March 24, 2003 Lecture #7

Reading: Chapter 5, pp. 159-191. Chapter 6.Next class we will discuss chapters 7 and 8

Homework -For next time: Ch. 5.: 1, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17

Chapter 6, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

Comments on problems: (Chapter 5)

On problem 6, add the following: Illustrate ATC, AVC and MC in a graph.a. Graphically, what is the relationship between ATC and AVC? Why?b. Graphically, what is the relationship between MC, ATC and AVC? Why?Also: Hint : notice that qty increases in increments of 100.

On problem 15 notice that the restaurateur could have simply sold the license back to the state for $65,000. Instead she tried to sell it for $70,000

ReviewIV. Costs and the Production Process.

A. The production process3. Optimal use of a single input.4. Long Run Production

a. Algebraic Production Functionsb. Isocosts and Isoquantsc. Optimal use of multiple inputs

PreviewC. Costs.

1. The relationship of production functions to cost functions.2. Short run costs.

a. Cost curvesb. Sunk vs. Variable Costs

3. Long-Run Costsa. Long Run Average Costsb. Economics of Scale

4. Multiple Output Cost functionsa. Economies of Scopeb. Cost complementarities

78

Lecture

C. Costs and the Theory of the Firm

1. The Relationship of Production Functions to Cost Functions. To provide some context for this discussion, consider the problem of producing blueberry tarts in my house. We may have the following relationship.

(a)Inputs:

(Number of Workers)

(b)Outputs

(Number of Blueberry Pies)

(c)Marginal

Pies

(d)Marginal Costs Per pie (Assume that labor costs $20 per unit, and

that ingredients are free)0 01 5 5 $20/5 =$42 15 10 $20/10=$23 23 8 $20/8 = $2.54 29 6 $20/6 = 3.335 33 4 $20/5 =$56 35 2 $20/2 = $10

In the lecture on short run production, we focused on the relationship between the number of workers (column a) and the marginal productivity of those workers (column c). A closely related question pertains to the relationship between the number of pies made (column b) and the marginal costs of making pies (column d).

Observations- After exhausting gains from specialization the relationship between units of labor and marginal productivity is inverse. This motivates the labor demand curve we developed last time in class.

0

2

4

6

8

10

12

0 2 4 6 8

Units of Labor (Column a)

Mar

gina

l Num

ber o

f Pi

es

(Col

umn

c)

79

- Conversely, the marginal cost curve first falls, and then, upon exhausting gains from specialization, increases.

$0

$2

$4

$6

$8

$10

$12

0 10 20 30 40

Units of Output (pies column b)

Mar

gina

l Cos

ts E

xtra

Pies

(C

olum

n d)

- Intuitively, marginal costs increase as Marginal productive decreases, because the marginal productivity increases imply that more labor is “imbedded in each unit of output.

Now we focus on this latter view of the relationship between inputs and outputs. We start with the single output case, first in the short run, and then in the long run. Then we consider some aspects of costs in a multi-product environment.

2. Short Run Costs. Recall that the short run is defined as a timeframe where there are unavoidable input commitments, as well as variable inputs. The short run cost function may be used to describe this relation.

a. Cost function components. Fixed costs: Costs associated with fixed input commitments. These costs do not change with the level of output

Variable costs: Costs associated with the variable components. These costs vary with the level of output.

b. Total cost relationships. One way to represent these costs is in terms of total expenditures. For example, consider the following table, where K is fixed at 2 and where L can vary

80

Graphically, these relationships appear as follows:

Total Costs

0

1000

2000

3000

4000

5000

6000

0 500 1000 1500 2000 2500Quantity

Cos

ts

Observations

-Notice that the TVC and the TC curves both take on the shape of a “recliner”: that is, first increasing at a decreasing rate, and then increasing at an increasing rate. The difference between the two curves is TFC, which is a fixed amount.

-Notice also that the slope of the line tangent to either TVC or TC is the marginal cost. Marginal costs first decrease and then increase due to the law of diminishing returns. (This is the same logic as diminishing marginal productivity: At the outset, gains from division of labor increase. Thus marginal productivity increases, and marginal costs increase, reflecting gains from specialization. Later, as the law of diminishing returns sets in, marginal productivity falls, as marginal costs increase. Intuitively, more labor is “imbedded” in each unit of output.)

