Intermediate microeconomic analysis : theory and applications 0134707087

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a

Library of Congress Cataloging in Publication Data

Douglas, Evan J., (date) Intermediate microeconomic analysis. Includes bibliographies and index. 1. Microeconomics. I. Title. HB172.D68

ISBN

330

0-13-470708-7

81-15716

AACR2

Editorial/production supervision and interior design by Margaret Rizzi Cover design by Frederick Charles Ltd. Manufacturing buyer: Ed O’Dougherty ©1982 by Prentice-Hall, Inc., Englewood Cliffs, N.J. 07632

All rights reserved. No part of this book may be reproduced in any form or by any means without permission in writing from the publisher. Printed in the United States of America TOMO Se Ome ae Om woo 4s 32.

ISBN

0-13-470708-?

Prentice-Hall International, Inc.,London Prentice-Hall of Australia Pty. Limited, Sydney Prentice-Hall of Canada, Ltd., Toronto Prentice-Hall of India Private Limited, New Delhi Prentice-Hall of Japan, Inc., Tokyo Prentice-Hall of Southeast Asia Pte. Ltd., Singapore Whitehall Books Limited, Wellington, New Zealand

To the memory

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Contents

PREFACE

XV

PART

Introduction AN INTRODUCTION TO MICROECONOMIC ANALYSIS I. INTRODUCTION

Microeconomics and Macroeconomics

«
MP > 0)

(MP*< 0)

Fig. 5-3, the production process is in stage 2 between the labor inputs L, and Ly». The rational producer chooses to produce with a particular level of labor input within this range, depending, as we shall later see, upon the marginal cost of and marginal revenue for the output unit produced. Essentially, the producer continues producing extra units of output, that is, continues adding labor units, until the next output unit is no longer profitable. Stage 3 of the short run production process occurs at and after the point where the marginal product of labor becomes negative. In Fig. 5-3 we show stage 3 to the right of labor input L,. Recall that marginal product is negative when the total product curve is falling. Thus, no rational producer would knowingly stray into stage 3, since the addition of extra labor (at extra cost) causes output and sales revenue to decline. Thus the firm chooses to produce in stage 2 of its short run production function, since stages 1 and 3 provide a profit incentive to stay out of them. EXAMPLE:

Although at this point we cannot say exactly where in stage 2 the rational producer should stop adding labor, we can demonstrate the principle involved. Consider an extreme case where the price of the fixed factor is zero. In the frontier days, for example, a settler might crest a hill and decide to farm the land stretching before him in the valley below. Although this land is free, it is in fixed supply, being bordered by a river and wooded hillsides. How much labor should the settler add to this land? Since the land is free, its degree of utilization will not influence profitability. Rather it is the labor, which has a cost, that should be utilized with discretion. Being on the frontier and far from any towns where cash is useful, let us suppose the settler can hire workers by paying them in kind, for example, grain, beans, or chicken, at a rate equal to their average product. In order to maximize his surplus of foodstuffs (for eventual sale), the settler should hire workers up to the point where the ratio of output to labor is maximized; that is, where the average product of labor reaches its maximum, at the start of stage 2. To go any further would add more to costs—foodstuffs paid—than it would to the output of foodstuffs and would thus reduce the surplus of foodstuffs to be

116

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

sold. Thus where capital is free and labor has a cost, the producer should employ labor only up to the start of stage 2. Now take the opposite situation. In agrarian China, at about the same time, the fertile river valleys were crowded with equally fertile families pursuing an existence supported by rice farming. Land was relatively scarce, and the owner had to pay an annual payment to an avaricious landlord. Labor, in the form of many children, was, on the other hand, free. In this situation, how much labor should the farmer add to his small plot of land? Since all costs of production are fixed and none are variable, it is clear that labor should be added until total product is maximized, thus maximizing the surplus of rice remaining for the farmer and his hungry family. This would occur at the end of stage 2. NOTE:

When the fixed factor is free, the producer should choose the start of stage 2, and when the variable factor is free, the producer should choose the end of stage si When both factors have a cost, it follows that if the variable factor is relatively expensive, compared with the fixed factor, production tends to be optimal toward the early part of stage 2. Alternatively, if the fixed factor is relatively expensive, production tends to be optimal toward the latter part of stage 2. We shall return to this issue later, to show the exact amount of the variable factor that should be utilized when both fixed and variable factors have a cost involved.

IV. RETURNS

TO SCALE

The long run analogy to increasing, constant, and decreasing returns to a variable factor in the short run is the increasing, constant, and decreasing returns to all factors in the long run, when all are variable. By increasing the inputs of all factors in the same proportion, that is, by increasing the scale of the firm’s operation, we expect output to increase by some proportion.

Increasing, Constant, and Decreasing Returns to Scale DEFINITION: Returns to scale are defined in terms of the proportionate increase in output relative to the proportionate increase in all inputs. If, for example, the inputs of both labor and capital are doubled, and output more than doubles, we speak of increasing returns to scale. If output increases by asmaller proportion, there are decreasing returns to scale. If output increases by the same proportion as capital and labor were increased, this indicates constant returns to scale.

EXAMPLE:

Suppose we have a situation in which 1 unit of capital and 2 units of labor are being combined to produce 3 units of output, as in Table 5-1 . Now let us consider increasing the scale of operations by augmenting the input of both factors, but keeping the same factor proportions, or capital-labor ratio. We demonstrate this in Table 5—3, which is an extension of Table 5—1 to larger scales of operation. Notice that capital and labor are combined in the ratio 1:2 in each row of Table The Theory of Production and Supply

117

5-3: Thus factor proportions are constant as the scale of operations is progressively increased. Returns to scale are determined by the ratio of the percentage increase in output to the percentage increase in scale of plant, as shown in the last column of Table 5—3. Thus capital and labor together become more efficient until the sixth scale of plant—6 capital and 12 labor—at which combination there are constant returns to scale. This is followed by decreasing returns for the seventh and subsequent scales of operation. Ws

TABLE

\

5-3

Returns to Scale Exhibited by the Relative Increases in Scale and Output Inputs

Output Percentage of Preceding

Units of Capital

Percentage of Preceding

Output in

and Labor

Row (%)

Units

Row (%)

land 2 2 and 4 3 and6 4and8 5 and 10 6 and 12 7 and 14 8 and 16

— 200 150 1382S 2s 120 116.7 114.3

3 19 62 110 198 238 213 300

— 633 326 SUT 180 120 HOLS 110

Returns to

Scale — increasing increasing increasing increasing constant decreasing decreasing

How can we show the returns to scale on the output hill? Note that we wish to show the impact on the production surface as all factors are increased in the same proportion. A ray from the origin along the base of the grid will reflect a constant ratio between capital and labor. If we slice the output hill along such a ray, the shape of the production surface along this slice shows the information we seek. Two such slices are shown in Fig. 5—4. Since returns to scale refer to the rate of change of output (vertical rise), as all inputs are changed in a constant proportion (horizontal run), the slope of the line cut into the production surface indicates whether there are increasing, constant, or decreasing returns to scale. When this line is convex from below, there are increasing returns to scale; when

it is concave from below, there are decreasing returns to scale. A straight line over any distance represents an area of constant returns to scale. (In the production function shown here, constant returns prevail only momentarily, at the inflection point.) An Example: The Supertanker

During the Six-Day War in the Middle East in June 1967, several large ships were sunk in the Suez Canal, thus bringing to an abrupt halt the vigorous oil tanker traffic between the oil-rich Middle East countries and Europe and North America. While hostilities continued to simmer, this traffic was forced to take the long way to Europe and North America, around the southern tip of Africa. As time passed, two things became obvious: First, that the Suez Canal would not quickly 118

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

FIGURE

5-4

Returns to Scale Exhibited by the Production Surface Output units (Q)

Capital units

(K)

be reopened (it took exactly eight years); and second, that the existing ships were too small for the economical transportation of oil over this longer distance. The Suez Canal had acted as a constraint on the size of the tankers, since it was restricted to ships drawing thirty-seven feet or less. The removal of this constraint and the requirement to travel much greater distances led to a substantial change in the nature of the oil transportation industry and the emergence of the supertanker. The output of the oil transportation industry may be measured as gallons per mile per day transported. Larger ships carry more gallons per mile and tend to be slower. The supertankers, however, although significantly slower, were able to carry substantially greater loads. For example, suppose ship A carried 100 million gallons at 8 miles per hour, or 192 miles per day. This ship’s output rate is therefore 520,833 gallons per mile per day. Now suppose ship B carried 40% more oil but is only 20% slower. It therefore carries 140 million gallons at 6.4 miles per hour or 153.6 miles per day. Its output rate is thus 911,458 gallons per mile per day, which represents 75% more than the smaller ship. Finally, suppose that the larger ship costs 50% more initially (capital input) and costs 50% more to operate (labor input). In this case there are significant economies of scale associated with the larger ship. Given the dramatic shift to supertankers that followed the 1967 closing of the Suez Canal, one might assume this to have been the case. The Theory of Production and Supply

119

V. ISOQUANT—ISOCOST

ANALYSIS

Weare now ready to bring the cost of the inputs into the analysis, in order to find the economically-most-efficient combination of inputs for each output level or, conversely, how to maximize the output for any given level of expenditure on inputs. We shall do this with the aid of two new concepts: the isoquant curve and the isocost curve. We see immediately that these are analogous to the indifference curve and budget line in the consumer choice problem. DEFINITION: . An isoquant is a line joining combinations of inputs which generate the same ___ level of output. The word “‘isoquant’’ comes from the Greek word iso meaning equal and the Latin word quantus meaning quantity. Note that we can find isoquant curves from the output hill by slicing the hill horizontally at any particular output level. Any horizontal slice in the output hill will result in a curved line being cut into the production surface. This line is an isoquant, since it shows the various combinations of labor and capital that can be used to produce a particular output level. Since the output level is constant for each isoquant curve, we can depict them in two dimensions as in Fig. 5—5. Note that isoquant lines are, in effect, contour lines on the production surface, since all points on a particular line show equal elevation above the base of the output hill.® FIGURE

5-5

!soquant Curves: Contour Lines on the Output Hill

Capital units

(K)

Labor units

(L)

°To conform with the traditional representation of isoquant curves, capital is shown on the vertical axis and labor on the horizontal axis.

