker and employer to ha\·e the worker O\\:n the tools : the employer saves the costs of careless­ness; the worker is bette r supplied with tools if their cost is less.

. tive W aoe Structure compett . . 259

. . g? 'fhcsc addttwnnl costs of traininrr arc t 1ntn . . o wo · th d'

of tra f r college (tmtJOn, books, and so on). and th. e trect outlaysb f~re his earnings begin. JJiving costs d~ring c lie four year d la.Y e b th l o cge are not e d' t' onnl cost ecausc ey nrc a ready covered by th .

ad 1 1 • f 1 1 R e mcome nn ' .11 be earned 1 1c enters 1. e should go thro h th 1 · ch Wl · · ug c fol-w 11 rithmetic (assummg an mterest rate of 8 towing a per cent):

0 upation A . cc resent value of an annutty of The P I $lZ.l891 , so the present va ue of

3000 X $12.1891 = $36,567.

~1 ~cr year for 48 years is ltfettme earnings in A are

Occupation B . The present value of an annmty of Sl per year for 4 years .

1. $3 3121. If direct college costs are S1500 per year, the presen~ vaiue of these costs is 1500 X S3:3121 = S4,96S.

Z. The present value of an annmty ~f ~1 ~r year for 44 years is

512.0771. When he leav~s college, hts _ltfettme earnings will have a. present value of SSo (hts annual earnm~s) x 12.0771. To discount this sum back four years to age 17, tt must be multiplied by

0.7350.

The two occupations will therefore have equal present values of

lifetime earnings if

SB X 12.0771 X 0 .7350 - $4,968 = 536,567

So = $4679.

It may be noticed that the interest costs of th: four year. d~lay · receiving income in B account for most of the dtfference; eltmma­~on of di rect school costs would reduce S;; o~l! ~o $4,_119.: Of course a lower interest rate would reduce the equthbnum difference.

To the investment in formal schooling we should also add the ·nvestment in acquiring knowledge and skill on the job. If for men ~r equal age and schooling one job will give experience in one ye~r that increases future income by $20 a year (as compared to e>..lJen­ence in the others), clearly it is a more attractive ~ob, ~nd hence in equilibrium earnings must be appropriately lower m this occupa-

' Since the various components of the difference are not a~?it~ve, there is no simple wny of breaking up the difference between the equtlibnum earn· ings in A nnd B, but . . . <Is resent ,-a]ue per

1 The four year shorter worlting life m B Lea to ~ P - t less than . dollnr of only $12.1891 - Sl2.0771 = SO.ll2, or about per cen

in A. r s4 968 or about 14 per 2. The costs of training ha\·c a present \·alue o • •

cent of the present value of cnmings in A.

260 . Wage Thel>ry tion.' Even today in Jllost econotnJCI) the amount invested in ac . ing training in the labor fo rce fa r exceeds the amount inv {JIJ J ~-

. ested 1 training through fo rmal education . n The life pattern of earnings in an occupation invariably d'

1 · t' 1'h · · · •sp ays a ris ing and then falling sec JOn. e nsmg sectiOn is due t increase in ability a ttributable to experience; the fal!in~r 0 ~he

d ( . . o secbon is due to dec•·en. cd competence an smcc earnmgs depend

I h ) upon amount of w01·k as wei as t e wage rate lesser amount (time intensity) of work. The lengths of these segments will obvious~!' depend upon the nature of the work, and the 1960 patterns . Y

. f th . g•ven in Figure 16-1 d1splay some o e val'lety we observe.

Ins tability of Employment

An occupation that offers steady employment will y ield lar · h t th · h · ger earnm~s, at t e sam~ wage ra e, an one m w 1ch unemployment

is at tunes substantial. If a postal clerk earns $4,000 a year similar occupation in which unemployment. averaged 5 per c~n~ would have to pay $4,000/ 0.95 = $4,211 to y1eld the same expected return. If the unemployment rate could be estimated accurately and i f men did not tend to stay unemployed longer when they re: ceived unemployment insura nce, the premium for unemployment in­surance would be 8211 a year (plus costs of administration ). The worker in the occupation with unemployment may be repelled by the uncertainties in employmen t and income, and demand an extra premium for undertaking them ; we now turn to this question.

Uncertainty

Within an occupation there wi ll be dispersion of earnings even for workers of the same age, training, and experience. Much of this difference will be due to differences in personal ability (a matter discussed in Chapter 18) but some will be due to other factors. Variations in unemployment have just been cited as one example, but others can be added: fluctuations in output due to weather (which affects many trades besides farming); fluctuations in amount of work due to business conditions; and so on. These forces will cause fluctuations over time in the average earnings for all members of the occupation.

• Earnings will be lower by the present value of the future income stream, whi<'h depends upon the age of the workers. If the nge is 24, and 40 years of the additional earnings will be receh·ed after the year, at 8 per cent the present value is $221.

. . Wa(Je Stru.cture 261 pet~-ttve

Co11l· d . t of truly random forrcs will ulso operate A f to on ~c · ac ry A sec d by fi rc; only one fla I c. mun can get the hug d

1 c close . h h dl Th e or cr; fll:lY J I injuries can h•t ap azar ~· C!"C random factors have person~ndencY to cancel out over t1mc, out they do not average souJC

0 :g a: I

"' 0 0 0 .... 0

"' '0 c: 0

"' ~ 0 s;; !:::. uJ :E 0 c..> z w ~ 0::: uJ :a

OCCUPATION AND EDUCATION CLASS

Physicians and Surgeons College , 4 Years + '

~--""'I Accountants and Aud1tors,

25-34 35-44 45-54 AGE CLASSES

College , 4 Years+

Bookeepers, H1gh School, 4 Years

Corpenters, High School I - 3 Years

Laborers ( except Form and M1ne ), Elementary School, 0 -7 Years

Form Laborers, Elementary School, 0- 7 Years

55-64

Figure 16-l. Life earning patterns for white males in selected occupations.

out completely in a human lifetime; if the standtud deviation .of the annual incomes in a n occupation is $1 ,000, the standard devia­tion of a lifetime average is about $160,• so 2.5 per cent of the occu-

• The standard deviation of the mean is tT/ \(ii, and n is taken here as 40

years. The standard deviat ion will be largN tf, as is hkely, there 15 sorne correlation of year-to-year fluctuations in earnings.

~ I U der Competition

E'

262 . . lV age TheOry pation will have hfet1me averages S320 above, and an equ 1 ber $320 below, the OCCUpational average.G a nurn.

Of two occupations with equal averages but unequal dispe . tt t. ? W rstons

which will be the more a rae tve. e may note one certain ff • · 1 t d' · ·1 e ect· the occupation w1th t te grea er 15pers10n w1 I pay more in . ·

taxes. A progressive income tax takes more from two incotncome $5,000 and SlO,OOO th~n it .takes from two inc~mes of $7,S:e~~f will make the occupat10n w1th the more stable mcomes more att 8

tive, since it is income after tax that workers will seek to equ 1:ac-. h' ff t 'd th · 1 a tze. Puttmg t 1s tax e ec asi e, ere 1s no c ear answer to our

tion. Some people believe in their good luck, and will prefequ~­occupation with larger prizes; others will take the opposite c~ . e

h k h I b h . . . 01ce.

How t e mar et as a w o e e aves IS espeCially difficult to det _ mine, bec~use all obsen:ed disper~ion is co~pounded of the effe:~ of uncertamty and of differences m the abthty of individuals a d dispersion due to the latter cause is not relevant to the choice.' F: _ tunately our knowledge is incomplete; there is still work for futu~ generations of economists. e

Other Factors

The foregoing list of factors which influence t he occupational structure of wages is essentially that of Adam Smith. Research since his time has quantified some of these factors, but it has not revealed many others of comparable size.

Differences in living costs have proved to be one substantial fac­tor. Costs are consistently higher the larger the community in which one lives, so occupations which are concentrated in large cities must have higher average earnings than those concentrated in small cities. Thus it has been estimated that average incomes of lawyers would be 20 per cent lower if they were distributed among city sizes in the same proportion as population.'

Several other factors have been of comparable importance but of narrower scope. Prestige and social esteem are important in a few occupations, but more often the esteem attaches to those occu-

• This dispersion of individual earnings is independent of that due to fluctuations in average earnings of the occupation over time which also may command a risk premium. '

• M: Friedman and Simon Kuznets, Income from Independent ProjessioMl Practu;e (New York: National Bureau of Economic Research, 1945), p. 184.

I

lf ages n . . . . 263 . which ea.rnmgs are large. Ractal dtscnmination h h

· ns 10 . • • fl 7 as ad pa~~portant but dechmng m uence. an 1•"

S lJNDER COMPETITION ~~GE . . h

d ·re of workers to maximize t e net advantages of w k

'fhe esl h' h · ld th · or . ad them to jobs w tc yie . e m~XImum sum of net mone-\Vlll le . s (that is, after deductmg all dtfferential costs) plus non-

rY return 'd f . k d ta returns (av01 ance o ns , an so on). If all workers rnone~ den tical ability, we could be confident that the long-run were 0 1

rve of labor to any one occupation (and even more to supplY culocality) would be approximately horizontal. The only ~ ... y one k' f . . I . ..., that could be rna mg or a nsmg supp Y pnce would be a f~~ce st of training, but we would rather expect training costs r1510gllco an industry grew and special training facilities (external to fa as 'b

mi·es) became feast le. econo f 1 b'l't d d ·

8. e men are not o equa a 1 1 Y, an o not have Identical

ftnc nces for types of work, it is possible that the expansion of

pre ere · f 1 t't d l'ki an occupation will requue men o esser ap I u e or 1 ng for the k This will be much more true of broad categories-con­

wt%c~ion workers, engineers-than it will be of specific occupations ~arpenters, chemical engineers-because the specific occupation

n draw workers from similar fields. ca If there is a major expansion of demand for a large class of work­rs as has occurred in the professional fields ill the last hundred

e e~rs one would therefore expect some increase in the relative ~age~ of this group. As men of lesser n.ative abi~ty en~red_ physics or law or medicine, the cost of a. umt of theu services m these occupations would rise. The rise would be governed by the rise in training costs (and the higher costs of attracting men with stronger attachments to other work). Since the distribution of abilities is presumably more or less normal, with each small decrease in a~ili~ there will be a larger number of eligible workers, and the nse m wages should not be sharp. If we accept Adam Smith's view that there is little native difference between a porter and a philosopher, the rise of wages would be negligible. In actual fact, however,. the earnings of professional classes have fallen relative to less-tramed workers, for reasons we shall shortly discuss.

'See G. Becker, The Economics of D~cTimination (Chicago: University of Chicago Press, 1957).

264 Wage Theor,

:rhe long run in ~n occupnti_on_ will h~ve a length de Y chtcfly upon the penod of spectahzed traming. If the nu~cndent lawyers has been stable and is now to expand, it will re . bcr of yea rs before additionnl law school students can be gradqu~e three if the expnnsion is large it will take perhaps 5 or 10 year:~ d, 8lld la"·yers_' earnings to an equilibrium level.8 Actually the Pet~o~st.ore be considerably shorter because lawyers are typical of most may t ions in that m nny t rained men practice law part time 'foccupa.

. · ' I at all and constitute an Important source of supply if relative . ' · · 1 earmnga r1se m aw.

The implications of these remarks are that t he long t·un curve of an occupation wi ll be highly elastic and that th supbply

. . ' e s ort run !SUpply curve Will be less elastic, the shorter the period d the more highly specialized the labor (as measured by its p ~nd r · 1 · · ) erto o spec1a trammg .

H ottrs of Labor. Even if the number of workers in an occupat' is fixed, the amount of work they do will depend upon the ho:n of work. The efficiency of work will itself vary with hours a~ there is some evidence that efficiency increases at first, but ~ven­tually diminishes so that at some level (varying with the work) the marginal product of another hour's work becomes negative. Whether this is at 50 hours or 100 hours a week is an open question.

For the individual worker earnings will vary either proportion­ately with hours, or in greater proportion if overtime is paid at a higher t ime rate. When the wage rate rises, he may wish to in­crease or decrease his hours of work. He will normally wish more leisure as his income rises, but the cost of an hour of leisure is the amount that he could earn, and with a rise in wage rates leisure has become more expensive.9 Identifying these effects with income and

• Even then the structure of earnings as between inexperienced and experi­enced lawyers will not be in equiHbrium. Equilibrium in the structure of earnings of experienced and inexperienced lawyers, however, must be defined in terms of the growth of the occupation: experienced lawyers will earn mo~e relati\'e to neophytes in a growing than in n stable occupation, because thctr number will be relatively smaller in t.he growing occupation.