K L Q FC VC TC (K*1000) (L*400) FC + VC

2 0 0 2000 0 20002 1 76 2000 400 24002 2 248 2000 800 28002 3 492 2000 1200 32002 4 784 2000 1600 36002 5 1100 2000 2000 40002 6 1416 2000 2400 44002 7 1708 2000 2800 48002 8 1952 2000 3200 52002 9 2124 2000 3600 56002 10 2200 2000 4000 60002 11 2156 2000 4400 6400

81

FC

TVC

TC

MC

c. Average Cost Relationships. The same relationships can be generated by dividing costs by quantity, to get per unit costs. In this case:

Q AFC AVC ATC MC076 26.32 5.26 31.58 5.26248 8.06 3.23 11.29 2.33492 4.07 2.44 6.50 1.64784 2.55 2.04 4.59 1.371100 1.82 1.82 3.64 1.271416 1.41 1.69 3.11 1.271708 1.17 1.64 2.81 1.371952 1.02 1.64 2.66 1.642124 0.94 1.69 2.64 2.33

AFC = TFC/Q (Average Fixed Costs)AVC = TVC/Q (Average Variable Costs)ATC = TC/Q (Average Total CostsMC = TC/Q

Graphically, these curves are represented as

Observations- ATC and AVC approach each other as quantity expands. This is because the difference between the two curves is AFC. AFC is a fixed quantity allocated over an increasing number of units.

- MC intersects ATC and AVC at their minimum points. This follows for the same reason that MP intersects AP at its peak: The marginal drives the average. The averages reflect the same information as the marginal. The

82

0

2

4

6

8

10

12

0 500 1000 1500 2000 2500

Quantity

$ MC

ATC

AVC

marginal is more volatile, however, because it is not weighed down by the effects of any output other than the current increment.

d. Algebraic Forms of the Cost Function. As with production functions, the appropriate specification of the cost function depends on the underlying cost relationships. However, a cubic cost function is often used, because it is sufficiently general to allow any relationship.

If C(Q) f + aQ + bQ2 + cQ3

Notice that fixed costs are f.Marginal costs are the derivative of C(Q), or

C’(Q) = a + 2bQ + 3cQ2

Notice that other cost relations are easily derived. For instance, average variable costs are

AVC = a + bQ + cQ2

Example: Suppose C(Q) = 20 + 3Q2

What are marginal costs, average fixed costs, average variable costs and average total costs when Q=10? When are average total costs minimized? (To be worked in class)

e. Sunk vs. Variable Costs. A final distinction (and one we’ve made before). Fixed costs may be divided into two components: Sunk costs and recoverable costs. Sunk costs are costs forever lost after they are paid. This is an important distinction, for the opportunity costs of recoverable assets and sunk cost assets is remarkably different.

Example: Suppose you are choosing between the purchase of a Toyota Corolla (for $12,500) and a GEO Probe (for $11,000). After a year the book value on the cars will be $11,000 and $7,000. What are the sunk cost components associated with the purchase of each car? How does this difference affect your decision to undertake a 5 year loan to pay for the cars?

3. Long-Run Costs. In the Long run, all costs are variable. As I indicated at the outset of this chapter, the long run may be viewed as the planning horizon, since the project for the firm is to pick the optimal plant size. Information about the Long-Run Average Cost curve is very useful for determining the structure of an industry.

a. Long Run Average Costs. The long run average cost curve (LRAC) is the envelope of all short run costs curves. That is, the LRAC is the tangency of all efficient production points on for each plant size.

83

ATC0

ATC1 ATC3

ATC2

Economics of Diseconomies of ScaleScale Efficient Plant Size Q

In the above chart, the bold line is the LRAC. Note that the efficient scale of operation is not at the point of minimum marginal costs unless the firm is at an optimal plant size.

b. Economics of Scale

Economies of scale arise when LRAC falls as the plant expands.

Diseconomies of scale arise when LRAC increases as the plant expands.