120

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

Technical Efficiency and Inefficiency—Ridge Lines

A combination of capital and labor is technically efficient if none of either factor can be subtracted without reducing the output level, given ceteris paribus. All combinations on negatively sloped sections of the isoquant curves are technically efficient, since if one factor input is reduced while the other factor input is held constant, output will decline, and the new input combination will lie on a lower isoquant curve. On the other hand, all combinations on positively sloped sections of isoquant curves are technically inefficient, since some of both factors may be subtracted without reducing output. In terms of Fig. 5-5, output level Q, can be produced by different combinations of capital and labor at points A, B, and C. Combination C is technically inefficient, however, since the same output level could be produced at combinationA by subtracting L; — L; units of labor or at combination B by subtracting both L; — L, units of labor and K, — K, units of capital. By the same process of reasoning, all points on positively sloped sections of the isoquants are techni-

cally inefficient combinations of the inputs. For each isoquant curve it is evident that the points where the curve becomes vertical and horizontal (points E and B in the preceding case) are the limits to the technically efficient input combinations for producing that output level. If we mark all isoquants at the points of verticality and horizontality and if we join these points, we can divide the entire input space between the set of input combinations that is technically efficient and the set that is technically inefficient. DEFINITION: In Fig. 5-6 we show the ridge lines OR and OT, which are the loci of the points of verticality and horizontality, respectively. Between the ridge lines lie all technically efficient input combinations, namely, those lying on negatively sloped sections of the isoquant curves. Outside the ridge lines, on the positively sloped sections of the isoquant curves, lie all the technically inefficient combinations. The Marginal Rate of Technical Substitution DEFINITION: The marginal rate of technical substitution, (MRTS), is the rate at which labor — can be substituted for capital in the production process, such that output re- | mains unchanged. Note that it is equal to the amount of capital that can be subtracted from the production process for a one-unit increase in labor added to the

production process. Thus

MRTS = —

(5-5)

where AK is the decrement to capital that will just allow output to remain unchanged given a one-unit increment, AL, to the labor input. Thus the marginal

rate of technical substitution reflects the slope of an isoquant curve, and will be

negative for all technically efficient combinations of the factors and positive for all technically inefficient combinations. The Theory of Production and Supply

121

FIGURE

5-6

Ridge Lines, Showing the Technically Efficient Combinations Capital (K)

Labor (L)

NOTE:

Wecan show that a positive value for the marginal rate of technical substitution means that the marginal product of either labor or capital is negative. In Fig. 5—7 we show two situations. First, suppose some capital is added to the production process at Point A, while holding labor input constant at Ly. Adding K, — K, FIGURE

5-7

Negative Marginal Productivity of Inputs outside the Ridge Lines

Labor (L)

122

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

units of capital actually causes output to fall from Q, to Q,, since point B lies on a lower isoquant curve. Thus the marginal product of this capital must be negative, since its impact is to reduce the output level. Alternatively, if we add labor to the combination represented by point C, while holding capital constant at Ko, output falls from Q, to Q,;. Thus the additional labor input, L, — L,, must have a negative marginal product, since it causes the total product to decline. By analogy with the consumer’s MRS, it may be anticipated that the producer’s MRTS is equal to the ratio of the marginal products of the two inputs. The proof is as follows. Consider Fig. 5—8. Points A and B lie on isoquant curve Q, and represent input combinations (L,, K, and Lz, K,), which produce Q, units of output.

FIGURE

5-8

Marginal Rate of Technical Substitution Is Equal to the Ratio of the Marginal Products Capital units

(K)

Ky

Labor units

(L)

Let us make the move from pointA to B in two separate steps. If we first take away from the production process K, — K, units of capital, output falls to Qi units, and the firm is at point C in Fig. 5-8. The reduction in output, Q2 — Qi, is equal to the marginal product of capital times the number of units removed from the production process. That is Q. —Q,

=

(K> —

K,) MP,

or

AQ = AK - MPx The Theory of Production and Supply

(5-6)

123

Now if we add labor to the new level of capital, so that the firm moves from point C toB, output returns to Q:. The increase in output, Q2 — Q;, is then equal to the marginal product of labor times the number of units of labor added. That is Q, 7 Gq, —

or

(L, —

L;) MP,

AQ=AL- MP,

(5-7) ~

Since the left-hand sides of Eqs. (5-6) and (5—7) are both equal to AQ, it follows that the right-hand sides are also equal. That is AK

%

MP,

=

AL

Y

MP,

Rearranging terms, we have

AK —= AL

MP, MPx

5-8 Soa)

Now, since MRTS = AK/AL by definition in Eq. (5—5), we have

MRTS NOTE:

3

=

MP, MP,

5-9 Save

MP, is negative for reductions of the capital input inside the ridge lines and positive for reductions of capital above the upper ridge line, shown as OR in Fig. 5-7. Oppositely, MP, is positive for increments to the labor input inside the ridge lines and it is negative for increments to labor below the lower ridge line, shown as OT in Fig. 5—7. Thus MRTS is negative inside the ridge lines and positive outside the ridge lines, as discussed previously. It can be shown that the ridge lines encompass the stage 2 labor input levels for every level of capital input. To the left of the ridge line OR, additional labor input increases output at a faster rate, implying that the capital input is too large for the labor input and that it would exhibit a negative marginal product if varied. The line OR thus delineates the boundary between stage 1 and stage 2, as labor is varied for each level of capital input. To the right of ridge line OT, additional labor has a negative marginal product. Thus line OT delineates the boundary between stage 2 and stage 3, as labor is varied for each level of capital input. Together the ridge lines OR and OT encompass the stage 2 combinations of labor and capital, and we should expect the producer to choose an input combination close to the ridge line OR if labor is relatively expensive or, alternatively, close to the ridge line OT if capital is relatively expensive. Let us see why.

Economic Efficiency: Isocost Lines

The actual combination of capital and labor chosen to produce each output level (in the long run situation where the firm is free to vary all inputs) depends on the relative prices of the inputs. Only one of the technically efficient ways of producing each output level is economically efficient: Only one allows the lowest cost of producing that output level. 124

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

DEFINITION: Isocost lines are analogous to the budget lines of consumer behavior theory and show combinations of capital and labor that cost the same. Let us express the firm’s expenditure on inputs as

where E is the total dollar expenditure, Px and P, are the unit prices of capital and labor, respectively, and K and L are the number of physical units of capital and labor employed in the production process. This can be restated as

eT

(5-11)

This form is perhaps more recognizable as a linear equation explaining K in terms of L and three known values. It can therefore be plotted in the same space as the isoquant curves. The intercept of the isocost line on the capital axis occurs when the labor input is zero; it is therefore simply the total expenditure divided by the price of the capital units (that is, E/Px, since P,/Px - L is zero when L is zero), resulting in a certain physical quantity of capital units. As we begin to purchase units of labor, it is evident that our purchases of capital units for the same expenditure (isocost) level, must be reduced in the ratio of the price of labor to the price of capital. The negative of the ratio of input prices, —P,/Px, is thus the slope of the isocost line. FIGURE

5-9

Isoquant-Isocost Analysis Showing Short Run and Long Run Expansion Paths

Capital units (K)

EP (Long run expansion

path) TP (Short run expansion

path)

>

N

WN

Labor

units

(L)

For each input level there will be a minimum-cost combination of the factors necessary to produce that output level. In Fig. 5-9 we show three isoquant curves representing 20, 40, and 60 units of output. The cost of producing 20 The Theory of Production and Supply

125

A, since any other capital/labor combination producunits is minimized at point ing 20 units, such as at A’, lies to the right of the isocost line MN and would thus require a larger total expenditure to purchase. Recall that the intercept on the capital axis is equal to E/Px, where Px is presumed to remain unchanged. Hence larger total expenditures are represented by higher intercept points and higher isocost lines. Similarly, the output level of 40 units is produced at least cost at the input combination represented by pointB, and 60 units are produced at least cost at the input combination at point C. nie ft RULE:

The condition for output maximization, given a particular cost or total expenditure level, is that the isocost curve must be tangent to the highest attainable

isoquant curve. Alternatively, to minimize cost for any given output level, the isoquant curve representing that output level must be tangent to the lowest attainable isocost curve. This tangency requirement means that the slopes of the isoquant and isocost curves must be equal. The slope of the isoquant curve is the MRTS, or the ratio of the marginal products, MP; /MPx. The slope of the isocost curve is the ratio of the prices, —Px/Px. Thus the output-maximizing, or costminimizing condition, can be expressed as

MRTS = —P,/P x

(5-12)

or MP,

a

MP,

—P,

poe

(5-13)

or, by rearranging terms,’

MP, _ MPx pi dally

(5-14)

Thus the output-maximizing, or cost-minimizing, condition can be stated as follows: the ratio of marginal products must equal the ratio of factor prices—Eq. (S—13)—or the ratio of marginal product to price must be the same for both (or all) products—Eq. (5-14). Generalizing to n inputs, the output-maximizing (cost-minimizing) condition is

MP, _MP,_ MP; Bi pee Ps ae

‘MP ee

Pi sete

The Expansion Path: Long Run and Short Run DEFINITION: A locus of the tangency points between various isoquants and various isocosts is called the expansion path, since it shows the least cost combinations of

labor and capital a firm would choose as it expanded its output level, supposing it is free to vary both labor and capital, where input prices and the state of technology are constant. This expansion path is shown as the line EP in Fig. 5-9. Note that this must be the long run expansion path, since all factors must be

’The negative sign drops out because MP, will be a negative number.

126

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

variable to allow the adjustment in both capital and labor involved in the movement along the line EP.® Suppose that the firm wishes to produce 40 units of output, and thus selects the combination of factors represented by point B on the long run expansion path. The firm’s capital input is now fixed at K* units, and the firm is ina short run situation. If the firm wishes to vary its output level in the short run, it must simply add or subtract labor to or from the fixed capital input K*. The short run expansion path is, therefore, a horizontal line at the capital input level K*, shown as line TP in Fig. 5-9. This short run expansion path is, in fact, the total product curve viewed from above the output hill. Notice that for every output level except the one where TP crosses EP, it costs more to produce the output in the short run than it does in the long run. The isocost line that intersects each isoquant curve on the TP line must lie farther to the right when compared with the isocost line that is tangent to each isoquant curve. This is demonstrated in Fig. 5—9 for the output level of 20 units. In the long run situation, the optimal input combination is at pointA, and the lowest attainable isocost line is shown as MN. In the short run situation with capital input of K*, 20 units must be produced by the input combination represented by point A’, since the firm is constrained to the short run expansion path TP. The minimum cost of producing 20 units with combinationA’ is shown by the isocost line M’N’, which lies to the right of the line MN. The short run situation costs more than the long run situation for all except one output level, because the firm is unable in the short run to change the input of capital, and is thus forced to have an inappropriate factor combination for all except one output level. In the case shown, only at the output of 40 units does the level of capital (K*) allow the tangency situation of economic efficiency to be attained. An Example: The Cotton Textile Industry

The cotton textile and apparel industry is remarkable in that it is found around the world with significantly differing degrees of capital and labor intensiveness. In North America, for example, this industry is relatively capital intensive, using computer-controlled equipment and relatively few people per unit of output. In many less developed countries, on the other hand, production processes are relatively labor intensive, with dozens of people using much more rudimentary equipment in order to produce a given output level. Does this mean that the industry is inefficient in these less developed countries? Quite the contrary, as we shall see. In terms of isoquant-isocost analysis, firms in both situations are trying to attain tangency between their isocost line and the appropriate isoquant line. Suppose a firm in each group wishes to produce a particular output level, shown 8The isoquant-isocost analysis can be converted for use in short run production problems where some of the variable factors are substitutable in production. For example, if more labor means less wastage of raw materials, we could find the optimal input level, given the present size of plant, by putting labor on one axis and raw materials on the other and by finding the tangency points between the isoquant and isocost lines.

The Theory of Production and Supply

27,

as Q* in Fig. 5-10. In the less-developed economy, labor is relatively cheap, whereas capital is relatively expensive, giving rise to an isocost line like M Ni. The economically efficient input combination for the firm in this situation is thus K,, L;, where the isocost curve is tangent to the isoquant at pointA. In the more highly developed country, labor is relatively expensive, and capital is relatively cheap, giving rise to an isocost line like M,N2, which is tangent to the isoquant line at point B, indicating that K, and L, constitute the economically efficient input combination for the firm in the more developed economy. FIGURE

5-10

Different Economically Efficient Combinations in Different Economic Situations

Labor

Thus both situations are probably both technically and economically efficient given the factor productivities and factor prices facing the firm in each situation. The crunch comes for the North Americans when their economically efficient input combination for any given output level costs more than the economically efficient input combination in less-developed economies. Hence the North American textile industry finds itself subject to the competition of imported textiles that are sold at a lower price in their market.

VI. FACTOR SUBSTITUTION AS A RESULT OF CHANGED RELATIVE FACTOR PRICES Economic efficiency depends upon the relative factor prices. If the price of one factor changes,with ceteris paribus, the profit maximizing firm attempts to substitute away from the factor that has become relatively more expensive in favor of the factor that has become relatively less expensive.

EXAMPLE:

An example of this in the real world is the substitution of capital for labor in many production processes as a result of the cost of labor having increased relative to the cost of capital. Suppose that the initial situation for a particular firm

128

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

is at pointA in Fig. 5-11. Given the initial factor price ratio, the initial isocost curve, M,N,, is tangent to the isoquant curve at the combination of labor and capital (L,, K,). Suppose now that labor prices rise, due, for example, to a new agreement with a labor union or to legislation requiring the firm’s increased contribution to an employee health scheme or similar benefits. Imagine that the increase in the cost of labor is such that the isocost line swings down from M,N,

to M,N>. The same total expenditure now buys a considerably reduced set of labor and capital combinations. If the firm wishes to maintain its output level at Q; (in order to hold its market share, for example), it will need to spend more money on the inputs in order to produce Q, units of output. Immediately after the change in the wage rate, the firm is still in a short run situation and is constrained to the capital input level shown as K,. The firm must continue to use K, and L, to produce Q;; the total expenditure on these inputs is, however, considerably greater. Given the new ratio of input prices, the new isocost line allowing pointA to be reached must have the same slope as M,N,; this new line is shown as M.N;3. Notice that instead of being tangent to the isoquant at pointA, it crosses the isoquant at pointA. FIGURE

5-11

Factor Substitution as the Result of a Change in Relative Factor Prices

Capital

(K)

Ko

Ky

In the long run, the firm wishes to move from pointA to the tangency point B, given the new price ratio for the inputs. The firm, therefore, begins making plans to increase its input of capital to the level shown as Kg, and as soon as this capital is installed, it reduces its labor requirements to L». Thus the firm substitutes away from labor and in favor of capital when the price of labor increases relative to that of capital, given time to adjust the input of all factors. Notice that the final isocost line, shown as M3N,, represents a lower level of total expendiThe Theory of Production and Supply

129

ture on inputs as compared to the isocost line M,N3. Given the change in factor

prices and time to adjust its capital input, the firm is able to reduce its expenses by choosing the combination of inputs that is economically efficient in the long run. History gives us the opportunity to observe this trend: As the price of labor increases relative to that of capital, we observe production processes becoming relatively more capital intensive with the introduction of such labor-saving equipment as mobile assembly lines by Henry Ford, for instance, and the more recent use of computerized robots in production processes.

Vil. SUMMARY Using the output hill as a pedagogical model of the production process, we demonstrated the main concepts and principles of production theory. This simple model allows the introduction and discussion of such notions as fixed and variable inputs, the short and long run, the law of variable proportions, returns to scale, and technical efficiency in production. Fixed factors are those that cannot be augmented in the short run and, therefore, do not vary with the output level. Variable factors can be augmented or reduced at relatively short notice and vary directly with the output level. The long run is a situation in which the firm may choose among various alternative combinations of all inputs, before committing itself to a short run situation, in which the inputs of some factors are fixed. The law of variable proportions concerns the behavior of marginal product of the variable inputs in the short run, whereas returns to scale are long run phenomena, observed in a hy-

pothetical sense by considering the relative changes in output possible for changes in the scale of operations among the various combinations available in the long run. Technical efficiency is available within a range of input combinations where the marginal product of all factors is positive for increased inputs of those factors. Economic efficiency is obtained by introducing the cost of the inputs to find the least cost combination of inputs for a given output level. In the short run, economic efficiency is constrained by fixed capital input, whereas in the long run, the optimal capital input level can also be selected. We saw that changing factor-price ratios lead to substitution of one input for another as a rational (cost minimizing) response of producers. In the next chapter there is a full discussion of all cost concepts that flow from production theory; in Chap. 7 we examine linear programming analysis as a means of finding the cost minimizing input combination for a firm with multiple production processes.