• In an indifference curve analysis, let the axes be hours of leisure and money income. The budget line will have the slope of the wage rate, for it is defined by

Money Income = (24 - L) Wage Rate, where L is hours of leisure. E\'en if leisure is a normal good, increases in wage rates can lead to larger or smaller amounts of leisure being consumed.

mpetitive Wages ~nw ~5

~ ·wtion, we may say that historically the dominant eff sub:,li 1 t of income: Hours have fallen by more th ~t h~s been t 11\ • an a thtrd 10 resent centuly. . . the P 't has been sa1d that m n modern industrial .

Often I 1 . soc1ety the . . d 1 worker has no contro over h1s hours of work a d: d

· dtvt ua . 1• k • n m eed tD . ngruous to vtsua Ize a wor er strolling over to ., i ·t is 1nco . h .. oreman 1 ·ng "I 'm lennng t e assembly line now for 1 h . d saY• • , . . . • ave JUst an . . ed utility. Tlus IS a pervaslVc problem in social lif .t

)f\Xlt111Z • d . e-1 :ould be just as mcongruous to or er a ticket to the symphony or-

concert in a town of 500 people. chcstra · l · t't t' l · · The rigidity of ~0~1-n 1~s hl u IOI~ s, 1owcver, 1s e~s11y exaggerated.

. ._ much flextbihty m ours m many occupatiOns. Even within 'The I e 1::. . · • ( h'

Pation there are vanattons tenc mg loads vary among cot-an occu k d

f om 18 hours a wee 0'''11 to zero) . If n majority of worker~ leges r h I . . "

refer longer or shorter ours, emp oyers wtll find 1t profitsble to P . to this demand because they Cl'l.n get better or cheaper workers catet . · 1

d ·ng so. It wtll remn.m true t 1at anyone whose tastes differ by Ol • . tly from those of his fellows wtll be compelled to pay a subst.an-

~::; price (by way of choice of work) to behave differently.

NONCOMPETITIVE WAGES

There are two major noncompetitive factors which affect the wage s tructure, and we consider them in turn.

Opportunity and Wealth

John Stuart Mill created a doctrine of noncompeting groups in

1848:

So complete, indeed, has hitherto been t~e separation, so strongly marked the line of demarcation, between the dtfferent grades of labourers, as to be almost equivalent to an hereditary distinction of caste; each employment being chiefly recruited from the children of. lh_ose al~eady .em-

ployed in it or in employments of the same rank with 1t m soctrankal est~­, . . ·r . . all . r a lower ' llllve tion or from the chtldren of persons who, t ongm ) 0 . f .

' I . t ' The ltberal pro CSSIODS succeeded in raising themselves by t letr exer .IOns. . th 'dl f .tb the professional or e I e are mostly supplied by the sons o el er ~ ru'ted p from

. k.lled 1 employments are . u classes: the more h1ghly s 1 manua nk ·th them: . . h 1 f tradP<>men who ra WI the sons of slulled arttzans, or t e c ass 0 - . . . d unskilled

the lower classes of skilled employments are in a sllllllar case, an

' I I

m ~~~~ I b rs with occasional exceptions, remain from father to son in th . a oure , f

1 1 . e1r

pristine condition. Consequcn.tly the wages o. eac 1 c ass have hitherto been I t ... d b\' the increare of Its own population, ruther than of the g" regu a , . . .:nera) lotion of the country. If the profess10ns are overstocked it is b popu ... . . , ecause

the clnss of society fr~m wh1ch they have always maml~· been supplied, has greatly increased m . number, and because mo~t of that class have numerous families, and brmg up some at least. of thei r sons to professions."

The essence of this doctr~n~ is that workers are not able to ac. quire the education and trammg necessary to enter the occupati much higher than those in which they were born. This vertical i~~ mobility is due to. t~eir ina~ility to borrow the_ capital necessary to undergo the trammg reqmred by the professional workers and skilled technicians. Even though the implicit rate of return on in. Yestment in such training is 20 or 30 per cent a year, it will persist if few families can afford to make the investment.

The extent of such departures in wages from complete equaliza­tion of net advantages may well have been very large even when Mill wrote, but data for that period are very poor. In 1910 we can give an example, which also serves to illustrate the method of finding the internal rate of return. College teachers earned an average of $1,750 a year; urban public school teachers, $700. As­sume that the college teacher had four additional years of training, with expenditures on books, tuition, and so on, of $200 a year. The present value of a public school teacher's income was

$700 -.-, '/.

where i is the interest rate.11 The present value of the college teach­er's net income at the same age was

1750 200([1 + tl4 - 1) i(l + i) 4 i(l + i)4

If we equate these two values, we find that public school teaching and college teaching were equally remunerative at an interest rate of 21.2 per cent a year.

"Principles of Political Economy (London: Longmans, Green & Co., Ashley Edition), p. 393.

u This is of course the value of a perpetual income of $700. We could introduce the annuity values for limited working lives, but at a substantial cost in algebra-and the answer would not change much.

-------

· Wages 267 petit1.ve · J'{o1

1com· ther high interest rate, judged by what (sav) rail d

· ,1 ra • roa s 'fh~S IS •10 to get capita~,. and suggests that there were substantial

aid tn 19 eoples' ab1hty to borrow funds for educational pur-lp.'11jtat.ions ontp11 ated rate of interest is exaggerated to the extent ll The es 11 . . poses. O'C teacher~ were m~re able, and p~ssibly f~r other rea-that colle"' . 0 w1th all adjustments the mternal mtcrest rate ~~ but eve . . 5ons, b bly be fntrly !ugh. '"0uid pro a .· e in family income, and the increased subsidization ' reat ~~ .

'fhe g h rc reduced the Importance of \\'ealth as a requisite of school~, a~ecker has found that the internal rnte of return on to educatJOdn. tion in 1950 had fallen to about 10 per cent or to

II e e ucn Tl d . ' 11 co eg t after income taxes. 13 1c octrme of noncompetinO' t 7 per cen 1 ld b I b "' nbou . 1. s in manv parts of t lC wor , ut 1as ecome almost Ps still ru e . grou

obsolete here.

lJnions . . nodern noncompetitive force on wages is the labor !he mt'JO: ~or union is for the labor market the equivalent of

umon. T 110

. at! e product market. Unions vary immensely in their h carte m 1 ·

t e . · raising wage rates. At one extreme, a few umons ff ttveness m · · · f b

e ec b bl reduced average wages slightly m the process o o -have pro a y netary 1-eturns for their members. u At the other ex-. · non-mo · · · tammg . have occasionally raised wages as much as 100 per treme, umont~ com})etitive level but seldom has a differential of cent above le I I f t' ~~

I 25 r)er cent persisted for any cngt 1 o ·Ime. more t 1an t I . h . . · faces problems in organizing a tmde w uc are m prm-

The umon · · · t 1 Th I more (lifficult than those met m orgamzmg a car e . e ciple muc 1 . t tl b f ·ket·s is usually Immensely larger t. Ian 1e num er number o wot · · 11

fi d tl'e mte of turnover of workers m a craft Is usua Y of rms, an •

I t h were on average older, and their lifetime u For exam pi~, clod] beg~n es:al~~~ proportion to thnt of public school teachers average salary "ou e 1

than 1,750/700. "U d . t ent l·n College Edncation'r" Proceedings of the "G. Becker, ~ ermv~s I? American Econonnc Assoctat~on (May ~g~). f Uni\·ersitv Professors. To the

"An example is the Amencnn Associnllon ° · need for appoint-extent that the A.A.U.P. has p~rsuaded. profe~o~:r~!i~h<~osts to the employ­ments on indefinite tenure (for ~1fe) • wlu~h ha' ~ . Ia cr money income. ing institutions, they h:we s\Jbstltutecl tins. secun!) f~r t' ~ wage rates is H.

"The basic work on I he effee.ts of umo~s ~n &e ~ 1~ Stales: An Empiri­Gregg Lewis, Vt1ionism ancl R.elal.tue l~ages tnt_ e 19~/ cal Inquiry (Chicago: Unive!'Slty of Ch1cago Press, ·

268 Wage Theat-y much higher than that of firms. In a legal environment h . to unions as the American Jaw is to cartels, there wou~~ ostlle

· ~no umons. Even with a highly favorable legal environment, union

found chiefly in crafts and industries in which the !abo: are now is relatively concentrated, either geographically or in term ~arket ber of employers. Thus unions have usually been strong ~. 0 ~~~ and in fixed route transportation (especially railroads and m_ ~llung both of which are geographically limited labor markets. T~r tnes), explanation applies to the building trades, the clothing trad e (sName y k ) d . . ( . 11 es ew

or f , adn ph~mfltm~ ~spdec1ta . y ne_whspapers). The industrial unions arebb oun cd 1e y m. rn us nes w

1 It . few employers-automobiles

ru er pro ucts, pnmary meta s, aircraft and heavy el t . ' . ' ec riCa)

goods. In a ll these cases the umon has not had to overcom th immense organizational task of organizing many small plantae e f I . 1 . f h . , or o 1avmg a arge non-umon sector o t e mdustry whose com t'

t o ld k b 0 1 0 pe 1~ 1on wou rna e su stant1a wage mcreases impossible. ?iven cont~ol over the 1'1Upply of labor, the extent to which a

un10n can ra1~e. wage rates above t he competitive level depends upon the elastiCity of demand for the members' services. The rules of derived demand are fully applicable, so we should find that union effects on wage rates are larger,

1. The less elastic the demand for the product. The coal miners' unions could obtain higher wages before oil and gas became major rival fuels; the workers for D epartment of D efense contractors can get higher wages than those working for the commercial markets.

2. T he poorer the substitutes for labor. For example, plasterers face the rivalry of plaster board so the demand for their services will be more elastic than that for plumbers. The chief long-run sub­stitution for labor will of course come from capital equipment.

3. The less elastic the supply of other productive factors. The major instance of this rule is that existing capital goods are in in­elastic supply in the short run, so union wages can rise substantially when an industJ·y has much durable capital. In the long run most co-operating factors have elastic supplies, but mining land is an important exception.

Some illustrative estimates of the impact of unions on relative wages are reproduced in T ables 16-1 and 16-2. In these estimates

mpetitive Wages f/OliCO Table 16-1

Effects of U~ions o n Wages of Members Relative to

269

Non-unaon Workers, Selected Occupation!!

~========================U=NI=O=N=E=P=P=ECT=={~A=S=P=ER========= YEAR CENTAOE

occtJPATlON

'}ding craftsmen S]rilled b~uilding labor ColXIJl)OD •

. us coal mmers 'tuJI)lDO 't ]31 in local t ransl

Motormen . . ) (large c1t1es

]3arberB . "'I airline pilots Co1X1IIlerc1 .. Seamen

bber t ire workers . Ru I thing manufacturmg

1939 1939

1956-57 1958 1954 1956

1950's 1936-38 1946-57

OF NO:-i-UNION WAGES)

25% 5

53 12 19 27 20 14 0

Men's co . H G. Lewis, Un ionism and Relotiv• ll"aou in lht Unil•d Stalto: An Ernpiricallnquiru

souiiC" ·u •. rsi~y of Chicago Preee, 1963), Che. 3, 6. (Chicago: n•ve

PERIOD

1923-29 1931-33 1939-41 1945-49 1957-59

Table 16-2

Effects of All Unions on Wages of Members Relative to Non-union Workers, 1923-59

AVERAGE EXTENT

OF UNIONI SM

7-8% 7- 8

18-20 24-27

27

EXCESS OF UN ION WAGES OVER NON-UNION WAGES (.\S

PERCENTAGE OF NON-UNIO~ WAGES)

15-20% more than 25

l Q-20 o-5

IQ-15

souac>:: Lewie, Unioniem and Relatice Wage, in tile Uniltd Statu, P· 193.

the measure of union effect is the excess of union wages over those of non-unionized workers of similar characteristics (age, sex, u~b~n­ization, training, and so on) .16 The tendency of collective bargammg to introduce short-run rigidities in wage contrac~s and. hence ~or union wages to fall relative to non-union wages m peno~ of ~~­fiation, and to rise in periods of depression, is strongly evtdent m

the economy-wide estimates. . . d. d tl se effects are composed

"Smce only relative wages are bemg stu 1.e. • •e . 1 d (2) non-union of (1) union wages higher than the corn~et1tt\'~ le\ e 'r ~ proportions of wages lower than the competitive level, w1th we~ghts 0 e the laborers in each class.