Minimum Efficient Scale (MES): The first point where LRAC is at a minimum

If a range exists where costs neither increase nor decrease, there exist constant returns to scale.

Application: The shape of the LRAC can determine how many firms can survive in an industry.

- Suppose that MES is 10,000 units, and that market demand, at a competitive price is 40,000 units. How many efficient firms can survive in the industry?- Suppose that MES is 10,000 units, but that diseconomies of scale set in very soon after achieving the optimal plant size. Can a single firm efficiently service the industry?- Suppose an industry is characterized by continuous diminishing returns to scale. What is the optimal industry structure?

4. Multiple Output Cost Functions. All of the insights pertaining to single product output apply to a multi-product firm. There are, however some interesting additional cost issues that arise. In finishing this chapter, consider two points: The notion of economies of scope, and economies of scale.

To illustrate, we will consider cost conditions for a firm that produces just two products: Q1 and Q2. Denote the cost function for this firm as C(Q1, Q2).

a. Economies of Scope: Exist when the joint production of two goods is less expensive that the production of both goods separately. Mathematically, if

84

C(Q1, 0) + C(0, Q2) > C(Q1, Q2)

Economies of scope are an important reason why firms produce multiple products. For example, it may be more efficient to produce both cars and light trucks in a single plant than to produce both good separately, the two products may share many parts of the same assembly (such as the chassis) and producing the products separately would require considerable duplicative construction.

b. Cost complementarities: These exist in the marginal cost of producing one good increases when the output of another product is increased. Mathematically, when:

MC 1(Q1, Q2)< 0Q2

This often arises when one product is a by-product of another. For example there are cost complementarities in the production of in the production of Flouride and Aluminum Ingot from Alumina.

Cost complementarities are an important reason for economies of scope.

These notions are conveniently expressed algebraically with at quadratic cost function:

C(Q1, Q2) = f + aQ1Q2 + Q12 + Q2

2

Then MC1 = aQ2 + 2Q1

Cost complementarities exist whenever a < 0.

Economies of scope exist whenever

C(Q1, 0) + C(0, Q2) > C(Q1, Q2)

C(Q1, 0) = f + Q12

C(0, Q 2) = f + Q22

Thus, economics of scope exist if

2f+ + Q12+ Q2

2 > f+ aQ1Q2 +Q12+Q2

2

Or if f - aQ1Q2 > 0.

Comparing the two conditions, it is seen that cost complementarities are a stronger condition than economies of scope. Given a<0, cost complementarities

85

always exist. However, economics of scope may also even without cost complementarities, if the costs of paying fixed set-up costs twice are sufficiently high.

Example: Suppose

C = 100 - .5Q1Q2 + Q12 + Q2

2

Do cost complementarities exist?

Do economies of scope exist? What about the case where

C = 100 + .5Q1Q2 + Q12 + Q2

2 ?

Notice the existence of economies of scope and cost complementarities have a lot to do with the effectiveness of mergers and the sales of subsidiaries. Sales of an unprofitable subsidiary may not reduce losses much, due to cost complementarities. Similarly, due to economies of scope, it may be the case that multi-product mergers are efficient.

V. The Organization of the Firm: Optimal Contracting, and Motivating Resources to Work Efficiently (Chapter 6)

A. Overview and Motivation. In the preceding chapter we discussed the decision rule for the optimal combination of inputs. That is, firms should hire resources until

MPL = MPK

w rassuming that the inputs are working on their production function. This rule suggests two important issues that are the subject of this chapter: (a) Is the firm obtaining resources at the minimum necessary price? Clearly, the firm will suffer inordinately high costs if this condition is not met. (b) Are inputs working efficiently? As mentioned in the first chapter, in many instances the incentives of individuals and firms do not naturally overlap. Compensation schemes may in many instances be altered to make incentives more compatible.

Consider these questions in turn.

A. Methods of Procuring Inputs:

1. There are three generic ways to acquire inputs:

a. Spot purchases. This is purchasing on an as needed basis at the then prevailing market price. Spot exchanges allow firms to avoid vertical integration, and to concentrate on their primary specialty. Homogenous inputs that are available at a competitive price are often purchased on a spot basis.