DISCUSSION

130

QUESTIONS

1.

Explain how a tabular representation of a production function represents both the long run and the short run situations at the same time.

2.

Suppose your production process has three inputs: machinery, highly skilled labor, and raw materials. If you wanted a new (larger or smaller)

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

machine, it would take six months to be fabricated, delivered, and installed. Your present workers are all under contract for another eight months. New workers would take three months to acquire, due to the lengthy process of advertising, interviewing, etc. Raw material supplies must be ordered four weeks in advance. How long is your short run? When can you make your long run decision to expand or contract your plant size? How does the law of variable proportions differ from the law of diminishing marginal returns? Why is the point of inflection on the total product curve the point where diminishing returns begin? Why is it economically efficient to operate somewhere in stage 2 of a short run production function, even if you don’t know what the costs of the inputs are?

Would you expect firms to expand exactly in scale magnifications of their earlier economically efficient input combinations? Explain using isoquantisocost analysis. The smoothness of an isoquant curve implies the ability to substitute continually small amounts of labor for capital. Given that fractions of labor and capital do not exist in a physical sense, how can we achieve the substitutions implied by a smooth isoquant curve? Explain why the short run cost of production exceeds the long run cost of production for every output level, except the one where the total product curve crosses the expansion path. Eric Fisher is an orchardist. He pays his fruitpickers on the basis of weight of fruit picked. For the past eight days he has been harvesting his Elberta peaches and has been hiring all the pickers who showed up each day. The following schedule shows the results over the period. Day

Pickers Employed

Peaches Picked (hundreds of pounds)

1 2 3 4 5 6 wh 8

6 17 9 5 12 3 14 15

38 76 56 32 74 15 80 78

a. Over what ranges do there appear to be increasing, constant, and diminishing returns to the variable factor? b. What number of pickers appears to be the most efficient in terms of output per picker? c. What number of pickers appears to be most efficient in terms of the utilization of the orchardist’s plant and equipment? The Theory of Production and Supply

131

10.

The Department of Highway Safety in a particular state wishes to install safety catch-fencing along the sides of all sections of roadway that are considered potentially dangerous. This fencing can be installed more or less capital intensively, since much of the installation process can be done either mechanically or manually—post-hole digging, wire-straining, fastening, painting, and so forth. The Department has a budget of only $80,000 and wishes to maximize the number of miles of safety fencing installed. Department engineers have derived the pradustion function indicated by the following table. Department accountants have indicated that these machine hours cost $25 per hour and labor will cost $10 per hour. (Material

cost are covered by a separate budget that is practically unlimited.) Production Function for Installation of Safety Fencing (Miles of fencing installed) Labor hours per year*

Machine hours per year*

70 86

102 TL

3

4

120 140

135 160

145 175

150 182

*Each labor or machine hour on the table represents 1,000 hours.

a. Using isoquant-isocost analysis, show graphically the technically efficient factor combinations as distinct from the technically inefficient factor combinations. b. Estimate the maximum output level that the Department can produce within its budget constraint and the factor combination that is required to achieve this level. c. Demonstrate what would happen if the cost of labor hours was to increase to $15 per hour. Estimate the new optimal factor combination and output level.

SUGGESTED

REFERENCES

BAUMOL, W.J., Economic Theory and Operations Analysis (4th ed.), chap. 11. Englewood Cliffs, N.J.: Prentice-Hall, 1977.

CHAMBERLIN, E. H., “Proportionality, Divisibility and Economies of Scale,’ Quarterly Journal of Economics, 1958, pp. 229-57. Cote, C.L., Microeconomics: A Contemporary Approach, chaps. 6, 7. New York: Harcourt Brace Jovanovich, Inc., 1973. Douc.as, P. H., “Are There Laws (March 1948), 1—41.

of Production?’’ American

Economic

Review,

38

LEFTWICH,R.H., The Price System and Resource Allocation (7th ed.), chaps. 8, 9. Hinsdale, Ill.: The Dryden Press, 1979.

THOMPSON, A. A. JR., tice-Hall, 1973. 132

Economics of the Firm, chaps. 6-8. Englewood Cliffs, N.J.: Pren-

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

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The Costs | of Production and Supply INTRODUCTION

NOTE:

In the preceding chapter we examined the principles of production, looking for the optimal (least cost) combination of inputs that combine to produce each level of output. Since each of the inputs typically has a cost involved, it is a relatively simple step to proceed to the cost of producing each level of output. The cost of output is important to the supply decision of producers, since they wish to supply only if the market price exceeds the relevant costs of production. (Which costs are relevant depends upon the context in which the supply decision is made. This will be explained later.) For the most part, cost theory is, therefore, simply production theory with the costs of the inputs added. To find the cost functions, we must start from the appropriate production function and transform the physical units of inputs into the cost of these inputs for each output level. In this chapter, we proceed to derive the cost functions and the associated cost curves, which are implied by aay particular production function.

Since inputs are categorized as either fixed or variable in the short run, the various costs of production are also dichotomized as either fixed or variable. Total variable costs are thus the sum of all costs of variable inputs, and total fixed costs are the sum of all costs of fixed inputs in any short run situation. In the long run, all costs are variable, in the sense that the input of all factors can be varied. But

note that once the producer chooses a level of the fixed factors, and thereby 133

establishes a level of fixed costs, the firm is once again in a short run situation with both fixed and variable costs. In the following we first examine the short run cost curves to see how the law of variable proportions, or diminishing returns, in production manifests itself in the shape of the cost curves. We then consider the long run cost situation and the cost implications of economies and diseconomies of plant size and of scale. Finally, we consider some cost implications that arise not from the production process but as a result of the large size,,or multiplant, operation of the firm.

Il. THE SHORT RUN COST CURVES The Total Variable Cost Curve

In the short run, the firm is constrained to a fixed level of capital input and must increase or decrease output by changing the input of the variable factors. Thus, the firm’s input/output possibilities in the short run are described by the total product (TP) curve. The total variable cost (TVC) curve can be derived from the TP curve simply by multiplying the level of variable inputs by the cost per unit of those inputs and by plotting this cost data against the output level. Suppose that the variable factor units cost $10 each. The total product curve is shown on

the right-hand side of Fig. 6-1. Using the data from the total product curve and multiplying each unit of the variable factor by $10, we may plot the total cost of the variable input against the output, as in the left-hand side of Fig. 6—1. FIGURE

6-1

Relationship between the Total Product and Total Variable Cost Curves

Output units (Q) Total variable costs

Cost of variable

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PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

For simplicity we have chosen the scale on the left-hand side of the horizontal axis to be ten times that on the right-hand side. Thus the curve reflecting the total cost of the variable factors for all levels of output is a mirror image of the total product curve. Thus the shape of the total variable cost curve is derived directly from the form of the production function and the number of units of capital employed, since these factors underlie the shape of the total product curve. Average Variable and Marginal Costs

DEFINITION: Average variable cost is equal to TVC divided by output Q at every level of Q. That is,

AVC

TVC 0

(6-1)

In Fig. 6-2 we show the TVC curve tipped on its side—rotated 90° to the right— with the associated average variable and marginal cost curves. The AVC for each output level is equal to the ratio of the vertical distance from the quantity axis to the TVC curve, to the horizontal distance from the cost axis to the TVC curve. In terms of the graph, this amounts to the vertical rise over the horizontal run or to the slope of a ray from the origin that joins the point on the TVC curve. Average variable cost at pointA on the TVC curve is equal to the ratio AR/OR, or the value of the slope of the line 0A, and is shown as pointA’ on the AVC vertically below. It can be verified that the slopes of lines between the origin and points on the curve become progressively flatter as we begin to move up the TVC curve away from the origin. Thus the AVC, which is equal to the value of these slopes, must fall over this range. A point is reached, however, where the ray from the origin can become no flatter and still touch the TVC curve. Point C, where the ray is just tangent to the TVC curve in Fig. 6—2, signifies the lowest value for AVC. Since the rays become steeper for points on the TVC to the right of the tangency point, AVC must rise after this output level, as shown in Fig. 6-2. DEFINITION:

Marginal cost is the change in total costs due to a one-unit change in output.

MC = ——

(6-2)

where AQ = 1. Since output changes cause only variable costs to change, we can equivalently define marginal costs as the change in total variable costs for a oneunit change in output. Hence,

MC = ——

(6-3)

where AQ = 1. In this form you see that marginal cost is defined as the vertical rise over the horizontal run along the TVC curve for a one-unit change in output. MC is thus equal to the slope of the TVC curve at each output level. If we were to

The Costs of Production and Supply

135

FIGURE

6-2

Derivation of Average Variable and Marginal Cost Curves from Total Variable Cost Curve Total variable costs

A

($)

Output units

|

|

(Q)

Cost per unit

($/Q)

AR OR

as OT

Output units (Q)

put tangents against the TVC curve at every output level, we would see that the slopes of these tangents would fall at first, out to the point of inflection on the TVC curve, and would then rise. In Fig. 6—2 the point of inflection occurs at point B, where the TVC curve changes from convexity from above to concavity from above. The slope of the TVC becomes progressively flatter up to point B: it then becomes progressively steeper after point B, as output is increased. This indicates that the marginal cost curve is U-shaped, falling to a minimum at the output level where the TVC exhibits its inflection point and rising thereafter.