270 Wage Theory

Member::; of the Rjgo~ Cl.ub will ha.ve observed ~hat nothing has been said about the obJect.Ives of umon wage pohcy-no conv

be · k d N · en.

tjonal maximizing goal has en mvo ·~ . one, ~ fact, has Yet found general acceptance among economists. A maximum wage r t which is presumably ~he goa~ of the individual worker, makesan~ sense for a union: tlus maxnnum would often be obtained wh the absolute minimum number of workers was reached, and mi ~n involve a trifling membership.17 The aggregate payroll of mem~r: of the union makes more sense as a short run goal,Is but leav open the question of how many members the union wishes-the v es high wage rates of the United Mine Workers have been accoe~ panied by a very drastic decline in the number of miners. m

In fact the central problem of union wage demands is to det • mine the goal of union membership. The problem is formally ana~r­gous to that of a cartel in which a majority of the firms can v ~ to exclude any minority from an industry. The chief constra·

0

~ on reducing numbers are (1 ) t he majority of a given time ~n not wish to exclude itself, and may ~ave an expected working ~:: ?f 15 or 20 years; (2) .often the umon members wish to provide JObs for sons and sons-m-law ; and (3) the larger the number of ":o.rkers wh~ are forced out of employment, the greater is the proba­bJhty of thetr reappearance as non-union workers.

NOTES ON POPULATION

Sin~e thi~ book is by and for economists, ~·e shall concentrat~ our dts~uss1on on the aspects of population change about which economists have something to say. They have a good deal Je to say th~n they will in twenty years: population theory fell 0~~ of economics af~r the Malthusian theory was emphatically rejected hy the expenence of the nineteenth century in the western world and only rece~tly l~ave economists returned to the subject. ' . Let us begm wtth the Malthusian theory, not only because it IS th~ most fa•.nous of all population theories but also because it contams a port10n of truth.

Thomas R. Malthus was led to his theory by an argument with

" The practice of feathe b ddi · · than he wishes for a iv r e ng-requmng the employer to use more labor higher wages. g en output-clearly substitutes more employment for

u This goal is compatible with work--'>haring, which unions often demand.

population 211 • tes ort . h G d . h . NO h shared w1t o wm t e v1ew that man would rea h

b·s {tltbet, w 0

fection (which was not described as clearly as 0~ 1 of per d . . I . . e st.!lte . ·r onlY evil an mept soc1a mstltutions were abolished

ll lSb) 1 • d h h . ::~~~;ded: tTe~:es~~ ;:~~ean~ ~~c! :~ic~e~:~~e~o~a::l~~~:::

h PersiS . fi bl ..

for t e . 1

reforms. It was a pro ta e argument: An Essay 5ocifl f h bY t1IlY . (t798) became one o t e most famous books in his-

p ;f}'nl a t;to1~ I 0,~ Or · ven been read by some peop e.

nd hM e · ·t· h t.orY· a tial Malthusian propos1 ton was t at labor has a con-'fbe ~sse~ price, governed by the . conventional living standards

stant 5 PPk·ng classes. Should the wage rate fall below this level h wor 1 • • . ' of t e t' of miserY and v tce would lead to a nse m death rate" pera tOD · . . c

the_ 0 . turn would eventually lead to a riSe m wage rat~s to the wh1ch 1?

1 (llo::ubsistence") level. Should the wage rate rise abo,·e

nventJODll ~ . ( d 'b) . . . co. Jevel a decrease m deaths an poss1 y earher marnages, w1th tht~ . birth rates) would eventually restore wages to the equilib­a J'ISe 1D riulll level. . . . .

1·0

wage rates leads to a nse m populatiOn which in A nse t nds to lower wage rates, but suppose the demand for labor

t~:~ ~ore rapidly than the supply? Not possible, said Malthus: ~he potential rate of growth of population far exceeds any con-

·vable rate of increase in the demand for labor.19

In fact popula-cet 25 . t d . h . tion could easily double every years, as 1t 11a m t e Amer1can colonies, but output could gro'v only "arithmetically," that is. by constant increments per unit of time. And the slightest knowledge of the Jaws of progressions, as he said, showed that the population series, 1, 2, 4 , 8, 16, .. . would soon catch up wit.h the potential output of the richest land, which would grow as (say) 25, 50. 75.

100, . ... 20

The error in the theory was double: population did not grow at an increasing rate as the standard of living rose in England, and the output of the economy did grow at a ~<geometrical" rate

(on the order of 3 per cent a year).

u His own language differed : population would grow much more rapidly than the means of subsistence. But subsistence formed the dPJDand (wages­

fund) for labor. • 10 In fact, with these series, population = 2" and output (measured i~ sub­

SiStence !'er head) = 25n, the population outstrips the means of su~stence by ~he Plghth generation-200 years for a society starting with a capa<.'ltY for 25 tunes the initial population.

m ~~~ y ct there was tl~c portion of truth. The cost of rearing c . ry

is surely a determm:mt of the patterns of birth rates hi1dren · d · 1 · d · We obse in n soc1ety, an so IS t 1e mcome enved from children' rve

. A b . . . s Work Cons1dcr first costs. s ctwcen two fam1hes with equ 1 · .

comes, the cost of raising children will be less, the lower t~ real ~ll­costs of those goods and services which children con sume :e~:~~tive more of than adults. The money costs of rearing a child IVely ever, not easily determined. We can calculate the expendit are, how­directly on children, and by comparing expenditures onures tnade items (housing, food) of families with the same incomes b ctod~tnon · f 'I · t' 1 · u Iffer mg :um y compos1 10n, we can a so estimate the indire t -children . This latter component, however, will often bee cost~ of t l f ·1· · h · negative· 1us anu 1es w1t an mcome of $5,000 spend less on rec t ' ·

I 1 l .ld 1 · rea1on i( t 1ey 1a.vc two c u ren t 1an 1£ they have none. Once on th' f 't h ff · · · bl · e Inks

o 1d~tsome sue l 'led ect 1~ 1nev1hta .e: mco~e is given, and as ex-pfe1n1 1Tuhres on c n re~ nse, ot ~r Items (mcluding savings) must a . c cost of a chlld surely mcludes the value of the act· ·t· . 1v1 1es

g.1v.e~ up by the parents: the smaller amount of recreational ac-tivities, t he lesser amount of travel, and so forth.

The expenditures on children (including or excluding forego d

. r . ne ex-pen Itures o parents) will rise with the income of parents for t d'ff . l wo

1 erent reasons. ~he quahty. of the goods purchased for the child (room, food, clothmg, educatiOn, medical care, and so on) will be b.ctter,_ the richer the parents-the child's standard of living will r1se mth that of the parents. The cost of a child wiLh a given stan­dard of living also rises with parental income: one large cost is the t ime of the parents, and this is more valuable the higher the (wage) income of the parents.

Consider then returns. The labor services of a child are of much greater value to a farm family than to a city family. I ndeed chil­dren arc a significant source of the labor force on farms. AB late as 1950, for example, 44 per cent of the 16-year-old boys on farms were in the labor force, but only 24 per cent of urban boys were in the labor force. It is quite possible that on balance the returns from a child exceeded the costs for farmers unt il fa irly recent times. The wcll-lmown excess of ru ral over urban birth rates is at least pa rtly attributable to the differences in costs and returns.

Can we go a step farther and assert that the larger a family's income, the more children it will have? T he historical evidence from the early nineteenth century until 1940 was emphatically against

·----.. problems . . . 273

.6 d :Malthusmn v1ew: durmg a period of . 10d1 IC . . unprecedented

thiS Jl f nily income, average family SIZe fell conti'n 1 · n at . 1 1 . . uous y Th rises 1 • nal studies a so a most mvanably show the · e

sccho h'Jd B poorest fam cross· . g the most c I ren. ut the modest reversal f b' -

. )lnVIO l t' 0 lrth ihes . 1940 and t 1e sugges 1on of larger family .,;z t h' aftei ' . . . '" e a tghest

rlltes . some recent Slll veys, suggest the positive a"M . t' • 11es ID d f th . . .,.,.,cia IOD. 1ncot 1 nation offere or esc conf11ctmg data is that ff t' eXP a . d . . . e ec 1ve one d of contraceptive ev1ccs 1s fauly recent and is PO"'" .d wle . ge h 1 . 1 · ~~esse kno . ·~·idely by t e 11g 1er mcome classes so observed f .1 h 1no1 e " ' am1 y llluc , c:till depart from parental desires.

. S }11R) ~ b' h stzef the effect of i~come upon u't rates is in doubt, there is no

I th t higher mcomcs lead to lower death rates. The rich d ubL · ~ . . er

o . voids the consequences of malnutntion, acquires a larger 0cteLY a 1 s . 1 <:ervice and underta {CS a large number of public health edtca ~ ' m . (pure water systems, adequate sanitation and "O on)

erVJCeS . ' ~ · 5 esearch efforts are devoted to spec1a l health hazards, as in Large r .· t b . I . d 1' . .

t. atment of mal m in., u e1 cu osts, an po 10myehtls. The de-

the le . . f death rates m the lost century and n half has been such

chne o • . to increase life expectancy at birth to perhaps three times its

as 1

·n ancient times and primitive modern communities. }eve 1

RECOMMENDED READINGS

B cker G. "An Economic Annlysis of Fertility," in Demographic and eEco,:omi~ Change in Developed Countries, New York: NatioMI Bureau of Economic Research, 1960.

Hicks, J. R., The Theory of Wages, 2d cd., London: Macmi~~· 1963. Investment in Human Beinos, Supplement to Journal of Polttzcal Economy

(October, 1062). Lewis, H. G., Unionism and Relative Wages in the United States: An Em-

pirical Inquiry. Chicago: University of Chicago Press,_1963. Marshall, A., Principles of Economics, London: Mncmilbn, 1922, Bk. VI,

Ch. 3-5, 13. . Rees, A., The Economics of Trade Unions, Chicngo: University of Ch1cago

Press, 1962.

PROBLEMS · 1 · l · that the presence 1. It is a view widely held among econoro1c 11s onarls · ,

. 1 d "•afel)' valve up t.o of a large amount of unsettled, tillable nn was a " . · ~ e that 1890, because it pl'ovided unlimited employment alternatiVes. · ssum

274 . . . Wage Theory there were no costs (and ununportaut bme lags) m any shift he industrial centers and frontier . tween

(a) Would the sudden loss of all unsettled land have affected w if so, how? ages, anct (b) How would the presence of the "safety valve" affect the

1 · · 'f · d ·a1 eve! (}f employment at any gtven tune 1 m ustn wage rates were (l) ri . (2) completely flexible? gJd

(c) Would the workers have benefited more, during the period to 1 if we had also possessed Canada? 890,

2. Will a shift from a wage system which pays only for hours k in a mine lead to different earnings than one based upon "portal to W(}t ed

- -portal'' pay? 3. So-called "truck" wage systems involve payment of wages t h

worker in kind, usually at a store operated by the employer. Why 0 tule I · · h' f wo d an emp oyer mstttute t 1S system o wage payment? Is it compatibl . h

competition? [Compare G. Hilton, Journal of Political Economye r1t 1957.] ' une

4. Thornton's criticism of competitive wage determination (p. 10) be dealt with now. Assume many identical firms and a common w: rate. One firm now cuts its wage offer to reduce its costs and selling P · Analyse the effects on wages and prices. nee.

chapter seventeen

t;apital and Interest

The tangible resources of .an economy consist of its working popu­. or labor force, and Its stock of useful things, which we call

JatiOD, . 1 . d fi 't' . 'tal On this all-me us1ve e m Ion, capital includes consumer capl · d (houses, furniture) as well as producer goods (plants, rna-

goo s h b I d II t I" h. s) even cas a ances, an na ura resources, such as land.

c 10e ' fi · · f 't I · h' A more formal de. mt10.n o cap1 a Is: an~t mg (other than a free human being) whiCh yields valuable setv1ces over an appreeiable period of time.

Capital, then, consists of all economic goods except people and perishables. P~ople a~e excluded because th~y cannot be bought and sold-<lnly tbe1r services can be traded. Penshables, such as a piece of pie or a band recital, are excluded because we do not wish capital to be a synonym for wealth-we wish to exclude commodities whose value simply equals that of their undiscounted services. A capital good, because it yields services over an appreciable time period, inevitably involves the appraisal of future as well as present services.

We can present the capital of a family or a firm or a nation by a gigantic inventory. It will contain commodities of great dura­bility, like hydroelectric dams, and commodities of short life which are held as reserves, like stocks of coal. Such inventories have been made, at least for particular classes of capital goods: for example, American manufacturing corporations had total assets of $210 bil­lion, or roughly $15,000 per worker, in 1958.

