Scale Economies, Product Differentiation,and the Pattern of Trade

By PAUL KRUGMAN*

For some time now there has been con-siderable skepticism about the ability ofcomparative cost theory to explain the ac-tual pattetTi of international trade. Neitherthe extensive trade among the industrialcountries, nor the prevalence in this trade oftwo-way exchanges of differentiated prod-ucts, make much sense in terms of standardtheory. As a result, many people have con-cluded that a new framework for analyzingtrade is needed.' The main elements of sucha framework—economies of scale, the pos-sibihty of product differentiation, and im-perfect competition—have been discussedby such authors as Bela Balassa, HerbertGrubel (1967,1970), and Irving Kravis, andhave been "in the air" for many years. Inthis paper I present a simple formal analysiswhich incorporates these elements, and showhow it can be used to shed some light onsome issues which cannot be handled inmore conventional models. These include,in particular, the causes of trade betweeneconomies with similar factor endowments,and the role of a large domestic market inencouraging exports.

The basic model of this paper is one inwhich there are economies of scale in pro-duction and firms can costlessly differenti-ate their products. In this model, which isderived from recent work by Avinash Dixitand Joseph Stiglitz, equilibrium takes theform of Chamberlinian monopolistic com-petition: each firm has some monopolypower, but entry drives monopoly profits tozero. When two imperfectly competitiveeconomies of this kind are allowed to trade,increasing returns produce trade and gains

from trade even if the economies have iden-tical tastes, technology, and factor endow-ments. This basic model of trade is pre-sented in Section I. It is closely related to amodel I have developed elsewhere; in thispaper a somewhat more restrictive formula-tion of demand is used to make the analysisin later sections easier.

The rest of the paper is concerned withtwo extensions of the basic model. In Sec-tion II, I examine the effect of transporta-tion costs, and show that countries withlarger domestic markets will., other thingsequal, have higher wage rates. Section IIIthen deals with "home market" effects ontrade patterns. It provides a formal justifica-tion for the commonly made argument thatcountries will tend to export those goods forwhich they have relatively large domesticmarkets.

This paper makes no pretense of general-ity. The models presented rely on extremelyrestrictive assumptions about cost and util-ity. Nonetheless, it is to be hoped that thepaper provides some useful insights intothose aspects of international trade whichsimply cannot be treated in our usualmodels.

I. Tlie Basic Model

A. Assumptions of the Model

There are assumed to be a large numberof potential goods, all of which enter sym-metrically into demand. Specifically, we as-sume that all individuals in the economyhave the same utility function.

*Yale University and Massachusetts Institute ofTechnology.

'A paper which points out the difficulties in explain-ing the actual pattern of world trade in a comparativecost framework is the study of Gary Hufbauer andJohn Chilas.

(I)

where c^ is consumption of the /th good.The number of goods actually produced, n.

950

VOL. 70 NO. 5 KRUGMAN: PA TTERN OF TRADE 951

will be assumed to be large, although smallerthan the potential range of products.^

There will be assumed to be only onefactor of production, labor. All goods willbe produced with the same cost function:

(2)

where /,• is labor used in producing the ithgood and x, is output of that good. In otherwords, I assume a fixed cost and constantmarginal cost. Average cost declines at alllevels of output, although at a diminishingrate.

Output of each good must equal the sumof individual consumptions. If we can iden-tify individuals with workers, output mustequal consumption of a representative indi-vidual times the labor force:

(3) i=\ n

We also assume full employment, so thatthe total labor force must just be exhaustedby labor used in production:

(4)/ - I

Finally, we assume that firms maximizeprofits, but that there is free entry and exitof firms, so that in equilibrium profits willalways be zero.

B. Equilibrium in a Closed Economy

We can now proceed to analyze equi-librium in a closed economy described bythe assumptions just laid out. The analysisproceeds in three stages. First I analyze con-sumer behavior to derive demand functions.Then profit-maximizing behavior by firms isderived, treating the number of firms asgiven. Finally, the assumption of free entryis used to determine the equilibrium numberof firms.