NOTE:

It is important to notice that while the marginal cost curve lies below the average variable cost curve, the latter is falling. In effect, the lower marginal costis pulling down the average. Conversely, when the MC curve lies above the AVC curve, the latter must be rising: it is pulled up by the marginal costs. It follows that when the MC crosses the AVC, the AVC must be at its minimum value. This can be verified in Fig. 6—2 at point C on the TVC curve. Marginal costs and average variable costs must be equal, since both are given by the slope of the tangent to the TVC curve at that point. Marginal costs are the value counterpart of the marginal product of the

136

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

variable factors. When marginal productivity of labor is falling, marginal cost of output is rising and vice versa. If the efficiency of the marginal units of the variable factor is constant, then output can be produced at a constant level of marginal cost. These relationships can be confirmed by another look at Figs. 6-1 and 6—2. Notice that when the TP curve in Fig. 6-1 is concave from above, exhibiting increasing marginal productivity of the variable factor(s), the TVC curve in Fig. 6—2 is convex from above, indicating decreasing marginal costs per unit of output. Alternatively, when diminishing returns set in for the variable factor(s) after the inflection point in Fig. 6-1, the TVC curve begins to increase at an increasing rate, and marginal costs are increasing over this range. Note that diminishing returns are first indicated when MC begins to rise, even though AVC continues to fall for several more units after this point. This is because MC, although rising, still lies below AVC over this range and, therefore, continues to pull down the average variable costs. Short Run Average Costs DEFINITION:

Short run average costs (SAC) are defined as Total Costs (TC) per unit of

output.

TC SAC = OQ

(6-4)

Total costs are the sum of TVC and Total Fixed Costs (TFC). To complete the short run cost picture, therefore, we need to add the costs of the fixed factors. TFC show as a horizontal line when plotted against output, as shown in Fig. 6-3, since these costs are constant whatever the level of output. To find the total of fixed and variable costs, we add vertically the TFC and TVC curves on the graph. This, in effect, causes the TVC curve to be moved upward a constant distance

equal to the total fixed costs. Thus the total cost (TC) curve and the TVC curve have the same shape, as is evident in Fig. 6-3. As noted previously, the marginal cost curve can thus be derived from the TC curve instead of the TVC curve. Average total costs, or short run average costs (SAC), may be derived from the TC curve by the same technique as was used to derive the AVC curve. The slope of a ray from the origin to a point on the TC curve gives the value of SAC for each output level. Thus at point B in the upper part of Fig. 6-3, SAC is equal to the ratio BF/OF, or the slope of the line OB. At the same output level, AVC = CF/OF, or the slope of the line OC. In the lower part of the figure, these values are shown as points B’ and C’, respectively. Given the shape of the TC curve, SAC must fall at first, reach a minimum, and thenrise. Notice that the minimum point “of the SAC curve, found where the ray from the origin is just tangent to the TC curve, is the point where MC= SAC, since both are equal to the slope of the TC

curve at that point.

DEFINITION:

Average fixed costs (AFC) are defined as total fixed costs per unit of output.

AFC = ——

(6-5) The Costs of Production and Supply

137

FIGURE

6-3

Derivation of the Short Run Average Cost Curve

Total costs

($)

Per unit costs

($/Q) BF OF

0

Output units (Q)

An alternate method of deriving the short run average cost curve is to find the AFC curve and to add this to the AVC curve. The AFC curve shown in Fig. 6-4 slopes downward to the right as output is increased. Since TFC is constant, fixed cost per unit must decline progressively as output increases, since the fixed costs are spread over progressively more units of output. In fact, the AFC curve is a rectangular hyperbola and approaches both axes asymptotically.1 Adding AFC vertically to the AVC for each output level, we derive the SAC curve. For example, at output level Q,, we take the amount shown as AFC, and add it to the average variable costs at that output level. Similarly, at output Q., we take the smaller average fixed costs, shown as AFC;, and add that amount to AVC to find

the total short run average costs for output level Qy. Notice that the SAC curve continues to fall after the AVC curve has begun to rise. This is because the fall in AFC outweighs the rise in AVC for a time. Sooner or later, however, we expect the cost effects of diminishing returns to the ‘Rectangular hyperbolas take the form y = k/x, where k is a constant. In this case y is AFC, k is TFC, and x is Q. Notice that yx = k, which is to say that the product of the coordinates of any point on a rectangular hyperbola always equal the same number or, alternatively, that the area under any point on the rectangular hyperbola is the same. In our case, of course, AFC - Q = TFC, since TFC is constant regardless of output variations. 138

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

FIGURE

6-4

Vertical Summation of the AFC and AVC Curves to Derive the SAC Curve

$/Q

variable factors to outweigh the effects of reducing fixed costs per unit and the SAC curve to begin to rise. This happens, of course, when the marginal costs rise up to and exceed the average total costs. The Short Run Supply Decision

In the short run, the firm must incur its fixed costs, since it cannot, by definition, change the input of these factors of production. The firm’s variable costs, on the other hand, are discretionary, in the sense that the firm may decide whether or not to incur these costs, since the input of variable factors can be varied all the way back to zero. What induces a firm to incur costs? We argued briefly in Chap. 1 that the firm is profit-oriented and incurs costs when it expects to more than cover those costs with revenues. Thus a firm will set up a plant and incur fixed and variable costs to produce a particular product, because it expects to more than cover these fixed and variable costs with revenues and thereby make a profit. Once committed to its present size of plant, however, the firm is obliged to incur the fixed costs of that plant in the short run. Variable costs, on the other hand, will only be incurred if the firm expects revenues to exceed these variable

costs. Suppose price exceeds average variable cost, but is less than the average total cost, meaning that the firm makes a loss. If the firm ceases production, it

incurs no variable costs, earns no revenues, and therefore makes a loss equal to its fixed costs, which must be paid whether or not the firm produces anything. If the firm continues production when P is greater than AVC but is less than SAC, there is, for each unit sold, some excess of revenue over variable costs that con-

tributes toward the fixed costs. Therefore, the firm reduces its losses by producing the product when SAC > P > AVC, rather than by ceasing production.

RULE:

Thus the firm decides to incur variable costs, and hence supply the product to the market, whenever price exceeds the firm’s average variable cost level. If price The Costs of Production and Supply

139

also exceeds the SAC level, the firm makes a profit. If price falls below SAC, the firm suffers a loss, but it can minimize those losses by staying in production as long as P > AVG. If price slips below AVC, the firm minimizes losses by ceasing production and waiting until either the price rises above AVC again or until it can liquidate its fixed factors and terminate the associated fixed costs. The latter option implies a long run situation, of course. In most business situations, the rule governing the decision ‘‘to supply or not to supply” is more clearly stated in terms of totahrevenues and total variable costs, rather than in terms of (per unit) P > AVC. That is, if TR > TVC then the firm should supply its product(s), whereas if TR < TVC it should not incur the variable costs and, consequently, not supply the product(s). This rule is equivalent to the P > AVC rule, since totals divided by quantity demanded equal the per-unit values. But in the real world, quantity demanded tends to vary day by day and month by month due to seasonal factors, chance circumstances, weather

conditions, and competing attractions. In effect the demand curve shifts back and forth in response to these shift factors. Most firms cannot change their prices daily to reflect the differing states of demand that eventuate. Rather, they set prices on the basis of some notion of the average, or normal, demand situation and hold these prices steady as sales fluctuate daily, monthly, or seasonally around this conceptually normal volume. Hence price is constant while AVC varies substantially from day to day depending on the volume produced. In such a situation the firm might find it easier to decide whether or not to supply its product in the short run on the basis of whether or not it expects TR to exceed TMG;

EXAMPLE:

During a severe snowstorm many stores will close early or remain closed for the day, since the manager predicts that sales would be so small that it is not worth opening the store and incurring the associated variable costs. Or, for example, a coffee shop might stay open until 3 A.M. on Saturday night, but close at midnight or earlier on weeknights, based on the manager’s expectation that sales revenues would or would not cover the total variable costs involved. Finally, an

amusement park might decide not to open on a much publicized ‘‘children’s day”’ at the zoo. In all these cases, fixed costs are being incurred and would be incurred regardless of whether or not the firm is open for business. The supply decision depends upon whether or not the total sales revenue is expected to exceed the discretionary total variable costs relevant to the time period under consideration.