But capital can also be viewed as an accumulated fund of general productive power: as past income incorporated in particular physi­cal forms, or as particular forms which will yield money income

275

Po

276 Capital and 1 nterest in the future. We can add the values of plants, and 1 houses, and inventories to obtain total wealth. The a~d, and

. tl . f . lntere t rate makes 1ts appeara-nce as , 1e pnce o time, the price th t 8 ' . . 1 h' a allow us to rompnre next years mcome wtt 1 t ts year's income. s

CONSUMPTION LOANS AND SAVINGS

Most capital is used by business firms for income-product' · · · t t b · h ng Pur poses, but tt JS convemen · o egm t e study of capital in a · · -

economy where capital is not productive. Let us assume t~tntp_le this simple economy there is only one product· say coc at In

. · ' oanuts They are grown on free land wtthout the use of any capital . · ment, and therefore labor is the only productive service eqS~P-

b d h . · 1nce

cocoanuts can e store , owever, we may still have savin d borrowing, which we shall now examine. g an

The choice between consuming this year's income (cocoanuts) this year or next year is an ordinary problem in consumer behavi and can be analysed by the techniques presented in Chapter 4. or,

The consumer will have indifference curves relating consumption this year and each succeeding year. It is true that future consump­tion will be uncertain because future phenomena are uncertain: one may die before next year, or goods may be rationed, or new goods may appear, and so on. But one must make a forecast of uncertain events, and we shall assume that the consumer attaches a definite amount of utility to given amounts of consumption expenditure in

fu ture years.1

Let us consider only two years, although the analysis holds for any number. The indifference curves will have a conventional shape (see Figure 17-1) . If the consumer has no accumulated wealth, he wil1 have a budget line given by the present value of the two years' incomes,

y2 Present Value= Y1 + 1 + i'

where i is the appropriate interest rate. At this stage in the analysis this interest rate is arbitrary, and can be positive, zero, or negative.

1 The certainty of eventual death does not terminate this series of consump­tion expenditures, for a man attaches utili ty to the sums his heirs will con­sume. If he did not, the only insurance that men would buy would be annuities terminating at death.

. 1 oans and Savings 1,.,ptwn ·"

Co1lstt . -et of incomes, the budget line mav be wrt'tt

g1ven::. • ~n forB '

y 2 = (1 + i)(Present Value - y1),

277

lope of the budget line is - ( 1 + 1) . If the initial . 5o tbe 8 d y (which in our example is much small thmcomes l' an ~ . · er an y ) are . l • 'dual will save S dollars this year, and spend (Y + 1

'

1ndtVl S · I · ~ S X we . ) d nars next year, so IS 11s current saving In th [1 + t] o · . e con-

I 5' ~--1 I I

--~-- -1.. _s_ I I

!

I

L---~~----------~------~------------~.~ 0 ~· ~

Figure 17-1

verse case, where Y' 2

is much larger than Y'1, he will borrowS' this year and consume ( Y 2 - S' [ 1 + i]) next year.

If 1 his income is equal in each year, how will he behave? In ~he

· · ·11 1· 1 a 45° hne absence of an interest rate, h1s mcomes WI 1e a ong (Figure 17-2) . If he considered consumption in the two years to be

. . . (l'k I ) would have slopes of symmetncal the md1fference curves 1 e h - 1 along tl;e 45° line and equal amounts would be consm~edd.effac

. . f .• d the broken m I er-year. If the present consumphon IS pre el re · • tl 1

: allv greater 1an ' ence curve (II) would have a slope numenc "

• . ..

2i8 Capital and l nt ere~t

and he would consume more this year than next. In this lat~ we would say that he has a positive time preference. r case

At any interest rate, and with any set of incomes (wag ) . the two years, an individual \\-ill wish t{) borrow or lend a sp::i.fi Ill amount of cocoanuts. We may therefore construct a supply ed

d d ( ·c h . curve l if he is a lender) or a eman curve 1 e 18 a borrower). These

Figure 17-2

curves may be added together, to obtain the market supply and demand and thus to determine the interest rate. The interest rate can be positive or negative, as we illustrate in Figure 17-3.2

What factors determine whether a person will borrow or lend? The foregoing analysis t·eyeals two factors :

1. The pattern of income through time. If income is rising, the consumer will normally wish to borrow in early years so that his conswnption will be more unifonn through time. In terms of our

• ~ o lender will pay more in interest to a borrower than it would cost to store the cocoanuts for the year, howe\•er.

. LoMIS and Savings 2i9 ,,mP tt or1

CO''s 1 ger Y: and the smaller Y,, the larger the amount . lfl'il1u, the ar ...:ely when income is falling, the consumer will

dlfl!>' d ConVC• " ' . rowe · ., for future consumptiOn. IJOf rh·yeat- . h l . ~,·c in ea. ·terest rate. T he hig er t 1e mterest rate, the greater the - 2. 'fhe 10 •· g a nd the greater the return to lending. In terms

f bOrro"ln cost o

i

Figure 17-3

of our diagram the higher the interest rate the steeper is ~h~ bud~et line and the f~rther to the left will lie the tangency wJt an !D-, difference curve.3 d d

The absolute income of the consumer is often also intro uce

di · t this substitu-. " 1 h" ffect in ad uon o l • Strictly ~&king, there IS also a w.ea t e f Interest," Jouma

lion effect: see Martin Bailey, "Savmg and the Rate 0

oj Political Econom11, 65 (1957) , 279-305.

sw ··-

~ t possibilities

280 Capital and lnt ere8t

as a major factor, with the plausible expectation that riche will save hu·gcr fractions of their income than poorer peo rl J>eopJe large amount of statistical e\-idence that points in this ~·e. ~he

b . . I 'II . h lrection has been shown to e a statishca 1 us1on, owever,4 and th · · · t b t th · · · e effect of mcome on savmg IS a es ra er mmor, If mcome is d fi

a a longer tenn aYcragc income of the family unit. e neq

The tastes of people are a fina l factor of possibly maJ· or inft . -~ Many economrsts have asserted that most people are "im t' ,;

, · · t' f , . h pa rent or have a 'pos1tJve . 1me ~re erence ~~ t e following sense: If typical person had his chmce of equal mcomes this year and a year, or a larger income this year and a correspondingly sm nl~xt income next year,5 he would prefer t he latter pattern. Since b

8 er

sumption we exclude all risks, and also a ll interest on saving: ~­preference is a simple myopia with respect to future needs. Th : some people are so constituted hardly seems disputable, but the~ are also extremely frugal people who seem to overvalue the futur . it is said that the older families of Basel consider it profligate ~ live on the interest of one's capital- they believe one should liv on the interest on the interest. No one has been able to prove tha~ there is any strong tendency for the society as a whole either to over or under-value future consumption relative to present consumption.

At this state, then, the primary influence on saving in our cocoa­nut economy will be the time structure of wage income. In an econ­omy with a stable population and stable national income, there will be as many people with falling incomes as with rising incomes and the supply and demand for savings will be equal at a zero interest rate. If population or per capita income is rising, more people will wish to borrow (because they expect rising incomes) than will wish to lend and a positive interest rate will be necessary to bring de­mand and supply to equality.

In a world of only two time periods, such as we have contem­plated, if a family saves in one period, it dissaves an equal amount

• The explanation lies in the association of transitorily high or low incomes with transitorily high or low savings; see p. 35 above, and especially M. Friedman, A Theorv of the Co118tLmption Function (New York: National Bureau of Economic Research, 1957).

• Notice: we hold the total income of the two years constant. If interest were allowed on the first ye.ar's income, obviously everyone would prefer to receive both years' income now, and invest a portion to increase his aggre­gate inoome.

281 est'f1len · · · th d [ntl ,. nte discoun t mg ) m e secon period. Therefo th

Prop•~<· . . . re e ner RP f mily 0 qm1.ls rts savmg, or Its total debt equal 'ts

(11 I of a a . h' 1 1' . s I Pitt\ . Even m t 1s cnsc t 1c equa 1ty rs only superfici 1. ell o~·rng. . ta t f . a .

net bOr~ a stock, as of some ms n o . trme, whereas savings are apitlll IS 't of time. H ence we must say that savings were N

c per uni . d d th t . flo"' ·ng a given per10 , an a capital was N cocoanuts ll uts duri cocoan d of the period. . .,t the en form another function: they serve as a reserve for " . gs per

savtn . h emergencies. The worker may become ill , or unem-1. g Wlt to h' th' . dell rn d eeds a reserve carry 1m over IS penod. Or un-

p}oyed, an n may arise. A highly negotiable reserve is therefore 1 expenses · t · usua ·

1 In a regime of uncertam Y some savmgs will be made

!Ilost ~se!:e· absence of fa11ing inc~mes, ~ositive interest rates, or even 10 f nee " simply to provide this reserve. In our simple

. pre ere , 11tune 1 viously the reserve must take the form of cocoanuts ; econoill~ 0

) society t.he function is served not only by money sav­in a roo bernk account or currency) but also by holding assets (a . gs (a an . d'l bo lD k ) against which one can rea 1 y rrow. house, stoc se then ·with a savings function, in which the fraction

We emerg ' d ( ) h . . 1 's income that is saved depen s upon 1 t e t1me pat-f a faml Y . 0 h family's income, (2) the mterest rate, (3) the extent

tern of tt ~ ties against which reserves are to be held, and ( 4) indi-o£ uncer am . . h .

1 "ta tes" (family size, age, and so on). In addition, t e jrac-

vidua s · h b I te I I f · . f · n"e saved may vary w1th t e a so u eve o mcome, twn o mco ' . . ~ . ntly this dependence IS weak at best. We note m passmg but appare . . rage savings run at about one-tenth of national mcome that on ave . .

·. h u 'ted States and that this annual increment of savmg IS rnte m ' . . . on the order of 3 per cent of the existing caprtal stock.

INVESTMENT POSSIBILITIES

So far we have ignored any possibility of investment in o~ sim­ple cocoanut economy. Let us now assume that it is posstble to invest cocoanuts to yield a return (obviously in cocoanutsffi) · .Fotr

t h I nd learn more e c1en example the laborer·s may go o sc 00 a . h 1 ~ethods' to collect t he cocoanuts, and the costs of att_en~ng sc

0

1°

· t t ·5 embodied 10 peop e. are paid in cocoanuts · bcl'e t he mves men 1 11 _

Or a machine of some 'sort is built to expedite the process of co ec tion; here the investment is embodied in a tool.

282 Ca'{Yital and 1 nter~t

It is in keeping with our general knowledge that the in process is subject to diminishing returns. Whether the investlllent

~ . h . . Vestllle takes the form of machmery or (t rough trammg) increa d . ~t of the worker, in our simplified economy, the enterprise :.u skin that additional investment will yield diminishing rates of 1 find This diminishing return arises because of the diseconomies 0~e!1Jrn. for the individual firm, not because of diminishing returns to .,~ale

h 11 di h. 1 caPital in the economy. ~~e s a . scuss. t 1s. atter problem below.) In modern societies relatively ht t!e mvestment is undertak di

rectly by the individual saver--chiefly in consumer durable en d­(homes, automobiles) and in small scale enterprises such as fa~ s and retail trade. The great preponderance of investment is und ng taken by specialized business enterprises or that most insatia~~~ of all consumers, the state. Nevertheless we shall assume for a tim that the individual consumer also makes investments. We do thi: chiefly out of deference for the precedent set by Irving Fisher whom we are following in this area, but incidentally to save on~ diagram.

This individual has a variety of possible investment opportuni­ties. On a farm, there is a whole array of machinery of varying productivity relative to cost, and in general each type of machine comes in different sizes and qualities. For the home builder (since this is also a form of investment) , there are obvious possibilities of varying the size of the home, its attractiveness, its equipment and furnishings, and so forth.

If increments of investments are ranked in descending order of productivity, the yields in income next year for increments of in­vestment this year will form an investment opportunity curve which is concave to the origin. That is to say: each additional equal incre­ment of this year's income devot-ed to investment will yield a smaller increment of income next year.

If the interest rate at which one can borrow (and lend) is con­stant the indjvidual can borrow a dollar on promise to repay ' (1 + i) dollars a year hence, so the budget line continues t<J have the slope - ( 1 + i). The assumption of a constant interest rate, however, is implicitly a strong assumption: normally one would have to pay higher interest rates, the more he borrows, simply ~e­cause the risk of default increases as the borrower's own equtty becomes smaller relative to the loan. Our assumption of constant

t Possibilities 283 tmen . .

/II res . mplies that there IS no nsk of default, and theref t rates 1 . . ore

. t.eres · e of investments 1s certam. IO 1 outconl . d. .d I b tl1at t 1e .. b ·um of the m 1v1 ua can now e presented in a sm· _ · uth n · ·

Th.e e:ro (Figure 17-4). Th~ mvestment _opport:unity curve VRF Je diagr 001binations of mcomes available m year 2 as one

g .:: the c d 1 f d displaY~ his investment (measure e twar from OF) . The maxi-increases

Yz r v

c

0

I ----t--

1 I I I I

A p

Figure 17-4

. . d h v RF exceeds the budget mum year two income IS achieve w ere . . I t) where . . t (what 1 ~ eqmva en ·

line FM by the maximum amoun ~ or ., th investment op-a budget line TP, parallel to F M, IS t.angen. ~ to. e t ent AF and

. t· mt w1th mves m · ' portunity curve. R 1s the op 1mum P0 . ' R . . 1 · . t ent plus mterest of H · retums beyond ongma mve::; m . · year 1 rela-

f nee for mcome m The consumer has a strong pre ere . d wn If the · 1· ff nee curve IS ra · · tive to year 2, however, as the m< J ere

....