^To be fully rigorous, we would have to use theconcept of a continuum of potential products.

The reason that a Chamberlinian ap-proach is useful here is that, in spite ofimperfect competition, the equiUbrium ofthe model is determinate in all essentialrespects because the special nature of de-mand rules out strategic interdependenceamong firms. Because firms can costlesslydifferentiate their products, and all productsenter symmetrically into demand, two firmswill never want to produce the same prod-uct; each good will be produced by only onefirm. At the same time, if the number ofgoods produced is large, the effect of theprice of any one good on the demand forany other will be negligible. The result isthat each firm can ignore the effect of itsactions on other firms' behavior, ehminatingthe indeterminacies of oligopoly.

Consider, then, an individual maximizing(1) subject to a budget constraint. The first-order conditions from that maximum prob-lem have the form

(5) J =!,...,«

where p, is the price of the / th good and \ isthe shadow price on the budget constraint,that is, the marginal utility of income. Sinceall individuals are alike, (5) can be re-arranged to show the demand curve for the(th good, which we have already argued isthe demand curve facing the single firmproducing that good:

(6) O-i /=!,...,n

Provided that there are a large number ofgoods being produced, the pricing decisionof any one firm will have a negligible effecton the marginal utility of income. In thatcase, (6) implies that each firm faces a de-mand curve with an elasticity of 1/(1—fl),and the profit-maximizing price is therefore

(7) /=!,. . . ,«

where w is the wage rate, and prices andwages can be defined in terms of any (com-mon!) unit. Note that since 6, fi, and w arethe same for all firms, prices are the same

952 THE A ME RICA N ECONOMIC RE VIE W DECEMBER 1980

for all goods and we can adopt the shorthandP=Pi for all /.

The price/) is independent of output giventhe special assumptions about cost and util-ity (which is the reason for making theseparticular assumptions). To determine prof-itability, however, we need to look at out-put. Profits of the firm producing good / are

(8)

If profits are positive, new firms will en-ter, causing the marginal utility of income torise and profits to fall until profits are drivento zero. In equilibrium, then 77- = 0, implyingfor the output of a representative firm:

(9) x,=

Thus output per firm is determined by thezero-profit condition. Again, since a, (i, and9 are the same for all firms we can use theshorthand x = Xi for all /.

Finally, we can determine the number ofgoods produced by using the condition offull employment. From (4) and (9), we have

(10) n =L{\-9)

C. Effects of Trade

Now suppose that two countries of thekind just analyzed open trade with oneanother at zero transportation cost. To makethe point most clearly, suppose that thecountries have the same tastes and technolo-gies; since we are in a one-factor worldthere cannot be any differences in factorendowments. What will happen?

In this model there are none of the con-ventional reasons for trade; but there willnevertheless be both trade and gains fromtrade. Trade will occur because, in the pres-ence of increasing returns, each good (i.e.,each differentiated product) will be pro-duced in only one country^ for the samereasons that each good is produced by onlyone firm. Gains from trade will occur be-cause the world economy will produce a

greater diversity of goods than would eithercountry alone, offering each individual awider range of choice.

We can easily characterize the worldeconomy's equilibrium. The symmetry of thesituation ensures that the two countries willhave the same wage rate, and that the priceof any good produced in either country willbe the same. The number of goods pro-duced in each country can be determinedfrom the full-employment condition

(11) n = L(\-e)/a; n*=L*{\-9)/a

where L* is the labor force of the secondcountry and n* the number of goods pro-duced there.