Ill. THE LONG RUN COST CURVES The Long Run Average Cost Curve DEFINITION:

The long run average cost (LAC) curve shows the least cost of production for

each output level when all inputs may be varied. We can derive the LAC curve from the expansion path generated by isoquant-isocost analysis. You will recall that the expansion path is the locus of the points of tangency between a series of 140

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

isoquant and isocost curves, showing the least cost (or economically efficient) factor combination for each output level, when all inputs are free to vary. The expansion path thus contains all the data we need to construct the LAC curve. Each isoquant curve represents a particular output level; the minimum total expenditure necessary to produce each level can be calculated as the intercept value of the tangent isocost line on the vertical axis multiplied by the price of capital. Similarly, we could derive any short run average cost curve from the isoquant-isocost analysis. Consider Fig. 6-5, which is similar to Fig. 5-9 in Chap. 5. In Fig. 6-5 we show the capital input fixed at the level K*; in Chap. 5 we discussed that for all output levels other than 40 units, it would cost more to

produce those output levels in the short run situation (constrained to K*) than it would in the long run situation, where the economically efficient combination

of both labor and capital is employed. The production of 20 units in the short run, with capital K* and with the input combination represented by point B’, must cost more than the long run solution at A, since the isocost line passing through B’ lies further to the right than the isocost line passing through pointA. Similarly, it must cost more to produce 60 units at B” in the short run than at the long run solution (point C). FIGURE

6-5

Short and Long Run Costs Derived from Isoquant-Isocost Analysis Capital

Labor

In Fig. 6-6 we show the long run total cost (LTC) and the short run total cost (STC), which can be derived from the expansion path (EP) and total product (TP) curves in Fig. 6—5. Note that at 40 units of output, STC = LTC, whereas STC lies above LTC for both higher and lower levels of output. In the lower part of Fig. 6-6, we show the associated SAC and LAC curves. Since SAC = STCG/Q and LAG = LTCIQ, each can be expressed as the value of the slope of the ray joining the origin and a point on the total cost curve. For Q = 40, the SAC = LAC, since The Costs of Production and Supply

141

STC = LTC. For smaller and larger output levels, SAC must exceed LAC, since

STC exceeds LTC. Hence SAC is tangent to LAC at the output level of 40 units.

The minimum value of the LAC curve occurs at point S’, since the ray from the

origin to a point on the LTC curve reaches its minimum slope at point S on the LTC curve. After the output level designated T, the LAC curve must begin to rise, since rays from the origin to points on the LTC curve to the right of point S must have progressively steeper slopes. Thus, the LAC curve derived from a cubic production function will fall to a minimum and later rise. FIGURE

6-6

Derivation of Short and Long Run Average Cost Curves from the Total Cost Curves Total costs

($)

0

‘

Per unit

Output units

(Q)

costs

($/Q)

Ra 0Q Sis OT Output units

(Q)

Alternatively, we may derive the long run average cost curve by finding the SAC curves which relate to every level of fixed factors. Each level of capital (fixed factor) input will give rise to a TP curve, from which we can derive a TVC curve, and ultimately obtain the appropriate SAC curve as we did in the preceding section. This procedure gives us a series of SAC curves, each with a slightly larger capital input level as we move from left to right, as shown in Fig. 6-7. Each one of these SAC curves must be just tangent to the LAC curve, for the same reasons as the preceding situation in which the SAC curve is tangent to the LAC curve at 40 units of output. Thus each SAC curve sits on the LAC curve or, 142

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

FIGURE

6-7

The Long Run Average Cost Curve: Envelope Curve of all Short Run Average Cost Curves Total costs

($)

Some of the infinite number of SAC curves

Output units

(Q)

in other words, the LAC curve is the ‘“‘envelope curve” of all these short run curves. That is, it is made up of the points on the various SAC curves that allow each output level to be produced at the lowest possible cost when the firm is free to vary the input of all resources. A corollary of this is that for any point on the LAC curve there is a SAC curve just tangent at that point.

NOTE:

The LAC curve may not be a smooth U-shaped line for every firm in the real world, since the smooth U-shape depends upon the availability of a large number of plant sizes, with the sizes of these plants varying by relatively small increments from the smallest available to the largest available. In many industries there are only a few alternative sizes of plant, each significantly different in size from the next largest and the next smallest.

EXAMPLE:

Consider the case of a small private airline company that plans to initiate a feeder service from a remote area to a major city. In choosing the aircraft for this route, the firm must, in effect, choose its size of plant, since light aircraft are available in 4-, 6-, 8-, and 10-seat models. In this case, plant sizes are available only in discretely increasing, rather than continuously increasing, sizes, and the LAC curve will exhibit a series of kinks or scallops rather than be a smooth line. In Fig. 6—8 we show the LAC curve as the heavy line encompassing only those sections of each SAC curve which allow output to be produced at lowest cost. The four SAC

curves represent the available plant sizes, with the sub-

scripts indicating the maximum number of seats in each plant size. Note that each SAC becomes vertical at the point where it reaches its maximum output (passenger) level. The LAC curve is the envelope curve of these four SAC curves; it contains kinks at points A, B, and C, where it becomes less costly (per passenger) to choose the next largest plant size. The Costs of Production and Supply

143

FIGURE

6-8

Long Run Average Costs with Discrete Plant Size Differences Average costs

SAC 4

($/Q)

SAC ‘

SACen

SACg

Output per

1

2:

3

4

5

6

U

8

9

10

flight (passengers)

Note that if there were an aircraft available that seated 5 passengers (including the pilot), the SAC curve of that plant size would have nestled between SAC, and SAGg, and it would have caused the kink in the LAC curve at pointA to disappear. Similarly, if planes were also available with 7 and 9 seats, the other kinks might be removed or at least replaced by smaller kinks. With plant size continuously variable, the LAC curve would be a smooth line. In the real world,

however, the LAC curve is most likely to exhibit kinks due to plant size not being continuously variable. The Long Run Marginal Cost Curve

DEFINITION: The long run marginal cost (LMC) curve shows the marginal cost of producing each additional unit of output when the firm is free to vary the inputs of all factors of production. As you should by now expect, the LMC lies below the LAC when the latter is falling, and it lies above the LAC when the latter is rising. In fact, LAC falls precisely because the LMC lies below it, pulling down the average cost. Similarly, LAC rises precisely because the marginal units cost more than the average to produce. In Fig. 6-9 we show the LMC associated with a particular LAC curve and three short run cost situations. Notice that at output level Q,, the short run aver-

age cost is equal to the long run average cost at PointA. It follows that short run

marginal cost must equal LMC at this output level, since the two averages have converged upon each other precisely because the two marginals were converging on the same value (at point B). Similarly, at output level Q, we have SAC, = LAC = LMC = MC). We know that the LMC must pass through the minimum point of the LAC curve and that the short run MC must pass through the mini144

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

mum SAC point. Since SAC = LAC at the minimum points of both, we have the above four-way equality. Finally, at output level Q;, average short run and long run costs are equal at point D, because marginal short run and long run costs are equal at point E. FIGURE

6-9

Long Run Marginal Costs and Their Relationship to Other Cost Curves

Per unit costs

($/Q)

LAC

IV. RETURNS TO PLANT SIZE, SCALE, AND FIRM SIZE Economies and Diseconomies of Plant Size

DEFINITION: Economies of plant size, or increasing returns to plant size, are evident when the LAC curve slopes downward to the right, indicating that successively larger plant sizes have corresponding SAC curves lying lower and to the right. These economies arise due to such factors as a large enough output level that allows the firm to utilize more efficient capital-intensive methods, for instance, com-

puter-controlled assembly lines, and allows personnel to specialize in the areas of their greatest expertise. After some point, increasing inefficiencies in other areas, due, perhaps, to the increasing bureaucracy of larger establishments, offset these cost advantages. The firm experiences diseconomies of plant size when successively larger plant sizes exhibit SAC curves that lie progressively higher and to the right.

NOTE:

The LAC curve is not the locus of the minimum points of each SAC curve. Since each SAC curve is tangent to the LAC curve, this is true only if the LAC curve is horizontal. If economies

and diseconomies

of plant size exist, the LAC curve

will at first be negatively sloping and then positively sloping. Thus tangencies with SAC curves must occur at first on negatively sloping parts of SAC curves The Costs of Production and Supply

145

and then on positively sloping parts. It follows that SAC curves are tangent to the left of their minimum points when there are economies of plant size and tangent to the right of their minimum points when there are diseconomies of plant size. Only for the SAC curve that is tangent to the minimum point of the LAC curve, often called the optimal size of plant, will the minimum point of an SAC curve be a point on the LAC curve. This is evident in Fig. 6—9.

Economies and Diseconomies of Scale

It is important to make the distinction between economies of scale, which are the cost counterpart of increasing returns to scale, and economies of plant size, as reflected by the long run average cost curve. Economies of scale are found when all factors are increased in the same proportion. This involves an expansion path in isoquant analysis that is a straight line from the origin, reflecting a constant capital-labor ratio. Economies of plant size derive from the least cost expansion path, which is not necessarily a straight line, although it does ema-

nate from the origin. That is, firms are unlikely to want to expand all inputs in the same proportion (as they increase their output under long run conditions), because a different capital-labor ratiois likely to be cost minimizing due to differing marginal productivities of the inputs at different input levels. In terms of the production surface, the least cost expansion path is the route taken up the output hill when one always steps in the steepest direction, whereas an increase in scale requires movement up the output hill in a constant direction.”