:.: •'

284 Capital and lnt individual's wage income in the two years is given by ( ereat L, the individual's budget line will be given by TP, w~~~ .P<lint budget line through L (or FM) plus the excess of returns Is the on investment (!JR = MT). The individual will requi ov.er costs of AF (for investment) and OB (for consumption) in pre . Incomes he will borrow A.F + OB- OQ, and repay this sum pl en~d 1, so in period 2. us Interest

The main point is, of course, that investment opportun·t· · d d f · 1 1 Ies no\\· mcrease the eman or capita , and create a positive int eYen if none would appear in the consumption loan mar~et rate modern industrial so~iety the investmen~ demand for cap~t~lln a exceeds the consumpbon demand except m times of war a d far ductive uses of capital dominate the interest rate. ' n Pro-

CAPITAL AND INVESTMENT

I nvestment is a flow of resources devoted to the producti f f t . h . 1 . k on o u ure mcomc, w ereas cap1ta IS a stoc of resources. Thus inv t-ment i.s the annual (or other time period) increment to the st~:k of capital. . Suppose that the supply. of c~pital is infinitely elastic at a given mterest rate: the commumty will (eventually) Sl.!PPIY any amount of savings-resources for investment-at this interest rate. In anv one year the amount of investment will he limited to the availabl~ amount of new savings, but each year a new supply of savings allows additional investment. We naturally seek to know two things: how much capital will ultimately be demanded at this inter­est rate; and how rapidly this eventual level of capital will be approached.

It is possible (but not necessary, as we shall see) that a day will come when there no longer exists an investment opportunity which will yield the given r ate of return. The economy will pre­sumably become stationary at this point: capital will only be maintained. Moreover population must presumably have become stationary, for continued population growth would surely create ad­ditional investment opportunities in both producer and consumer capital goods. Hence only if a stationary economy eventually is reached can we state that there is a definite schedule relating the marginal product (rate of interest) of capital to its quantity.

d Its Returns 28 ·tol an . . . 5 CoP~ t which this stationary state lS approached tb

te a • - e rate 'fhe ra. ~trnent occurs-would presumably be governed b th

. h 1nve~ h . . Y e t "'hlC f savings at t e gtven mterest rate. An attem t t a ·HtY o . p o vllilnbl 1 . her level of mvestment would lead to a rise in 1· t

11 • a ng . . 1

n er-)11jntll10 1 . 11 would ratiOn cap1ta demands to the most produ n w 11C . . c-

est. rates But the annual mvestment ~s so small a part of the tive uses. d capital stock that we may mfer that only a small rise accumulate. tes would be necessary to lead to a substantial curtail­in ioteres~ 1 ~ stment: the schedule of the marginal efficiency of lllent of 10

' es it is called, would be fairly elastic. trnent, a · "l"b · · inves ct there may extst no eqUI I rJUm quantity of capital for

Jn fa . t st rate as we shall now see. ·ven tn ere ' a gl

TAL AND ITS RETURNS CAP I

·nal returns to any productive service decrease as its The rnargl f d" · · h" t C · · . reases by the law o 1mm1s mg re urns. ap1tal 1s

tity !DC ' • · quan "ly subJ. ect to this law because, unhke all other produc-t necessart

no s it takes on all forms, and therefore we cannot prop-tive resource ' "

h ld "other factors constant. eriY 0 .d the labor force. In a society which excludes enforceable

ConSI er h 1 . t . th t" 1 bor contracts, we nevert e ess can mves . m e quan -tty

Jong-runl.:y of the labor force. Let us put aside the fact that a and qua 1 · · W t"ll · . . b" tl 5 may come from nsmg wages. · e may s 1 mcrease nse m tr 1 • • . . . d the labor supply by appropnate. mvestments. m samtatlon an ublic health measures, by industnal safety devtces! and so on. We

p tly ·Increase the quality of the labor force by tmmense annual curren · b · · f th · t t ·n t}1e formal education and on-the-JO tratmng o e mves mens I . labor force. It has been estimated, in fact, that th.e annual mvest-ment in labor skills in the United States substantially exceeds t~e investment in tangible capital goods. Although we can ~ect di­minishing returns to capital when given. workers are gnren ~ore and more equipment, marginal returns w11l surely fall less raptdly when we increase the quantity and quality of the workers. th t

Or consider the natural resources-all the productive fadctorbst .~11 d "I d" We no ou WI the classical economists subsumed un er an · . . f ...

· t ive cultivatiOn o " get diminishing returns from the more m ens . . . · thods of mcreasmg given piece of land. But we can mvest 10 me · f 1 borers

. 1 d . t as we can or a . the effective quantity or quahty of an , JUS

-

286 Capital and 1 . . . ntereat Land can be impro:ect by dram~ge, Irrigation, and the l"k aeccssibility can be mereased by mvestments in transport

5I e. l~

In the cnse of natural resources such as oil or coal we Y~tetlls. d . ~n~

in exploration for n ew eposits. ·vest Finally, diminishing returns rests on a "given state of

arts"-a given level of technological knowledge. Yet inve t the k I d · · s ment · the d iscovery of new now e ge ts stlll another way in h ' lll

. I Th It' t' f " w tch w may employ captta . e cu ·Iva ton o research and dev 1 e . I b . e oprnent" m recent decades 1as ecome so extensive that this type f . ·

· l ' k l b 0 Invest-ment ts no longer 1 e Y to e overlooked or undere t' . d s tmated

If labor and natura, resources an the state of know! d · change when capital increases, diminishing returns to cap~t g~ all highly uncertain. In fact the theory of capital becomes a ~ are of general economic growth, and if the rate of saving from I·n eory · f f d' · · h' come IS c?ns

1tant,t an asser 1t~n o f tmmtds tt~g ~eturns to capital is almost

eqUiva ent o an asser IOn o retar a ton m e<'onomic growth.

RECOMMENDED READINGS

Fisher, I ., The Theory of Interest, New York : Macmillan, 1930. Friedman, M ., Price Theory, Chicago: Aldine, 1962. Hirshleifer, J ., "On the Theory of Optimal Investment Decision," Journal

of Political Economy (August 1958). Knight, F . H ., "D iminishing Returns from Investment," Journal of Political

Economy (March 1944) . Lutz, F ., and V. Lutz, The Theory of Investment of the Firm, Princeton,

N.J.: Princeton University Press, 1951.

PROBLEMS

1. An individual has wage incomes of $1,000 this year and M,OOO next year. His utility function is U = C.'I'C,'I' where Co and C, are consump­tion in years 0 and 1. How much will he borrow in year 0 if the interest rate is 0? If it is 10 per cent?

2. The inte rest rate for loans for one year a re 7 per cent at the beginning of 1900 and 5 per cent at the beginning of 1901. What will the interest rate be on loans for two years at the beginning of 1900?

3. The economy consists of an industry and the government. The indus­try borrows half its capital at 4 per cent (bonds) and raises the remainder at 8 per cent (st.ocks). The government can borrow a t 4 per cent. Should

287

frobl8~ dertake investment projects which yield 4 per cent ent un '

go"er[llll r 8 per cent? . . . tbe

6 per ceJlt, 0 . ation of the mterest rate. under Simplified conditions.

or 'fbe dete~ to Professor F. H. Kmght.) Crusoe builds a tool in 4.. exaxnple 15 ue the productivity of his labor by 5 per cent and lasts

('fh15 · ·ncreases 300 d ) d ys · 1t 1 f r simplicity, has ays .

z5 8 (each year, 0 . . . 5 years . h interest rate If the tool reqUires no repaus or main-

( ) W}la.t lS t e ·ation allowances do not yield interest? a d deprecl .

tenance an . th interest rate if the tool reqUires 5 days of repairs a (b) Wbat 15 ebe used during this time? year and c~no~ ·nterest rate under the conditions of part (b) if (c) ~a~ IS ~o~a~ces can also be invested to yield the current interest deprectatton a

rate?

-~--

ehapter eighteen

The Size Distribution of Income

Although the size distribution of income-the distribution f households by size of income-has been the most important questi~ of public policy over long periods and in many countries, it is ~ a11 the major topics discussed in this book, t he one that has be:n studied least. There are a thousand thousand criticisms and defenses of the income distributions of various societies, but they have em­phasized moral and ethical factors. These factors are important but so too are the economic aspects of the problem, and they will be our sole concern here.

The income of a household consists 6f its labor income and its property income. Of these the labor incomes are much the more important, accounting for something like four-fifths of national income.

LABOR INCOMES

The labor income of a household consists of the sum of the labor income of its members. Let us begin, however, at a still more basic level, the individual worker.

Earnings of the Individual Suppose all men in an occupation to be strictly homogeneous:

they have the same abilities, training, and experience (which is really training in a broad sense), and are therefore of equal age, and when employed work equally long with equal intensity. Their wages would still differ because of chance: luck in an older language, ran­dom fluctuation in a newer.

288

289 1 comes

ro.bllf 11- ts of luck are infinitely numerous but we may JJ ponen

'fbese coJJl . to rough ly t hree groups: . tbeJJl tn . . .

l¢1h' t 5 vic1ssitudes of health and accident. c 1 fac or-persons f tors-vicissitudes of any one employer, both

1· Ernployer

8~) and economic (bankruptcy). z. jcal (fire, flooto s vicissitudes in finding new jobs, or getting

pbY5 k t fac r -3. :Mar e of pay fo r given work.

1

best rate the

t-u.J z _.~0 <! ::> z z <!

Figure 18-1

High School Graduates

50 AGE

If we could find a group of identical workers, the differences in

their earnings would measure these factors. . . d tical Let us now still keep the members of the occupatiOn hl en . st

in abilities, and move them back to age 17' ';!en ff ~:~ th:v:h~~ce finished high school. Then let each young ~an ° e tream of two kinds of future income streams (Flgure 18-1) · ?netos m

1 b f e and begms ea · begins immediately- he enters the a or ore II for 4 years The second stream assumes that he goes on to co ege:

M k t" Journal of Politi­' On this last, see my "Information in the Labor ar e '

cal Economv, Supplement (October 1962).

290 The Size Distributi · · . on °1 Inc It IS negative (by the amount that his tuition b k 0711

e exceed part-time earnings), and then positive.' E

00h s, and so on

after formal education is completed because ac stream rise' k. d I men learn l s

wor mg, an t 1en eventually declines after so a so by ergies and abilities decline . me age, as their en-

These income streams can have the same d' t

l. d f d . 1scounted 1 Lle ay o gra uat10n from high school ~ and in . . va ue on · · t l d. ' competitiVe ~1um 1e 1scounted values will indeed be equal. The life . equilib-

mgs, as represented by these present values are .d t' -tune earn. t dd

. . ' I en 1cal y t h are now wo a 1tlonal sources of dispersion: · e t ere

1. The variation in earnings among individuals with . education because of age. giVen formal

2. The va.riation in e~rnings among individuals with because of formal educatiOn. given age

In fact we should not emphasize formal educatio be 1 I k

. n, cause one earn a so at wor ' and m most societies in tile ld can

t · · · · wor much rammg IS obtamed at work than in schools l.f '" Inore

b · ' .... e measure tra· ·

Y 1ts effect on earnings.3 mmg We have reached an interesting conclusion. If the · t. f . . . men m an occu

pa 1on were o Identical ab1lity, and worked equal pe · d d . -l

. te . rto s an With equa m ns1ty, the present value of their life time ea · be equal (chance factors aside) ' but their earnings in arnmngs would

I ·t . · d . · Y one year or s 101 pe110 of years would d1splav substant· 1 d' · Ch · ta lsperston

~nee fac~rs w?uld a lso be relatively less important over th~ entire workmg hfe, although there would not be com 1 t cancellation} P e e

There wo~t~d in fact be a larger dispersion, even under these as­su~ed con~1t10ns of identity of worker's competence at age 17, than ~h1s analys1s suggests. Some dispersion is essentially nominal and tf we could c.orrect earnings for differences in costs of livin~ and cost.s of workmg they would vanish. E xttm)1les are the higher wage

'Here we put aside ~he problem. of borrowing to go to school, by assuming th~t. loan funds are avmlable nt 11 gwen interest rate.