Individuals will still maximize the utilityfunction (1), but they will now distributetheir expenditure over both the n goods pro-duced in the home country and the n* goodsproduced in the foreign country. Because ofthe extended range of choice, welfare willincrease even though the "real wage" w/p(i.e., the wage rate in terms of a representa-tive good) remains unchanged. Also, thesymmetry of the problem allows us to de-termine trade flows. It is apparent that indi-viduals in the home country will spenda fraction n*/{n-^n*) of their income onforeign goods, while foreigners spend n/(n-l-rt*) of their income on home countryproducts. Thus the value of home coun-try imports measured in wage units is Ln*/{n-^n*) = LL''/{L-\-L*). This equals thevalue of foreign country imports, confirmingthat with equal wage rates in the twocountries we will have balance-of-paymentsequilibrium.

Notice, however, that while the volume oftrade is determinate, the direction of trade—which country produces which goods—isnot. This indeterminacy seems to be a gen-eral characteristic of models in which tradeis a consequence of economies of scale. Oneof the convenient features of the modelsconsidered in this paper is that nothing im-portant hinges on who produces what withina group of differentiated products. There isan indeterminacy, but it doesn't matter. Thisresult might not hold up in less specialmodels.

VOL. 70 NO. 5 KRUGMAN: PATTERN OF TRADE 953

Finally, I should note a peculiar featureof the effects of trade in this model. Bothbefore and after trade, equation (9) holds;that is, there is no effect of trade on thescale of production, and the gains from tradecome solely through increased product di-versity. This is an unsatisfactory result. Inanother paper I have developed a slightlydifferent model in which trade leads to anincrease in scale of production as well as anincrease in diversity.^ That model is, how-ever, more difficult to work with, so that itseems worth sacrificing some realism to gaintractability here.

U. Transport Costs

In this section I extend the model to allowfor some transportation costs. This is not initself an especially interesting extension al-though the main result^ that the largercountry will, other things equal, have thehigher wage rate^is somewhat surprising.The main purpose of the extension is, how-ever, to lay the groundwork for the analysisof home market effects in the next section.(These effects can obviously occur only ifthere are transportation costs.) I begin bydescribing the behavior of individual agents,then analyze the equilibrium.

A. Individual Behavior

Consider a world consisting of twocountries of the type analyzed in Section I,able to trade but only at a cost. Transpor-tation costs will be assumed to be of the"iceberg" type, that is, only a fraction g ofany good shipped arrives, with 1 — g lost intransit. This is a major simplifying assump-tion, as will be seen below.

' To get an increase in scale, we must assume thatthe demand facing each individual firm becomes moreelastic as the number of firms increases, whereas in thismodel the elasticity of demand remains unchanged.Increasing elasticity of demand when the variety ofproducts grows seems plausible, since the more finelydiiferentiated are the products, the better substitutesthey are likely to be for one another. Thus an increasein scale as well as diversity is probably the "normal"case. The constant elasticity case, however, is mucheasier to work with, which is my reason for using it inthis paper.

An individual in the home country willhave a choice over « products produced athome and n* products produced abroad.The price of a domestic product will be thesame as that received by the producer p.Foreign products, however, will cost morethan the producer's price; if foreign firmscharge p*, home country consumers willhave to pay the c.i.f. price p*=p*/g- Simi-larly, foreign buyers of domestic productswill psiy p=p/g-

Since the prices to consumers of goods ofdifferent countries will in general not bethe same, consumption of each importedgood will differ from consumption of eachdomestic good. Home country residents, forexample, in maximizing utility will consume(;j//*)'/^'~** units of a representative im-ported good for each unit of a representa-tive domestic good they consume.

To determine world equilibrium, however,it is not enough to look at consumption; wemust also take into account the quantities ofgoods used up in transit. If a domestic resi-dent consumes one unit of a foreign good,his combined direct and indirect demand isfor 1/g units. For determining total de-mand, then, we need to know the ratio oftotal demand by domestic residents for eachforeign product to demand for each domesticproduct. Letting a denote this ratio, anda* the corresponding ratio for the othercountry, we can show that

(12)

The overall demand pattern of each indi-vidual can then be derived from the require-ment that his spending just equal his wage;that is, in the home country we must have{np-¥on*p*)d=Wy where d is the consump-tion of a representative domestic good; andsimilarly in the foreign country.