Economies of Firm Size and Multiplant Operation

Certain other economies arise as a result of the absolute size of the firm. For example, larger firms are usually able to obtain discounts for bulk purchases of raw materials, which gives them a cost advantage over smaller firms. These cost advantages are often referred to as pecuniary economies of plant or firm size; they are clearly different from the economies of plant size which are dependent upon increasing efficiency in production. Many large firms derive further pecuniary economies as the result of operating more than one plant. These cost savings are likely to result from spreading certain under-utilized fixed costs, such as managerial talent, computer rental, and advertising expenditures, over more than one plant. The average cost curve for the first plant is, therefore, ex-

pected to sink downward to some degree as a result of the opening of a second and subsequent plants, since some part of the fixed costs previously charged to “If the production function is homogeneous, then the least cost expansion path isa straight line from the origin and the same ratio of inputs is optimal at all output levels. In this case there are both economies of scale and economies of plant size, if proportional increases in all inputs lead to greater proportional increases in output, or there are both diseconomies of scale and diseconomies of plant size, if output increases by proportionately less. See P. H. Douglas, “Are There Laws of Production?”

American Economic Review, 38 (March 1948), 1—41.

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PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

a single plant are now charged to one of the newer plants. This situation is illustrated in Fig. 6-10. FIGURE

6-10

Pecuniary Economies causing Cost Curves to sink downwards Per unit costs

($/Q)

Output units (Q)

EXAMPLE:

McDonald’s fast-food restaurant chain is a good example. In a couple of decades, this chain has burgeoned from a single fast-food store to a worldwide network of almost identical restaurants. Whether in North America, Europe, Asia,

or Australasia, one can walk right up to that familiar counter and place an order for a Big Mac, large french fries, apple turnover, and a milkshake. When it’s Big Mac time in Tokyo, it’s Egg McMuffin time in Toledo: The sun never sets on McDonald’s. Most of the phenomenal growth of McDonald’s can be attributed to franchising, whereby local entrepreneurs supply a substantial capital investment in return for part ownership in a new outlet and several container loads of furniture, signboards, equipment, and fixtures that characterize

a McDonald’s restau-

rant. This familiar environment attracts customers who have tried McDonald’s elsewhere and who know they can expect the same menu, the same high quality, and the same prices. (This lack of uncertainty as to prices and quality is very comforting to the wary consumer, who may have suffered disappointments and surprises at other fast-food stores.) In addition, McDonald’s

attracts new cus-

tomers and reinforces preference patterns of regular customers by substantial expenditures on advertising and other promotional efforts. On the cost side, there seems to be little indication that McDonald’s bene3Cost curves sink vertically downward only if there is an equivalent proportionate reduction in the prices of all factors. If the prices of variable factors are reduced by a larger proportion than the prices of those factors which are fixed in the short run, the cost curves sink downward to the left, due to the substitution that takes place between factors where possible. Conversely, if fixed factor prices are

reduced by the greater proportion, the curves sink downward to the right, as the firm substitutes in favor of the fixed factors.

The Costs of Production and Supply

147

fits from economies of plant size, since all their restaurants seem to fall within a relatively small size range, although this is largely determined by the size of local markets for each outlet. On the other hand, there is little doubt that Mc-

Donald’s benefits from economies of multiplant operation. Each additional plant (new outlet) probably allows McDonald’s to reduce the per unit cost of its foodstuffs, since these are prepared in central locations and shipped to each franchised outlet. Advertising and promotion costs per outlet are reduced as the number of outlets sharing these costs is increased, Also the cost of replacement chairs, tables, and wall decorations is expected to decrease as the market (number of outlets) for these products increases. Thus we expect the cost curves of any particular McDonald’s outlet to drift downward (in constant-value dollars, or real terms) over time as more and more outlets are opened.

V. ECONOMIC VERSUS ACCOUNTING CONCEPTS OF COSTS AND PROFITS The economist’s concept of profit differs from that of the accountant. Both consider profit as the excess of revenues over costs, but they regard costs differently. The accountant subtracts from revenues only the costs that are actually incurred, plus an apportionment of some of the previously incurred one-time expenditures, such as the cost of plant and machinery. Profits thus represent the net income to the owners of the firm; they are their reward for having invested time and capital in the venture. The economist, on the other hand, is concerned with

the wider notion of efficient allocation of resources; he or she is thus concerned that all resources are employed where they will earn the maximum for their owners. A means of ensuring this is to consider the opportunity cost of each resource. Opportunity Costs

DEFINITION: Opportunity costs, or alternative costs as they are often called, refer to the value of a resource in alternative employment. For resources that are purchased outright or hired, such as raw materials and labor inputs, there is no dispute between economists and accountants. The market price at which they are purchased or hired should reflect their opportunity cost, since the producer must bid for these goods in their respective markets. If he or she is not willing to pay at least what the resources are worth in their best alternative usage, the producer

would not be able to purchase the services of these resources. The difference arises with factors of production that are owned by the firm, such as land, buildings, equipment, and other assets. The accountant depreciates the cost of these assets by allocating a portion of the initial cost of the asset against the current period’s revenues. The depreciation charge is typically based on an estimate of the asset’s operating life, over which the initial cost is apportioned. The economist determines the opportunity cost of these services on the basis of what the land and buildings might have earned in alternative employment, or the interest which the capital tied up in those assets could have earned 148

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

in alternative investment, whichever is greater. The opportunity costs of the capital tied up in land, buildings, and equipment may be quite different from the depreciation charge made against revenues, since the latter is determined on an entirely different basis. Normal and Pure Profits

DEFINITION: Normal profits are earned when total revenues equal total costs, if total costs are calculated to reflect the opportunity costs of all services provided. If revenues just equal these costs, then all factors are earning the same in that particular employment as they could earn elsewhere. If revenues exceed these costs, we say that the firm is earning a pure, or economic, profit. Remembering that the owners of the firm are the effective suppliers of the services of the land and buildings mentioned, you will see that an economic profit means that the owners of the firm are earning more profit than they could by investing their capital elsewhere. The accounting profit must be adjusted for the opportunity cost of the owned resources—that is, what the firm would pay for the services of those resources if they were purchased or hired—before the alternative investment possibilities can be assessed. Accounting profit will exceed economic profit if some implicit opportunity costs are not subtracted from revenues. This is not to say that either the accountant’s or economist’s view of profit is incorrect; each is designed for a different purpose. The accountant’s purpose is to find, once the capital has been invested in a particular pursuit, the return to the owners of that capital. The economist’s purpose is to ensure that all resources are employed in their most efficient uses. The existence of economic profit confirms that this is so.

NOTE:

A normal profit (when TR = TC) does not mean no profit. Since total costs in the economic sense include the opportunity cost of all resources used, the return on capital invested is included as a cost, rather than counted as a residual in the accounting sense. Normal profit means a sufficient return on the owner’s investment in the firm, sufficient to prevent him or her from liquidating this investment and investing it in the next best alternative investment, since the return on the next best alternative investment opportunity is included as an economic cost

of production. Normal profit, therefore, means as much profit as the owners could get elsewhere. Normal Profits and Risk Considerations

Considering that investments are not equally risky, we need to qualify our concept of normal profits to take into account the different degrees of risk in investment opportunities. Investing one’s money in government bonds is relatively risk free, for example, since there is virtually no risk of default in modern mature economies. Dividends are paid on schedule, and bonds are redeemed on the due date as long as the government exists. Investing money in the development ofa new product, on the other hand, is relatively risky. The investor may not receive The Costs of Production and Supply

149

dividends on his or her investment, and in many cases may lose all the capital that was put in. This is why government bonds pay a relatively low rate of inter-

est (5% to 10%), whereas new product companies, companies prospecting for

oil and minerals, and other high-risk businesses must offer relatively high rates of interest (15% to 20%), in order to attract the required investment funds. Although people are generally averse to risk, they are willing to take risks, but only if there is a promise of sufficiently higher returns to compensate for the risks they are taking. The extra return on high-risk investments necessary to compensate investors is known as the risk premium. The higher the risk involved, the larger is the risk premium demanded by investors.* Since alternative investment opportunities could earn more or less, depending on the degree of risk, we must confine our considerations to alternative investments of the same or similar degree of risk, for the sake of comparability. In effect, this is the familiar ceteris paribus requirement: The comparison of one investment with other investments of equal risk. The highest return on these alternative investments of equal risk is the opportunity cost of investing in the chosen area. It follows that the opportunity cost of investing in a low-risk business is lower than the opportunity cost of investing in a relatively high-risk business. This in turn means that the normal profit of a low-risk business is lower than the normal profit of a high-risk business. In accounting terms, a firm in a low-risk business may be content to earn 8% return on investment after taxes, whereas a firm in a high-risk industry might require 15% return on investment after taxes, in order to keep them in that particular business.