See p. 259 above. • <?anceJlation would be incomplete been uS<' of dcnth nnd serious ailments

~wh1ch w~ have put a.side) and more genera!Jy because fluctulttions in earnings 10 succes:nve years will not be uncorrclated. The law of large numbers would ensure vtrtual elimination of chance from life-time etu-nings if the rurious eve.nts were inde1>endent.

]11.comes 291 {labor er cities, where costs of living are higher s and th

· )arg .. h . , e r11

tes JI'I ·ate of employees w o use thetr own cars on com . wuge 1 ·d . pany

highet ·r theY are not compensate duectly. These sources f vosi~es~ ~ispersion cannot be wl~olly eliminated at present (for e~-00nllnn 1·~ 00 satisfactory mdex number of the cost of living

I there ~ . . ) :lu1P e, Jl}ttnities of d1fferent s1zes , so they must be kept in mind in com . g J)resent day data.

· tcrpretln · fi 1 · in 111 • we must notice one na source of d1spersion of earn-~1oreovet, 1 b' l' · l\'r d' ff · h · J' tible with equa a 1 1ttes. 1J.en 1 er m t etr comparative

· · comPa d 1 · 'II JJig~ for money an e1sure, s? one man w1 work 40 weeks, desires

50 r one will work overtime when another does not. These

ther ' o . b ano. ,.11

yield different money mcomes ut may represent equal choices "I ..

n1S of utthty. . . . strea e enlarge our view to compare d1fferent occupatiOns-still

When w l b'l' . . . . the assumption of equa a 1 1tles-most of the differences reta.tnmg d I · t d' d F .

11 c:till be of the kin s we 1ave JUS Jscusse . or example, a

WI ,. ofessor will earn more than a highschool teacher of equal college pr · . bilit, because the former has mvested for three or four years 10

8 t. > a ph.D. Similar remarks can be made about duration of cret Jng d · f · B · dd. · ", k on-J·ob trnining, an s1ze o commumty. ut m a 1t10n we "or ' f d. . encounter two other source~ o 1spers1.on.

Some occupations have mcome~ which are much more stable ov~r

t. than those of other occupatiOns. The self-employed worker 1s .nne · · d d U h I · d ch more subject to fluctuations m ema.n tan t e sa ane :::~rker, so the annual eamings of t.he former will be higher in good •ears and lower in poor years. Over a pe1·iod of, say, five years, of ~ourse most of this difference will be eliminated, but nnnunl data will display large differences. In addition it is generally believed t.hat these occupations with unstable incomes repel \Vorkers. so an additional premium must be paid for bearing these fluctuations ..

We have not. introduced the most obvious of the sources of m­equality of earnings; differences in "ability." How much difi'erence

'The higher cost of living in a larger ci~· rests basically on th~ higher eosts nf lnnd. Housing <·osls ~ci~g highe~, wage roles n~ust ~~ h1~~ ~~ compensating amounts (to mamt.am equn.hty of re1\l earn1~1gs ''tth . _ workers in smallet· cit~cs) . Hence nll perso.nal ~n·ices (m~~ care, h~r~~~t and the like) will a lso be more expenSive m larger r1lle:.. T he. fa _,1 . . . . r I'· . t with tho--<e 10 SlUtu er enterprises m !urge c1lles can success u •...Y compe e · . b · bl · · d · 1 · 1 1 1 · d t tl ·tern"J...,.onomtes o tama e ClUes esp1te t 1e h1g 1er wage eve s 1S ue o 1e ex " .. ~

in large economic centers.

7 6 7 ~ '9 .,..

292 The Size Di8tribution of 1 nco711e there is in abilities of men, no one can say. In fact, ability is n measurcable: it consists of more than strength, or I.Q., or creat· ot

. )'k' f k IV ity, or courage, or tenacaty, or a 1 mg or wor , or personal charn; or handsome appearance, or unusual vocal cords. The only Ill •

. f . th . t· . . easure of ability we have, m act, IS e vana 10n m earmngs that re . h ff tnaan8 after we have subtracted out t e e ects of education age

. . b 1 , COJll-mumty stze, and other measura le factors.11 But then we are m· . chance factors. with a~i~ity, ~nd i~ pl~in fact, no one knows

1:;

to separate thts rema1~mg dispersiOn ~nto luck and ability. Indi­v;duals have the same dtfficulty: poor bndge players usually say th never get go~ :ards.7 Since able people congregate in certain occ~ pations-phystcJsts are on average more able than electricians-th aggregate effect of ability (and luck) on income is much great e than the effect within an occupation. er

The list of factors making for differences in money income in any year is formidably long, but it is not complete. The differences in ability and luck aside, we have discussed only differences due to voluntary decisions of men, which would exist in fully competi­tive markets. In addition, any real society will exhibit dispersion because of the workings of several other forces.

First, there will be differences in returns due to monopoly power. If a labor union, or a cartel, succeeds in raising the incomes of its members above the competitive level, an additional source of dispersion will be created. We shall not attempt any direct estimate of the magnitude of such forces,8 but for select groups earnings can be 20 or 50 per cent higher under favorable conditions than competition would allow.

Second, there nrc differences in earnings due to market imperfec­tions, quite aside from monopoly. The following are characteristic:

1. I t may be that the rate on investment in training is much higher than the going 1·at-e of interest for investments of comparable risk, and yet many people may not be able to borrow the funds to make this investment in themselves. We have indicated that this was probably an impoJ·tant source of dispersion at earlier times

• Since ability is surely positively correlated with education, and possibly with other factors we have enumerated, some of ita effects will be attributed to these other factors.

• In 1,000 hands, the influence of the cards is negli~~:ible. If men lind 1,000 years, we could confidently ascrihe their differences in earnings to ability.

• See the discussion in Chapter 16 of the effects of unions.

,, , rnmzu · m1 ' ,. v._ "'' 1

293 I coraes . . • Ahot

71 t s and it is still an Important source in many

/.P" ·ted Sta e ' th t h · he l]n1 ld also notice, however, a t P.re 1s substantial

·0 t We shou 1 · 1 011,ics. . the t raining of many peop e, provided by par-

ecoo ,jnvestrnent 1n tal rather than economic motives.11

0ver 0 paren 1 · t · · . acting 0 f . ight leads peop e to acqmre rammg wh1ch

eo~ 101perfect 01

1esw value as when a skilled craft is displaced "' h ve a o , I' . ves to

11 • 1 dvance. There are corresponc mg gams from un-

pr~ a technologtca ~ demand but they are of shorter duration since b) . creases IO . f

·pected JJl d't' nal specialists m a ew years. ex ·n ad 1 10

• 'II I h · can tral . against certam groups WI ower t e1r one · ·natiOn 3 DiscrHni . ous instances in history have of course been . the consptcu . rnes- to

,nc~ and religious groups. racial ther phenomenon popular with detergent box

t add 1100 · 1 ffi · We do no . If n able man bequeaths htg 1 o ce to an mcom-otJsm a · d' · d orators, nep . . · e a lly a bequest of property mcome tsgmse thiS IS gen r . . . h ffi

petent so.n, d the son would be ncher 1f the h1g o ce were ns wage mcome,baln pointrnent and the additional income of the

'th an a e ap . . £1 tilled ":

1 aid to the son in dividends. Bequest 1s an m uence

enterpnse were. P nly when the job, rather than the control I Wage mcome o

on rea b 11 of the enterprise, is owned y a person.

A roximat e M agnit udes . . Some PP acl·l of these sources of dispersion with great

n not measure c . ,,e can . . , ful to make at least a few rough cshmates. accuracy but It Is use . .

\ve shall employ two mcnsures of chsperston:

1 The Lorenz Curve. Income recipients are ranked fro~ lowest t h' best and against their cumulative number we plot their cm;;u­l:ti,:: per~;ntage of income received. T his curve would be a n~

'th a slope of 45o if all incomes were equal, for then K per ceo WI t f tl ggregate earn­of the recipients would receive K per cen o le a . th a ing~.u The coefficient of inequality for a Lorenz curve IS _e are

. h'ld' cdut"ntion with an mternal • A fond parent who invests $10,000 10 a c 1 ~ that child's mone,·

rate of return of 1 per cent, would. of co~~ 1~rc:c and the child we~ income if inatead the $10,000 were mveste m on given the income instead of t?e education.. p ,_ , Dictionary of Political

10 See, for example, t he article on Jews tn a'11raue 8

Economy. . litics It used to be said "Such instances exist, of course, even outsld~ po

0 ·ean countries unless

that one could not become a professor in certTf Et~:ess of economics in he married the previous professor's . daught~r. ~e:. otb~. these countries wa.s not nlways inconSJst~t w1th this .> P

"See mathematical note 15 in Appendix B .

.. 294

The Size Distrib•·t · b ... tonof l etween the cun·e and the diagonal line (see Fi ncolne

by the area under the diagonal. It obvious! ha gure 18-2) diVi of one (when the lowest 99.999 per cent y . s a lllaXilnurn ,, dl e<J

. . rece1 ve n · a u a m1mmum value of zero (when all incom 0 Income) e

es are equal) and 100 .

(/) (.!) z 2 a:: q w li.J I-q (.!) w a:: (.!) (.!) q u. 52 0 I-z w u a:: w a.. li.J > i= q _J

::> ~ ::> u

0

I l l I I I l I

40 70 CUMULATIVE PER CENT OF RECIPIENTS

(Ranked from Poorest to Richest)

100

Figure 18-2. Lorenz curve for hypothetical income distribution.

2. The Standm·d Deviation and the Coefficient of Variation (which is simply the standard deviation of a distribution of incomes divided by its mean).

The Lorenz curve is the more popular measure but the additive property of variances is a real advantage.13

. u That is, if given incomes have two sources of dispersion, say age and educa­tiOn, measured by .,., 2 and CT2

2, the dispersion of incomes due to the joint action of both sources is:

ft1cornes 295 [;abor .11 strate the magnitudes of the dispersions due to

an 1 u . d . age We c . from the earmngs ata m the 1960 Census W d 1cat1on . . e

nd e t n and the age-earnmgs and education-earnings rei ll alesme , . 18 3 d a-boo~e s given in Figures - an 18-4.•• The two measures ~jonships ~re na)' be applied to each relationship. The coefficient . erslon t s of dJsP . 16 are: of variation u $1,011

Age: M = $5,714 = 17.7%,

• q $1,001 Education: M = $5,502 = 18.2 %,

1 nz curves are given in Figures 18-5 and 18·6. Finally d the ore . . an bine age and educatwn, usmg a two-way classification

can com 1 I f h · we f various ages and eve s o sc oohng. The coefficient f workers o

o . tion then becomes of varJa · u $1,319 01 M = $5,717 = 23.1 -;o,

b Lorenz curve is shown in Figure 18-7. and .t e sion or inequality has no natural scale by which we can

DJsper II y 'd . th t a given number is large or sma . et a gu1 e 1s nec~c;sary say. te~pret a Lorenz curve or standard deviation. In the present to JD • d · th t f d. · d th natural basis for JU grng e amoun o 1spers10n ue case e 1 d · · f · f II I to age or education is the ~ta 1sper~10n o earmngs o a sa es-men working full time. Th1s underlymg Lorenz curve has been

11 These average relationships were calculated from a.. re~ression equation b don the 0.001 samplo of the 1960 Census. The equation IS: ;: -13190.02 + 87.01X 1 + 319.29X~ + 375.07X3- 3.83Xa2 + 16.51X,

, (12.41) (43.31) (46.46) (0.54) (9.53) + I ,498.88X, - 261.5I.t, + 1,342.02X,.

(814.49) (358.69) (342.04)

(R• = 0.190; N "" 1,802) The variables are: W- wages and salaries, 1959 (M = mean), X1 =weeks worked in 1959, Xt =years of school completed, Xa = age, X, = hours worked during census week, X~ = race (1 ... white, 0 .. nonwhite), X,= small city-population 50,000 or less (0 = no, 1 = yes), X, -large city- population 250,000 or more (0 - nod1 - Y.es>d by taking "The coefficients of variation and Lorenz cur~es are •. et:~m;~ and l&-4)

the wages at various ages or levels of schooling (l'lgur ch level and weighting them by the number of salesmen of each age or ea. of schooling.

296

~~. ~~-:~~~~~~~~--~-20 30 40 50 60 70 AGE Figure 18-3. E · f arnmgs o salesmen hy age (1960).

80

~ 70 ,g 0 0

060

~40 z z a:: ~ 30

Figure 18-4.

4 6 8 16 18 YEARS OF

Earnings of salesmen h y years of education (1960).

1 comes 297

Lobar 11 18_g and it can be calculated that the total ffi

. Figure . ' d h coe _ drll«<l 10 inequality 1s 0.287, an t at of age-and~schooling 0_128. ·ent of ·.,bJes account for 45 per cent of all mequalitv tl ·o vafl"' dd . bl h J • <~'}le5i t" ntinue to a van n es, sue as weeks worked . • uld co . . . , sue

"'e co . and race. D tspers!On m weeks worked, in fact ha UlillUOitY' ' S

of r<>

1()0

i ~ uJ uJ ~ t5 0:: l!)