86

b. Contract purchases. This is an agreement to purchase inputs under some continuing arrangement that specifies the terms of exchange. In many instances, particularly when the arrangement is fairly complicated, terms of the exchange are not entirely spelled out. These areas are a problem of incomplete contracts and are a basis for negotiation.

c. Internal production. Occurs when firms decide to go into the production of the needed input. Internal production can come at the cost of administrative overhead, and requires development of a specialization in production of the input.

Example. Suppose I sell ice cream cakes. I need ice cream as an input.

- If I go to a food wholesaler and make purchases as needed, I make a spot purchase.

-If I strike a one-year deal with Breyer’s, to use only their products, I have made a contractual arrangement.

-If I decide to make ice cream myself, I have gone into internal production.

2. Specialized Investments and Transactions Costs. If spot purchases are the easiest, allow the most efficient specialization, why aren’t all inputs acquired on a spot basis? The reason is that not all inputs are available on an essentially competitive basis. Rather, firms frequently must make specialized investments either to use or to produce particular inputs. Contracting could surmount this problem. However, in some instances the contract negotiation costs are too high, and internal production is necessary. Consider these terms in more detail

a. Specialized investment: An expenditure that must be made to all two parties to exchange that has little or no value in any alternative use.

i) Example: Suppose you produce applications software (e.g., word-processing programs). A specialized investment would be the production of code that enabled the program to work in a Windows 2000 environment. This extra code would be useless if you wanted to sell your software to the makers of Apple Computers.

ii) Types of Specialized Assets

-Site Specificity: Locating your plant close to a particular input. (Example: Locating an electricity plant close to a coal mine since it is less expensive to ship electricity than coal. The arrangement would make little sense if coal from the mine was not purchased by the electricity plant)

- Physical-Asset Specificity: The production or acquisition of specialized physical capital in order to use an input. For example, for a bicycle maker, a special machine needed to make wheel rims that work with a particular tire would be a specialized physical asset.

87

- Human capital: Workers learning specific skills to use a particular product. (Example, learning how to use products on the MS office suite)

iii. A relationship-specific exchange. This occurs when the parties to a transaction have made specialized investments. Notice that specialized investments make impossible the satisfaction of the many-buyers/ many-sellers assumption underlying competitive market theory. (One buyer or seller will always be better suited than others to buy or sell the input). Thus the presence specialized investment can create a need for contracting.

b. Transactions Costs. The costs of contracting are importantly affected by specialized investment, for three reasons

i.) Costly Bargaining. As mentioned above, specialized investment means that there are only a few parties that may efficiently engage in a buyer/seller relationship. Consequently, there is no “market price.” In fact, there is often a lot of difference between the minimum price necessary to induce supply, and the maximum acceptable purchase price, creating considerable room for bargaining.

ii) Underinvestment. Either the buyer or the seller may under-invest in the specialized inputs. (Who would spend a lot of time learning how to use UNIX, for example, if the university might shift exclusively to networked computers?)

iii) Opportunism. Once a firm has engaged in a specialized investment, the firm on the other side of the bargain has an incentive to take advantage of the sunk cost expenditure. (Suppose you spend $300 for three nights in an isolated resort hotel, meals not included. How much do you think they will charge for meals?)

A comment on opportunism: When one side of a bargain tries to take advantage of the specific investment made by another, a hold-up problem is created. Avoiding hold-up problems is often a reason for more formal arrangements, such as contracts or even internal production.

B. Optimal Input Procurement. Now we consider factors affecting the optimal input method. In general, more formal arrangements are called for as the relationship-specific capital is increased.

1. Spot Exchange. This is the most straightforward purchasing method. Given many buyers and sellers, a homogenous input, and no relationship-specific capital, input prices are determined by the intersection of market supply and market demand schedules.

However, reasons often exist that would induce a manager to bear the expense of drafting a contract: Specialized investments are insidious. For example, suppose you retail fresh fish in a cafe/restaurant store, and you need 500 pounds of fresh fish at 8:00 a.m. each day. Even though fish are homogenous, the size of the input need creates “hold-up” opportunities for both the buyer and the seller.