This behavior of individuals can now beused to analyze the behavior of firms. Theimportant point to notice is that the elastic-ity of export demand facing any given firmis 1/(1-6'), which is the same as the elastic-ity of domestic demand. Thus transportation

954 THE AMERICAN ECONOMIC REVIEW DECEMBER 1980

costs have no effect on firms' pricing policy;and the analysis of Section I can be carriedout as before, showing that transportationcosts also have no effect on the number offirms or output per firm in either country.

Writing out these conditions again, wehave

(13) ;j =

The only way in which introducingtransportation costs modifies the results ofSection I is in allowing the possibility thatwages may not be equal in the two countries;the number and size of firms are not af-fected. This strong result depends on theassumed form of the transport costs, whichshows at the same time how useful and howspecial the assumed form is.

B. Determination of Equilibrium

The model we have been working withhas a very strong structure—so strong thattransport costs have no effect on either thenumbers of goods produced in the countries,n and n*, or on the prices relative to wages,p/w and p*/w*. The only variable whichcan be affected is the relative wage rateyv/w* = <j3, which no longer need be equal toone.

We can determine w by looking at anyone of three equivalent market-clearing con-ditions: (i) equality of demand and supplyfor home country labor; (ii) equality of de-mand and supply for foreign country labor;(iii) balance-of-payments equilibrium. It willbe easiest to work in terms of the balance ofpayments. If we combine (12) with the otherequations of the model, it can be shown thatthe home country's balance of payments,measured in wage units of the other country,is

(14) B=-~—^L*~ an'n + an*

03L

a*L+L* L + aL*

FIGURE I

Since a and a* are both functions of= o:i, the condition 5 = 0 can be used to

determine the relative wage. The functionfi(w) is illustrated in Figure 1. The relativewage w is that relative wage at which theexpression in brackets in (4) is zero, and atwhich trade is therefore balanced. Since a isan increasing function of w and a* a de-creasing function of w, B(u>) will be nega-tive (positive) if and only if w is greaterOess) than w, which shows that to is theunique equilibrium relative wage.

We can use this result to establish a sim-ple proposition: that the larger country, otherthings equal, will have the higher wage. Tosee this, suppose that we were to compute5(to) for a)= 1. In that case we have CT = O * <1. The expression for the balance of pay-ments reduces to

(14') B = 1 IaL-\-L* L + aL*

But (14') will be positive if L>L*, negativeif L<L*. This means that the equilibriumrelative wage u must be greater than one ifL>L*, less than one if L<L*.

This is an interesting result. In a worldcharacterized by economies of scale, one

VOL. 70 NO. 5 KRUGMAN: PA TTERN OF TRADE 955

would expect workers to be better off inlarger economies, because of the larger sizeof the local market. In this model, however,there is a secondary benefit in the form ofbetter terms of trade with workers in the restof the world. This does, on reflection, makeintuitive sense. If production costs were thesame in both countries, it would always bemore profitable to produce near the largermarket, thus minimizing transportationcosts. To keep labor employed in bothcountries, this advantage must be offset by awage differential.

III. "Home Market" Effects on the Patternof Trade

In a world characterized both by increas-ing returns and by transportation costs, therewill obviously be an incentive to con-centrate production of a good near its largestmarket, even if there is some demand forthe good elsewhere. The reason is simplythat by concentrating production in oneplace, one can realize the scale economies,while by locating near the larger market,one minimizes transportation costs. Thispoint—which is more often emphasized inlocation theory than in trade theory—is thebasis for the common argument that coun-tries will tend to export those kinds of prod-ucts for which they have relatively largedomestic demand. Notice that this argumentis wholly dependent on increasing returns;in a world of diminishing returns strongdomestic demand for a good will tend tomake it an import rather than an export.But the point does not come through clearlyin models where increasing returns take theform of external economies (see W. M.Corden). One of the main contributions ofthe approach developed in this paper is thatby using this approach the home market canbe given a simple formal justification.