~ l5 50

tz uJ (.)

0:: uJ Cl.

ul 2: ~ ..J ::> :E ::> (.)

50 100 CUMULATIVE PER CENT OF RECIPIENTS

Figure 18-5. Lorenz distribution of earnings of salesmen identical in all respects except age.

an important effect on dispersion and it it not presented quantita­Lively only because it calls for as much explanation as wage dis-

persion itself. It may be instt'Uctivc, instead, to present the measures of in-

equality for salesmen in comparison with that of all male workers. Here again we include only those 18 and over who work full time

• ...... ------------------------.... ~~t·~· · :·~~· -~:;~~. ~~~ • r,-~

298 The Size Distribution 100 1 ----------------of l nconte

(f) <.!) z z a:: <X w w !;:t t.3 a:: <.!) <.!) <(

~50 1-z w <..> a:: w a. w ~ !;:t ...J :::> :E :::> <..>

50 CUMULATIVE PER CENT OF RECIPIENTS

100

~igure 18-6. Lorenz distribution of earnings of salesmen identical m all respects except education.

(that is, 50-52 weeks) in 1959, so unemployment has been set aside. The coefficients of variation are:

$3,609 Salesmen = $6,262 = 57.6%,

$3,142 All workers =

15,781

= 54.4 %.

T he all-wage-earners Lorenz curve is also shown in Figure 18-9. The two groups have virtually identical degrees of inequality of income distribution.

Family Wage Income

Families display an astonishing variety of patterns in number of wage earners, but the dominant pattern in multiple earner faro-

299

100 50 CUMULATIVE PER CENT OF RECIPIENTS

0

. 8 7 Lorenz distribution of earnings of salesmen identical Ftgure 1 - · d · in all respects except age and e ucat10n.

ilies is of course for the husband a nd :Wife to work. 141 T his is the only class of multiple earners we shall discuss. .

Leisure is a so-called normal good-people consume more le1sure as their income rises, prices remaining constant. \Ve should tbere-

.. The 1960 Census gives the following pattern of families (defined as two or more related persons) :

NUN»CR 1959 FAMILY J:ARNCR TTPil (1,000'$) MEDIAN ll<CO>la

None 4,840 11 ,400 One 23.466 6,179

Husband 19,614 Wife 1 ,318 Single Family Head 2, 630

Multiple 16.826 7,013 Hll.!lband-Wife 11 . 172 Ot.her 6, 653

In addition 13.2 million unrelated individuals had a median income of Sl,596·

300 The Size D~tributi . on of Ineo fore expect fewer wiYes to work m the labor force l'lte . . as the · of husbands nse. The facts are partially, but onl _Incomes keeping wi th this ex-pectation. If we compare diffe/ tParb~lly, in

· · · · II h en famtr n gtven tune, 1t JS genera y true t at the labor fore tes at - · e Partie' rate--a graciOUS phra e denotmg the fraction of a .

1P&tion gtven clah .,., of

100 1 - -------------

1/l (.!) z z Si w w ~ tB a:: <.!)

~

~50 1-z w u a:: w 0..

w > f= <1 _j ::> ::E ::> u

0 50 CUMULATIVE PER CENT OF RECIPIENTS

100

Figure 18-8. Lorenz distribution of all fu ll y employed male salesmen.

women who a rc in the labor force-,·arie. inversely with the hus­band's caming,..;. We illu::;t rute this characterist ic finding from the

1960 Census (Table 18-1 ). nut t,his ii-I only ha lf the story . Over the last hundred years, the

share of women in the labor force ha been ri&ing rapidly while ll\'(:ragc real earning~> of both 1uale and fema le workers have been

301

100 50

0

Figure 18-9. earners.

CUMULATIVE PER CENT OF RECIPIENTS Lorenz distribution of a ll full y employed male wage

nt 8

year-over time the familY ap~ars to rising about 2 per ~e f the wife The reconciliation with the have bought _less. letthsure or -sect iona.l data is to be found in the opposite findmg lD e cross

Table 18- 1 . . . R ~ of Wives in White,

Labor Foree Parucapauon a es Non-farm FaanUies with Husband Present

FAMILY TYPE

Children 6- 17 Children U oder 6

53 .9 32.3

-!9 .2 24 .6

49 .3 24 .5

47 0 21.5

39 .2 16.0

=

~~--------------s~···· ~

302 The Size Distributi on of Inc

nature of U.te ultern_atives t.o wor~ in the labor force. Fo 0

?/te the alternahves are m fact two: leisure ; and work w'th' r a Wife

. . I 1n th h • Leisure IS undoubtedly a normal good, and if we c ld e ome. work within the home, we would expect a rise in ou Put aside lead to a reduction in women's labor force part1·c· wt~ge rates ~ • • 1Pa 1on ( m fact taken place w1th males) because the income ff as ha8 wage rates would dominate the substitution eff ect.11 e ect of higher

The product.ive work of women within the hom h this relationship.18 The increasing labor force partici e t 'as tnodifiec)

· I I 1 · · · · pa lon of · wit 1 secu ar y r1smg mcomes IS due to three main forces: WIVes

1. A rise in real wages is a rise in the alternative t · h' h h cos of work· w1t m t e orne, as compared with working in the 1 b 10&

b · h 1 · a or force uymg ouse 10ld serV1ces. This secular rise in wage t and · r a es the f leads to a h1gher labor force participation. re ore

2. The advances in technology have reduced the cost f img many services previously performed within the h s o hpurchas-1 d. . ouse old ('

c u mg preparation of clothing and food laundry serv· '0• d ) . ' Ices, cleanin

an so on , and hence mcreased the comparative effici g, for money income.1v ency of work

3. Young children create a major demand for household . not cheaply obtainable in the market. The secular decl1· . sefr"'~es . I . ne m amily s1ze 1as greatly mcreased the share of time v.romen rna serv . t he labor force. Y e lD

The presence of multiple earners affects the distribution off .1 · . . . am1 y m.come m :anous ways. If the labor force participation rate of Wives were !~dependent of that of husbands, the effect of their work :vould b: to mcrease, and very substantially, the dispersion of fam­Ily em·01ngs. In fact, two relationships between wives' work and husband's earnings modify this. One force we have already noted:

. "~he cost of leisure is foregone earnings, so a. rise in wage rates is 11 ~1se m the cost of leisure, which would lead to a decline in leisure if real mcome were held constant.

,. For ~ ~uller analysis, see J. Mincer, "Labor Force Participation of Married Women,, lD Aspects of Labor Economics (New York : Notional Bureau of Econom1c Research, 1962).

••Th . e ~~come tax has been a counter force : if a wif<''s !!arnin~ nrc taxed at a mnrg1nal rat.e of (say) 30 per cent, n wife must earn $100 in the mfllket to J>Urcha.se $70 worth of household services.

303

I ~~ . erl1J 11 I' ·1ncome the la rger the share of Wives who

f rdP bane s ' . . rcr the htiS In addition, when a fam1ly has a temporar1ly

we lo\h labor force. b cause of ill healLh or unemployment of the e.llte~ t etJle-perhaps ethc labor force to offset this reduction :

· 1nco · enter · t . I t' h ' lo~ d-"'l'·es . . t that t here IS a strong nega 1ve re a 1ons 1p ban d' md1ca e d · hU: 's stu 1es f ce participation an trans1tory components

l itlcer ' labor or . f . f f ., ) 0 wives fi ds that the dispers10n o earnmgs o am1 y

wee f the n . bel. cotJle· In ac . families are essentially equal.20 T he mcomes of 1~ and of. entlreth husband and wife present had a coefficient heafsJllities w1th bo

27 for families with only husbands working in

of 3 · of 03 · (0309) f .,. . equahtY · 1. htly less inequality . among ami 1es of !0 here was s Ig t959, butt husband and wife worked.2t . biCh bOth !0\V

OPERTY INCOME pR .

· me of a household has two mam sources: cur-The p~oper!~~n~oheritance. These componen~ will first b_e dis-

rent sa.vmg, 1 and then their comparative roles will be ed separate Y, ·

cuss discussed.

Current Saving that all saving consists of temporary postponement

Let us assume . · tb t. but t hat no savings survive at the death of e

f consump 100 , . . • 0 Tb' result can be achieved by investmg the savmgs m an-saver. JS • • t . h' h . · b. h terminate at death. Then m a soc1e y m w 1c every-nmtJes w 1c · h

b d the same labor earnings and saved the same fractiOn eac one a . - h d' vear for (say) 25 years, and then dtssaved for 2<> years, ~ e. IS-tribution of property income would depend only ~n the age dJst rJbu­tion of the population . P eople entering and leavmg the labor force would have no property, and those at the terminus of the period of saving would have maximum pt·operty accumulation-and prop­erty incomes would be proportional to property if all investments yield the same rat.e of return.

"See "Labor Supply, Fnmily Income, nnd Consumption," Proceedings of American Economic Association (Mav 1959), 574-83.

"These measures, bnsed upon the 1960 Census, unrortunalely include also property income. The coefficient for all families, ~gardless of number of workers, was 0.333.

.. ! ; , .

304 The Size Distribution f o Inc

·we may calculate our· measures of dispersion on thes . 0111e sumptions, for an equal number of people in every age elstrnpie as.

C ass.22

INTEREST,. 6% ••A~

Coefficient or Variation of Interest I ncome 58. 6% 10

% 65.1~

The corresponding Lorenz curves are shown in Figure l8- • will be observed that these distributions have roughly the lO. _lt

b · · th" · same dt persion as In or mcomes WI rn an occupation. s. In the foregoing example, if we calculated the lifetime .

incomes of each person we would find them perfectly equaltnterest substantial inequality we observe is due to the brevity of th so _the unit (one year) for which income was observed. For such 1 e tnne

· ld b · ong run phenomena, 1t wou e more appropnate to compare wealth ( h value of income streams) than income in any year. If we cal It e the present value of the income from savings at (say) age ~~ate would find that it was equal for all individuals. we

If one goes to e.n even deeper concept of income, it is not cl that the distribution of "real" income is changed by savings. s~a~ pose two men with identical wage earnings prospects embark up~ lifetime savings programs, one saving 5 per cent of wage incorn: the other 10 per cent. If the choices were voluntary, we must con: elude that the extra interest income foregone by the person saving 5 per cent was at least offset by the pleasure derived from earlier consumption. The lifetime distribution of "real income" or utility could be perfectly equal even though lifetime money incomes differed substantially.

n The calculations are based upon a table of which the following are sample entries:

5% 10 %

CORnJeNT SAVINO& ACCUMULATED lNTERt;8T ACCOJ.S U&..ATZD INTIHtEfJT AO& rnow ZARNtNos 8AVIN08 INCOM& 8AVIN0" U~COJ.II

21 1100.00 SIOO.OO $5.00 $100.00 $10.00 22 100 .00 205.00 10.25 210 .00 21.00

45 100.00 4. 772.71 238. 64 0. 834.60 083.47 4B 0 5,011.35 250 .67 10.818.11\ I ,081.82 47 0 4,906.85 245.82 10,708.16 I ,070.82

60 0 2,953.46 147 .67 7,740.61 774.05 65 0 1,804.69 00.23 5 .189. 03 618.~0

The 5% return yields an annuity of $355.57 per year, and the 10% return $1,191.83 per year, starting at age 46.

305

Jnco11te 1 tion of wealth and the property in-proPert!l ate of nccu~u a e much influenced by differences in

aoth the r frorn wealt atr If we make a single investment of v d awn . estmen s. Illes f• rn on tnv . f rrnly distributed from 2 per cent to

cOteS of retu of interest uni o for accumulated sums after 5 and r!l t rntes Lorenz curves ·toO ll t the ., r cen, 1Z pe

tOO

100 50 0 CUMULATIVE. PE.R CE.NT OF RECIPIENTS

. 'b . f "ntcrest incom e generated by Figure 18-10. ~orenzdddt~tn ':'~~o~ opo~ulation with uniform annual lire pattern of savmg an ISSaYl "' ) savings (savings invested at 5 and 10% . .

. . 18 11 The increase of inequality 20 years are presented m Figure - . bl eat Almost no with the passage of time becomes remnf rkta yt glyr on. the extent

· t nor una e work has been done by economts s , u .· d n~d the stability of dispersion in rates. of r~turn over lo_ngw;~~;o ~~lieved that higher of these rates, for vanous mvestors. It lS

1Y1

. tors in areas d by the smn er mves interest rates are usually enrne

---·~~~------------------...