88

-The fish seller, with a truck full of fish may refuse to unload the product unless a premium is paid.

- The fish buyer (the restaurant owner), may call several trucks to deliver fish at once, and then bargain with the one offering the lowest price.

2. Contracts. When hold-up opportunities become high relative to the costs of negotiating a contract, contracting becomes optimal. Despite the costs of contract negotiation, formalizing a relationship into a contract can resolve numerous problems. A good contract, for example, eliminates the incentives to skimp on specific investments in capital and labor. (e.g., You will spend more on training workers that will be around for three or four years).

a. Optimal contract length. Once the decision has been made to negotiate a contract, the question of optimal contract length becomes a question. Optimal length is determined by the marginal cost of writing the contract, and the marginal benefit of extending contract terms.

i. Marginal costs increase with time. As the timeframe expands, more contingencies must be considered, increasing the negotiation costs.

ii. Marginal benefits include avoided transactions costs or bargaining and opportunism. These may be temporally related, but for the present, assume that they are constant.

Then a graphical representation of the optimal contract term problem is illustrated as follows:

$MC

MB

L* Time

b. Some comparative statics effects.i. Optimal contract length will increase if the level of specialized investment

increases. (As could be seen by an upward shift of the MB schedule). ii. Changes in the costs of writing contracts would also affect the optimal length.

For example, an increasingly uncertain environment would shift MC up. On the other hand, an increasingly standardized product and a more established market for the final product would shift MC down, extending the optimal contract.

3. Vertical Integration. When specialized investments generate transactions costs, and when the economic environment is plagued by uncertainty, vertical integration becomes necessary. The advantage of vertical integration is that the “middleman” is avoided,

89

reducing the latitude for opportunism. The cost is that the firm must develop expertise in development of a more primitive stage of the production process for its product. This often involves building a costly production facility, and often requires that the firm engage in some process that has little to do with their primary area of expertise.

4. The Economic Trade-Off. A summary of the relevant decision calculus is illustrated below. Spot Exchange

No Large spec-ialized invest-ments relativeto contracting Yes cost? Complex con-

tracting environ- ment relative to

cost of verticalintegration?

No Yes

Contract Vertically Integrate.

Spot exchange is optimal when there are few “hold-up” opportunities, or where the costs of those opportunities are small relative to contracting costs. When specialized investments become large, contracting or vertical integration is desirable. The choice among these latter alternatives depends on the complexity of the economic environment relative to the costs of integration.

Final comments.When a contract is called for, a formal contract is not always necessary., Despite

considerable specific investment, it is not always necessary to resort to written contracts. Buyers, for example often can “punish” opportunistic behavior by not purchasing from a seller again, and by spreading the word that they were treated badly. These reputational considerations can play a large role in unwritten, but highly efficient contracts.

Review Problem: Suppose you manufacture inboard motor-boats, and you agree to purchase 100,000 motors from Johnson Motor company for $1000 per motor, in two years time. Feeling that you are protected from opportunism, you customize your boat design to accommodate the Johnson motors. In the mean time, Johnson finds itself on the verge of bankruptcy, and says that it will go broke if the company doesn’t receive $1500 per motor.

a) Was the decision to contract a bad one?b) What should you do?c) Should this situation have been avoided?

90

B. Managerial Compensation and the Principal-Agent Problem. The second portion of this chapter deals with the issue of the optimal compensation structure for labor.

1. The Principal-Agent Problem. In a generic form, the problem is that a principal (the owner of a firm) is in many instances distinct from those who work there, and those who manage it (the agents). The agents are probably not opposed to the principal earning profits, but they are more interested in maximizing the arguments in their own utility functions, which includes leisure as well as income.)

To surmount this problem, a contract must be structured to make incentives of the principle and agent more compatible.

2. Structuring Contracts for Managers. The productivity of managers is particularly difficult to observe directly. If a firm

lost several million dollars in a year, it could be due to poor management, or it could be poor underlying economic conditions. In fact, the manager may have saved the firm from considerably higher losses (and the manager will make this claim whether he or she worked hard or not!)