I will begin by extending the basic closedeconomy model to one in which there aretwo industries (with many differentiatedproducts within each industry). It will thenbe shown for a simple case that when twocountries of this kind trade, each will be anet exporter in the industry for whose prod-

ucts it has the relatively larger demand. Fi-nally, some extensions and generalizationswill be discussed.

A. A Two-Industry Economy

As in Section I, we begin by analyzing aclosed economy. Assume that there are twoclasses of products, alpha and betay withmany potential products within each class.A tilde will distinguish beta products fromalpha products; for example, consumptionof products in the first class will be rep-resented as CJ,...,c„ while consumption ofproducts in second are C|,...,c^.

Demand for the two classes of productswill be assumed to arise from the presenceof two groups in the population.* There willbe one group with L members, which de-rives utility only from consumption of alphaproducts; and another group with L mem-bers, deriving utility only from beta prod-ucts. The utility functions of representativemembers of the two classes may by written

(15) t /=

For simplicity assume that not only the formof the utility function but the parameter 9 isthe same for both groups.

On the cost side, the two kinds of prod-ucts will be assumed to have identical costfunctions:

(16) l. =

J=\,...,n

where, /,, / are labor used in production ontypical goods in each class, and x^, Xj aretotal outputs of the goods.

The demand conditions now depend onthe population shares. By analogy with (3),

"An alternative would be to have all people alike,with a taste for both kinds of goods. The results aresimilar. In fact, if each industry receives a fixed shareof expenditure, they will be identical.

956 THE AMERICAN ECONOMIC REVIEW DECEMBER 1980

we have

(17) x, =

The full-employment condition, however,applies to the economy as a whole:

(18)

Finally, we continue to assume free entry,driving profits to zero. Now it is im-mediately apparent that the economy de-scribed by equations (I5)-(18) is very simi-lar to the economy described in equations(l)-(4). The price and output of a repre-sentative good—of either class^and thetotal number of products n + n are de-termined just as if all goods belonged to asingle industry. The only modification wemust make to the results of Section I is thatwe must divide the total production into twoindustries. A simple way of doing this is tonote that the sales of each industry mustequal the income of the appropriate groupin the population;

(19) = wL; = wL

But wages of the two groups must beequal, as must the prices and outputs of anyproducts of either industry. So this reducesto the result n/n = L/L: the shares of theindustries in the value of output equal theshares of the two demographic groups in thepopulation.

This extended model clearly differs onlytrivially from the model developed in Sec-tion I when the economy is taken to beclosed. When two such economies are al-lowed to trade, however, the extension al-lows some interesting results.

B. Demand and the Trade Pattern:A Simple Case

We can begin by considering a particularcase of trade between a pair of two-industrycountries in which the role of the domestic

market appears particularly clearly. Supposethat there are two countries of the type justdescribed, and that they can trade withtransport costs of the type analyzed in Sec-tion II.

In the home country, some fraction / ofthe population will be consumers of alphaproducts. The crucial simplification I wiDmake is to assume that the other country isa mirror image of the home country. Thelabor forces will be assumed to be equal, sothat

(20)

But in the foreign country the populationshares will be reversed, so that we have

(21)

If / is greater than one-half, then the homecountry has the larger domestic market forthe alpha industry's products; and con-versely. In this case there is a very simplehome market proposition: that the homecountry will be a net exporter of the firstindustry's products if f> 0.5. This proposi-tion turns out to be true.

The first step in showing this is to noticethat this is a wholly symmetrical world, sothat wage rates will be equal, as will theoutput and prices of all goods. (The casewas constructed for that purpose.) It followsthat the ratio of demand for each importedproduct to the demand for each domesticproduct is the same in both countries.