306

, , -~ ' ···~ :

· · ·v~ 307

The Size Dist 'b . · n utt0 where ma1·ket credit facilities are poor d 'f n of l nc0 tl t d . . . . ' an t tru t h· l'lle

ta ll·pcrsJOn m mtcre t rates offsets t e ts Wou)d wealth . 0 a degree disp . ar~e

Of · h · · · er,Hon · cou1 sc t e d1 tn but10n of a ccumul t d . 111

of t . . a e savmgs p roper y m come, ts more unequal th h • and eve

an t e fore · n lllor gotng ar e 100 ~----------------- gurnent

lJ..J 1-<t (.!) lJ..J a:: (.!) (.!) <t lL. 0 1- 50 :z lJ..J u a:: lJ..J Q,

lJ..J > ~ _J

:::::> ~ :::::> u

o-=------------~s~o ____________ __j 100

CUMULATIVE PER CENT OF RECIPIENTS

~igure 18-ll. Lorenz distribution of accumuJatcd w at 1 mterest rates varying from 2 to 12 % (after 5 years and eaf:e~ ;J years).

would suggest. The labo1· incomes of individuals, the main source of c~rrent savings, have a range of the order of magnitude of 100 to 1 1~1s~ad of the equality assumed a bove. ·we lump together inter· es.t, d1v1dends, rcnt.c:, a nd o ther property incomes: individually they wtll of course he le. s equnlly dis tributed than t hey are in the aggregate.

[nco me prtfplrt~

\\'enlth . . berite«<

1 li "l1tnvs n much larger degree of mequahty than

111 t ·enlt 1 l ' • f ' d d 0 l eritCC " • . 0111e sources so ar cons1 ere . ur argument

111 1 thcr 10c I I . . i the 0 d 'in..,s which arc equ a over ong penods of t1me n'· 0 I~tc stl\ t:> d · I · I f f ~ · ~ccunlll : . given year hol s w1t 1 spema. orce or inheri-lb~t I enUSJ Ill U

.. ,. un 'I ------ --------- ----::. ~re vc .

100

50 100 CUMULATIVE PER CENT OF RECIPIENTS

Figure 18-12: Lorenz distribu~ion ,of accumulated wealth after t years with w11form rate of con tnbut10n.

tances: the time span becomes, not a part of a man's life, but part of the life of a family . W e may illustrate this effect of the lengthen­ing time span by the Lorenz curves in Figure 18-12. Each is based upon a uniform annual rate of saving and 8 per cent interest (rein· rested). The coefficient of inequality rises from 0.47 to 0.71 as the

period lengthens fro m 30 to 90 years.

308 The Size Di8trib--• · <w.ton Of] · h · · f d · ?lcolll The ar1t mct1c o compoun mterest is inexorabl e

thing did not interfere, ancient fortunes would be in. e, ad?d if sollle I ere Jbly I . That they arc not- t 1at not even a dynasty's wealth arge,:,

without end-is due to the heavy hand of chance S accurnulat ... . · ooner • Q every accumulatmg fortune encounters one or both of th or later

to unending growth: e obstacles

I. A stupid or p1·otligntc heir; 2. An unstnble environment.

Some l'ocietics have sought to preserve large fortun . b k . es (In 1 d by a system of equcst nown as primogeniture, whereb h Ill! l

male heir had only a life estate in the family fortun y t e oldest not diminish it. This device has more or less thwarted fe al~dh 00Uld

• 00 IS hei but not rapac10us governments or swarming armies. Some fa .. rs. have sought to avoid the losses that are inevitable in any lllJI.1es of investment by diversification, but of course they then m otne 1hn~ h · 1 · 'b · us a low t e mcompetent 1e1rs to contrt ute to the diversification. It . ancient fortune which is a century old. 18 an

From this viewpoint capital accumulation is a gamble a d . k . I f h ' n We may mvo ·e m ana ogy a amous t eorem in probability on th

gambler's ruin. If a man possessing A dollars plays a fair g e f . t. 'h . I . B ame

o com ossmg Wit a nva possessmg dollars, and receives I I each time a head appears and loses $1 each time· a tail appears the former's probability of eventual ruin ( = loss of A dollars) i;

B A +B'

which approaches unity if the Clrival" consists of the rest of tbe world (so B is essentially infinite) .z• Sooner or later there occurs an adverse run of luck sufficient to destroy any finite fortune.

11 F or those who like such games, the following are the 1964 accumulations

of $1 invested at the death of the man in question : W.O.!< 1 % 57.,

Adam Smith (1790) S5. 65 1486.20 Caeur (U n.c.) t71 X l()t 33.545 X 1011

The sum of S33.6 X 10"' is essentially incomprehensible: Archimedes assumed that a grain of sand had a diameter less than 1/40 of a finger-breadth, and argued that a sphere the size of "the" universe would contain only 10" grains. [The Works of Archimedes, ed. by T. L. Heath (New York: Dover), pp. 221-32.]

.. The results arc similar if the coin is not fair; see W. Feller, An Intr~uc­tion to ProbabililJI TheoT'J/ and lt8 Applications, 2nd ed. (New York: W1ley, 1957), pp. 292 II.

309

t!l [ncome . . 1 0 a determin ant of the distribution er h u·s 1S a s . proP . nee of e f ily line will eventually d1e out, or

'fhe e~lstde wealth. The alrn t the division of property by inheri-'te ·tent t l R · f h

f jnhCr1

uch an ex 1 h Indeed i t is certam that one o t ese 0 uJtiplY to/f{use the wca: · lace-which one it wi 11 be depends 0

~0er wil~ 11 'eventuallY tn ef phildren.2~ Lotkn has shown that the t w1 mber o c 1 1 · ) rt'~ult5 tn'erage nu . name will vanish (no rna e 1etrs was 11pon t~~t that fl fnmlly eration of children, and 0.82 ultimately, probnbll~~ in the first gen f the 1920's, and that as an approxi­sbout

0· crican birth datba' l~ty equals the reciprocal of the average

· h Alll probn 1 1 wrtfoo this latter family-generation.~~~ rnll I ' of boys per nunlber •

d Savmg · h f •tance an tion of the comparnt1ve s ares o

tnbe~' useful to form sonl~c. no persons in the present accumulated It IS 'ng by tvmg . f th

·tance and savJ 't will give us some estimate o e inhcr:h It is useful ?ec~bus~. ~n of J)roperty income will be affected wen · h' 1 the d1stn u I h xtent to w IC, . tate tax such as we now ave. ~~ a highly pr~gressl~~=stwo sources, however' is very difficult. The . The separation of d here is to estimate the accumulated

Procedure that has been use d compare this with total wealth, so f l'ving persons, an . h . 1

~s,-ings 0 1. residual Even this crude approac mvo ves ~"<-

inheritance IS a 1 1 t,· ns in which the following are the major tremely elaborate ca cu n JO '

steps:

h b · group those living in 1960. 1. i~kde ~~r~~ l::r participation tables) the number at work 2· ~nd t · the past-back to 1890.

at.;~~al:u,~a~: their labor earnings, assuming they earn the average

worker in the economy· wa4~e ::ume that tht-y save 10 per cent of their labor income plus

interest on savings. f th ur-5. Assume that once they retire from the. labor orce, ey p

chase an annuity with their accumulated savmgs.

. d tel fo males and females, The calculatiOns are performe separa Y r . at interest rates of 4 and 8 per cent, and with wage mcomes cor­rected and uncorrected fo r price level changes.

• See Feller, Probabili.ty, pp. 224 II. . . p · . Actualites Sci-• Theorie analytique des associations biologaques, I1 ( ans.

eotitiquies et lndustrielles, 1939), pp. 123 II.

The Size Distri.b .

Tl • I . . . Ulton o( l

lC rc:.u bng wealth estimates are rep t d . . 1!co . ore m T b rne are e..':prcssed as mcome recei\·ed so ,._ a lc 18-.2

310

t. I . . as w be co . '"M 1onn mcomc data. It will be obserYed th t . mparab)e t "

0e)·

· a lnCOIU 0 " " saYtngs ranges from 26 to several hundr d e on acculll --. \ ' I e pe r cent c Ulat mcomc. \ lat can we say of the plau,ib'J't .

0 total pr eQ

t. h' . ~ I 1 ) of th I OJ>ert

sump 1ons w 1ch y1cld this wide array of 1 e a ternati . J Th "d fl t d" . resu ts? \c as

e c a e saYmgs-savings of h . . eac year prices-arc the appropriate measure ~·r . converted to

I savmgs a · 196()

ren assets whose values ri~e with th re In fact . ~ e general p · Put · mgs take a fixed-income form (bonds f • . nee level. Som l1l there arc presumably offsetting gains' i ort~xample), but eve~ ~a, •. borrowers . ' n · e event of infi t" ere a Ion, to

T a b le 18-2

Shnre o f Non inherited Wcal t l . ,... I In •·rope.-ty I (p c.- cent) ncom e, 1960•

I NCOME TYPE

1960 Dollars Current Dollars

INTEREST RATE = 4% 8%

40.9 242.9 26 · 1 124 0

• Pr~perty ineomc wu $90.1 billion the • . an arbotrarily eetimat.&d one-third of e~trepre~:,r!, ~eota, corporate income net il1! tncom~. • , t:rest. •ZKJ

The interest rate, however is a much establish. The rate we wiRh 'is of more difficult number to . t ~ course the realized te mvcs ments over long periods not the rat . . ra on all The realized rate takes acc~unt of II ;s.fromised by borrowers. finan.cial terms, and more basically a~ un~~~;:s of ~nterprises, in physical terms. Since inherited wealth cannot b:s~ul m~estments in cedurcs suggest that the realized interest rat egattve, our pro­more than perhaps 6 per cent. e could not have been

In short, inhel·ited wealth ma be a wealth or it may be a domi·nayt I very modest share of present

< n s 1are Our anal s· t uncertain with respect to 1 1 b · Y I S mus remain effects of certain . ev_e ' ut we can at least indicate the in a society will beo~o~~~~s vanables. The share of inherited wealth

- the higher the rate of increase of wage income -the J~ngcr the average working life of a person - the h~gher the rate of saving from income -the higher the yield of investment.

311

bl£111$ ~ s .

·cLvsi0 1 . . 1

tone of this chapter 1s of course due to

CO~ 11p1r1cn . d' 'b t' f . On

..-1\. ei d theon· of the s1ze 1stn u 1on o mcome. <tr :::> • • lope " 'fill' • re of !l de' e t . .., calculations should support the follow-

b~rn f a..-men a I·' • . . fl d b the!\ - these r. "'. . of· income bY s1ze 15 m uence y most '"en d·-t 1butJOn ~ sut e .·~· the 1"" .r . gnitudes of the economy (the rates of

the,J- · 0n11C mn . ing ba~ic econ _ tl rate of growth of mcome, and so forth ) of th~ nod oi intcre:>td, leoaraphic characteristics of the populat ion

«l'' " f the em "" d h l'k ) ~~'3" b. 1nnnY 0 . • · e bir th and death rates, an t e 1 e .

nd ) faroJl) s1Z ' . 5 structure, • f inequality of income can anse for reason s (sgel .,

0ae in the ded~ee 0

51·on of earnings of individuals, or changes

~ ct" " the Jsper . . · Jated to 1

.., res of property mcome. A fuller ana lysts unre nts or s 1.. . . their an:lOU . that educational and medtcal a dvances h ave ll1 • I believe, . . b t• f . ould sho'' •

1 r influence upon the d1stn u 1on o mcome

~~' 1 1 ad a urge · 1 d. t 'b t · Probnb Y 1 . r cies d irected to changm g t 1e 1s n u wn.

nlanY public po 1 th~O

RECOMMENDED R EA DIN GS "CI ice Chance, and the Personal Distribution of I ncome,"

· .Jman, M., 10 ' ? 290 Fnew-· p rt'cal Economy, 61 (1953), _77- . Jo~rnal 0~h: ~~ructure of Income, Philadelphia.: University of Penn­

J{ravJs, I., sylvania, 1962.

PROBLEMS I. The argument in the te:-.-t implies that the distribution of earnings

mthin an occupation will be more unequal,

(a) The more unequal the ages of the workers. (b) The more unequal the formal educational training of the workers.

(c) The more varied the si:~;es of communities in which they live.

Test these implications with the data on enrnings in the population census. 2. The members of an occupation each hnve an average income of $5,000

but in any one year it exceeds or falls short of this average by a random amount. For (say) 25 individuals, calcul:lte incomes in one year and an average of two years, where the random component is determined by coin flipping. 1vfore precisely, in each year the income of an individual exceeds S5,000 by S300 for each consecutive heads, and falls short by S300 for e3ch consecutive tails. Plot the Lorenz curves and calculate t he coefficient of inequality.

3. Why is the distribution of interest and dividend income much more unequal than that of rental income?