There are two basic types of incentives that may align the interests of managers and owners.

a. Incentive contracts. This is the most standard solution. Managers are paid some portion of the profits rather than a flat salary. Notice that in many instances this results in highly remunerative salaries. It is necessary, however, that the value of the firm increase.

In criticism of overly lucrative incentive contracts, observe that the profitability of the firm is affected by matters that are not under the control of management. For example profitability for many, many firms has increased substantially over the past five years, because of a robust domestic economy. Managers have enjoyed the benefit of good economic times as well as the reward for their skills.

b. External Incentives. In addition to internal incentives, managers are motivated by long term external concerns. In particular, if they demonstrate that they can generate wealth, then their managerial reputation will allow them to command a higher salary in other firms. Also, management should also be concerned about the threat of takeover, with the new owners replacing poor incumbent management with others.

Notice here that the problem of Executive compensation is not easily resolved.

Example: Former GE CEO Jack Welsh’s recent and very public divorce hearings have highlighted the problem of retirement compensation for top executives. Welsh’s retirement benefits include not only a “pension” and secretarial service, but a number of other perk’s including a $15 million Manhattan apartment, unlimited use of a Corporate Jet, and life-time courtside tickets to Knicks basketball games. While Welsh gave back many of these benefits as a face-saving move, how should Executives be compensated?

91

Example: Compare executive incentives in Europe (where CEO’s typically sign annual contracts with incentives in the U.S. (where CEO’s sign much more lucrative long-term packages)

3. The Manager-Worker Problem There is nothing unique about the relationship between stockholders and CEO’s. Managers also face similar problems in inducing the appropriate performance from workers. Several compensation schemes are possible.

a. Profit Sharing. Worker income can be tied to the profitability of the firm, as is typically the case for owners. This should induce greater productivity, and for reasons identical to the CEO/stockholder situation.

A practical drawback of this scheme is that the scale of payments is much lower, and workers don’t like to have their income seriously affected in poor economic times.

b. Revenue Sharing. Greater productivity can also be generated by tying compensation to sales. It is for this reason that waitresses often rely on tips, and that sales people for big ticket item consumer goods are often paid in term of commissions.

A problem with revenue sharing schemes is that they do not encourage workers to minimize costs. (Thus for example, while it is ok for a waiter to receive tips, a similarly motivated cook would feel motivated to increase the serving size!)

c. Piece Rates. Another alternative to hourly compensation is to pay on a per unit basis. This can motivate higher productivity. However, it can lead to poor quality. (Such a scheme works fine when quality is closely monitored. In academics, for example, paying faculty for publishing in high-quality journals is a sort of piece-rate compensation scheme that doesn’t encounter the quality-shirking problem.

d. Time clocks and time checks. Time clocks are a poor method of monitoring productivity. They monitor physical presence rather than effort. Time checks can be more effective. Time checks, however, must be random, they must occur with some frequency, and there must be a penalty associated with failure.

Notice: A problem with time checks is that they are based on punishments (“sticks”) rather than rewards (“carrots”). People tend to respond rather differently to the different psychological environment created under the alternative schemes.

Comment: The problem of both employee and executive compensation are caught up, in a fundamental way with the notion of ethical decision-making in the work place. The rather depressing frequency of executive mismanagement and accounting problems recently in the news provides highly relevant background.

a) Why do you think that auditors filed misleading audit reports for firms? b) Why are the CEO’s in power those that abuse their position?

I will assert (in lecture) that incentives in the system make the “muck” rise.

92

For Discussion:

Last July the Sarbenes-Oxley Act was signed into Law by President Bush. Among othe things the law did the following

a) Requires CEO’s to sign audit reports (but does not increase liability).b) Limited the provision of auditing and consulting servicesc) Requires the Board to have Outside membersd) Limits the amount of time that any one accounting firm can be the lead auditor

for a corporation.e) Forces executives to report immediately (within 2 days) the sale of company

stock.

The Sarbenes-Oxley Act did not address other issuesa) Allowing employees to sell stocks in 401(k) plan.b) Costing stock options.c) Failed to restore an old law that had lapsed where by investment firms, legal

firms and accounting firms were liable for corporate mismanagement.

What do you think? (For discussion in class)

93