(zi) a = a =g '< I

Next we want to determine the pattern ofproduction. The expenditure on goods in anindustry is the sum of domestic residents'and foreigners' expenditures on the goods,so we can write the expressions

(23) npx = n

n*px =

n + on*

an'

wL +an

wL'n + an* on + n*

where the price p of each product and the

VOL. 70 NO. 5 KRUGMAN. PATTERN OF TRADE 957

n/n

L/C

FIGURE 2

output X are the same in the two countries.We can use (23) to determine the relativenumber of products produced in eachcountry, n/n*.

To see this, suppose provisionally thatsome products in the alpha industry are pro-duced in both countries; i.e., n>0, n*>0.We can then divide the equations (23)through by n and «*, respectively, and re-arrange to get

(24) L/L* = {n + an*)/ian + n*)

which can be rearranged to give

L/L*-a(25) «/«* = l-aL/L*

Figure 2 shows the relationship (25). IfL/L*=\, so does n/n*; that is, if the de-mand patterns of the two countries are thesame, their production patterns will also bethe same, as we would expect. And as therelative size of either country's home marketrises for alpha goods, so does its domesticproduction, as long as L/L* lies in therange a<L/L*> \/a.

Outside that range, (25) appears to giveabsurd results. Recall, however, that the de-rivation of (24) was made on the provisionalassumption that n and n* were both non-zero. Clearly, if L/L* lies outside the range

from a to l/o, this assumption is not valid.What the figure suggests is that if L/L* isless than a, n = 0; the home country special-ized entirely in bela products, producing noalpha products (while the foreign countryproduces only alpha products). Conversely,if L/L* is greater than I/a, n*=0, and wehave the opposite pattern of specialization.

We can easily demonstrate that this solu-tion is in fact an equilibrium. Suppose thatthe home country produced no alpha prod-ucts, and that a firm attempted to startproduction of a single product. This firm'sprofit-maximizing f.o.b. price would be thesame as that of the foreign firm's. But itssales would be less, in the ratio

< lL + L*

Thus such a firm could not compete.This gives us our first result on the effect

of the home market. It says that if the twocountries have sufficiently dissimilar tasteseach will specialize in the industry for whichit has the larger home market. Obviously,also, each will be a net exporter of the classof goods in which it specializes. Thus theidea that the pattern of exports is de-termined by the home market is quite nicelyconfirmed.

We also get some illuminating results onthe conditions under which specializationwill be incomplete. Incomplete specializa-tion and two-way trade within the twoclasses of products will occur if the relativesize of the domestic markets for alpha goodslies in the range from o to l/o, where a =gtf/(i-fl) But g measures transportation costs,while d/(l-9) is, in equilibrium, the ratioof variable to fixed costs; ̂ that is, it is anindex of the importance of scale economies.So we have shown that the possibility ofincomplete specialization is greater, thegreater are transport costs and the less im-portant are economies of scale.

A final result we can take from this spe-cial case concerns the pattern of trade when

'One can see this by rearranging equation (9) to get

958 THE AMERICAN ECONOMIC REVIEW DECEMBER 1980

Specialization is incomplete. In this case eachcountry will both import and export prod-ucts in both classes (though not the sameproducts). But it remains true that, if onecountry has the larger home market for al-pha producers, it will be a net exporter in thealpha class and a net importer in the other.To see this, note that we can write the homecountry's trade balance in alpha products as

(26) anan + n*

wL*- an'n + an*

wL

an + n*

awL* r

an" Ln + an* L*

an + n* ^ ^

where we used (24) to eliminate the relativelabor supplies. This says that the sign of thetrade balance depends on whether the num-ber of alpha products produced in the homecountry is more or less than the numberproduced abroad. But we have already seenthat n/n* is an increasing function of L/L*in the relevant range. So the country withthe larger home market for the alpha-typeproducts will be a net exporter of thosegoods, even if specialization is not complete.

C. Generalizations and Extensions

The analysis we have just gone throughshows that there is some justification for theidea that countries export what they havehome markets for. The results were arrivedat, however, only for a special case designedto make matters as simple as possible. Ournext question must be the extent to whichthese results generalize.

One way in which generalization might bepursued is by abandoning the "mirrorimage" assumption: we can let the countrieshave arbitrary populations and demand pat-terns, while retaining all the other assump-tions of the model. It can be shown that inthat case, although the derivations becomemore complicated, the basic home marketresult is unchanged. Each country will be anet exporter in the industry for whose goodsit has a relatively larger demand. The dif-

ference is that wages will in general not beequal; in particular, smaller countries withabsolutely smaller markets for both kinds ofgoods will have to compensate for this dis-advantage with lower wages.

Another, perhaps more interesting, gener-alization would be to abandon the assumedsymmetry between the industries. Again, wewould Hke to be able to make sense of somearguments made by practical men. For ex-ample, is it true that large countries willhave an advantage in the production andexport of goods whose production is char-acterized by sizeable economies of scale?This is an explanation which is sometimesgiven for the United States' position as anexporter of aircraft.

A general analysis of the effects of asym-metry between industries would run to toogreat a length. We can learn something,however, by considering another specialcase. Suppose that the alpha production isthe same as in our last analysis, but that theproduction of beta goods is characterized byconstant returns to scale and perfect compe-tition. For simplicity, also assume that betagoods can be transported costlessly.

It is immediately apparent that in thiscase the possibility of trade in beta productswill ensure that wage rates are equal Butthis in turn means that we can apply theanalysis of Part B, above, to the alpha in-dustry. Whichever country has the largermarket for the products of that industry willbe a net exporter of alpha products and anet importer of beta products. In particular:if two countries have the same compositionof demand, the larger country will be a netexporter of the products whose productioninvolves economies of scale.

The analysis in this section has obviouslybeen suggestive rather than conclusive. Itrelies heavily on very special assumptionsand on the analysis of special cases. None-theless, the analysis does seem to confirmthe idea that, in the presence of increasingreturns, countries will tend to export thegoods for which they have large domesticmarkets. And the implications for the pat-tern of trade are similar to those suggestedby Steffan Linder, Grubel (1970), and others.

VOL. 70 NO. 5 KRUGMAN: PATTERN OF TRADE 959

REFERENCES

Bela Balassa, Trade Liberalization Among In-dustrial Countries, New York 1967.

W. M. CordeD, "A Note on Economies ofScale, the Size of the Domestic Marketand the Pattern of Trade," in I. A.McDougall and R. H. Snape, eds.. Studiesin International Economics, Amsterdam1970.

A. Dixit and J. Stiglitz, "Monopolistic Compe-tition and Optimum Product Diversity,"Amer. Econ. Rev., June 1977, 67, 297-308.

H. Grubel, "Intra-Industry Specialization andthe Pattern of Trade." Can. J. Econ., Aug.1967, 33, 374-388.

, "The Theory of Intra-IndustryTrade," in I. A. McDougall and R. H.

Snape, eds.. Studies in International Eco-nomics, Amsterdam 1970.

G. Hufbauer and J. Chilas, "Specialization byIndustrial Countries: Extent and Conse-quences," in Herbert Giersch, ed., TheInternational Division of Labor, Tubingen1974.

I. Kravis, "The Current Case for ImportLimitations," in United States EconomicPolicy in an Interdependent World, Com-mission on International Trade and Invest-ment Policy, Washington 1971.

P. Knigman, "Increasing Returns, Monop-olistic Competition, and InternationalTrade," J. Int. Econ., Nov. 1979, 9, 469-80.

Steffan Under, A n Essa^ on Trade and Trans-formation, New York 1961.