VI. SUMMARY In this chapter, we have transformed production theory into cost theory by incorporating the costs of the inputs into the model and by expressing those costs as a function of output. Variable costs are those that vary directly with output, whereas fixed costs are those that do not vary with output. The shape of the total variable cost curve depends on the shape of the total product curve. The existence of increasing, constant, or diminishing returns to the variable factor(s), if evident in the total product curve, is mirrored in the shape of the total variable cost curve. If there are increasing and later diminishing returns to the variable factor(s), then the average variable and marginal cost curves are U-shaped. Short run average costs are the vertical sum of the average variable and average fixed costs. Average fixed costs decline monotonically; thus short run average costs are U-shaped as long as the impact of diminishing returns to the variable factor(s) outweighs the decline in average fixed cost. The marginal cost curve pulls down both average variable and short run average costs when it lies below each of these curves; it pulls them up when it lies above each of these curves. It follows that the marginal cost curve passes through the minimum point of both the average variable and short run average cost curves. ‘Capital investment under conditions of risk and uncertainty, quantification of risk, and the notion of risk aversion are discussed in detail in Chap. 17.

150

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

The long run average cost curve is the envelope curve of all short run average cost curves available to the firm ata particular time, given prevailing factor prices and the current state of technology. The LAC curve is a smooth U-shape if it is possible to vary plant sizes by small increments and if there are economies and diseconomies of plant size to be realized. Returns to plant size and returns to scale are not identical concepts, since the latter requires the inputs of all factors to be augmented by the same proportion, whereas the former is not so restricted, and in most cases one would expect the least cost input ratio to change for different output levels. Economies of firm size, or pecuniary economies, are reflected in the reduced per-unit cost of inputs as the firm becomes larger or operates more than one plant. Bulk buying of many inputs and the ability to spread some fixed costs over several plants may reduce the average cost of production at all output levels. With all the cost curves, a change in the state of technology or a change in the prices of inputs causes the initial cost curves to become obsolete, and a new set of cost curves becomes appropriate. Cost and profit concepts of the economist differ from those of the accountant, since the economist includes the opportunity costs of all inputs to the production process. Services of owned resources are valued at their opportunity cost and added to the costs of other resources that are purchased or hired. If revenues just cover the total costs, we say the firm is making a normal profit. Pure or economic profits are realized if revenues exceed total costs so calculated. Given that the opportunity cost of the capital invested in resources depends on the degree of risk of the business in which the firm operates, normal profits in high-risk industries must exceed those gained in less-risky industries. In accounting terms, firms in a more risky industry require a higher rate of return on © capital invested, in order to induce them to stay in that industry rather than to invest their funds elsewhere.

DISCUSSION

QUESTIONS

1.

Explain, using only words, why the shape of the short run average cost curve depends upon the specific form of the production function. \_—

2.

Why can the marginal cost curve be derived from either the total variable cost curve or the short run total cost curve? ge

3.

Suppose the market price of a particular product falls. How far can it fall before the firm should decide to cease production rather than to continue supplying the product? Why?

4.

Under what circumstances will the long run average cost curve not be a smooth line? Explain.

5.

Comment on the following (erroneous) definition of the long run average cost curve: “It is the locus of the minimum points of all the short run average cost curves.’ Define it properly in your own words.

6.

The long run marginal cost (LMC) curve is completely unlike the short run marginal cost (SMC) curve, in that the firm would never see its marginal The Costs of Production and Supply

151

costs moving along the LMC curve, whereas it could with any SMC curve. Explain this statement. 7.

How would you know in practice whether or not your firm had benefited from economies of plant size after changing over to a larger plant?

8.

Distinguish between economies of scale, economies economies of multiplant operation.

9.

What changes must be made to some accounting cost categories, and what

of plant size, and

costs must be added, before the accountant’s costs and the economist’s costs add to the same total?

10.

Explain why the normal profit level is higher in some industries than in others. What would you expect the minimum level of normal profit to be and why?

SUGGESTED

REFERENCES

BAUMOL, W.J., Economic Theory and Operations Analysis (4th ed.), chap. 11. Englewood Cliffs, N.J.: Prentice-Hall, 1977. BiLas, R. A.,

Microeconomic Theory (2nd ed.), chap. 7. New York: McGraw-Hill, 1971.

Coe, C. L., Microeconomics: A Contemporary Approach, chap. 7. New York: Harcourt Brace Jovanovitch, Inc., 1973.

FERGUSON, C, E., and S.C. MAURICE, Economic Analysis: Theory and Application (3rd ed.), chap. 6. Homewood, III.: Richard D. Irwin, 1978.

HIRSHLEIFER, J., Price Theory and Applications, chap. 10. Englewood Cliffs, N.J.: Prentice-Hall, 1976. LEFTWICH,R.H., The Price System and Resource Allocation (7th ed.), chap. 9. Hinsdale, Ill.: The Dryden Press, 1979.

Beh

ares A. A. JR.,

Economics of the Firm, chap. 8. Englewood Cliffs, N.J.: Prentice-

Hall, 1973.

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PRODUCTION: THE SUPPLY SIDE OF THE PRODUCT MARKET

Linear Programming Analysis

1. INTRODUCTION When a firm produces more than one product and consequently has some equipment and other facilities involved in two or more production processes, it is a considerably more complex problem to find the least cost or profit maximizing output levels for each production process in the short run. Linear programming (LP) is an optimization technique that allows the solution of this problem in a relatively simple fashion. LP can be applied to solve a wide range of maximization and minimization problems, but in this chapter we shall confine its application to the multiproduct firm to find the combination of different products, and the underlying combinations of inputs to each production process, that maximizes the firm’s short-run profits. ! The multiproduct firm produces two or more products by applying labor and raw materials to fixed inputs of other factors, and wishes to find the profitmaximizing product mix. For example, a metal fabricating firm may produce five different products, each of which requires time on the power hacksaw, the lathe, and the drill press. These products require more or less time on each of these fixed facilities, and most likely contribute different amounts to the firm’s overheads and profits when sold. Similarly, a paint company may produce 1This chapter contains somewhat more advanced material and may be omitted without any loss of continuity in shorter courses or in courses concerned more with qualitative analysis.

153

paints of various types and colors, in various sized cans, and which take more or less of the available equipment time, have different levels of variable costs per liter, and have different prices per liter. The firm’s short run production problem is to find the profit-maximizing product mix subject to the constraints imposed by the limited availability of certain inputs. Linear programming is a special case of the more general (and much more complex) field of mathematical programming. We confine our attention here to linear programming, since it is a widely applicable technique in microeconomic situations and since an examination of non-linear programming would go beyond the level and scope of this text. The Linearity Assumptions

NOTE:

In order to apply linear programming to a particular problem, both the firm’s objective function and the constraints that confine the decision must be linear (or sufficiently approximated by linearity) over the range of outputs to which the decision applies. Supposing that the firm’s objective function is the maximization of contribution to overheads and profits, this implies that the profit contribution per unit of output must be constant in order for total contribution to be a linear function of output. For profit contribution per unit to be constant implies that both price and average variable costs are constant over the range of outputs affected by the decision. Under what circumstances are prices constant over a range of output lev-

els? This situation applies in markets in which the individual firm supplies such a small proportion of total industry output that it may presume that its output decisions will not influence the market price. In such cases the individual firm may assume that the market price for the various products in question will remain constant regardless of the product mix chosen by the firm. Clearly as we consider progressively larger firms, this assumption becomes more tenuous, unless the range of outputs being considered is correspondingly reduced. Thus a relatively large firm may consider that small variations in its output level will not cause a change in the price level. Constant average variable costs imply a situation of constant returns to the variable factor, as we saw in Chap. 6, and this may be a common experience within limited ranges of operation of many business firms. Moreover, constant average variable costs require that factor prices remain constant regardless of the level of demand we place upon these factors. Again this is probably a reasonable assumption for most short run decision-making situations. Contribution is the term given to the difference between total revenue and total variable cost; it

should, therefore, be interpreted as the contribution to overheads (fixed costs) and profits. Note that since profits and contribution differ by a constant amount, that is, fixed costs, maximization of contribution will cause maximization of profits, or minimization of losses, if contribution does not cover fixed costs. In the multiproduct firm situation, most fixed costs are joint costs to two or more production processes. Thus it is simpler, and it often avoids errors to leave these costs as a lump sum to be contributed to by each product, rather than to arbitrarily—or even scientifically—allocate portions of these joint costs to each product.

154

PRODUCTION: THE SUPPLY SIDE OF THE PRODUCTION MARKET

»

The second linearity requirement is that each of the possible outputs uses each of the constraints as a linear function of the output of each product. Thus if the first unit of product X uses 20 minutes of machine time, so must all subsequent units of product X. This should be interpreted as the first unit in the relevant range of outputs, rather than the very first unit produced. Thus the efficiency of the fixed resources is constant and does not depend on the output level of each particular product to be produced. Therefore, there will be a constant trade-off between the production of product X and product Y or, more generally, between any two products that are produced by any machine. In the following discussion, the emphasis will be on obtaining an understanding of the technique of linear programming analysis so that it may be correctly applied to product mix and other decision problems. We shall solve some simple LP problems both graphically and algebraically. More complex problems are best solved with the aid of a computer. Linear programming solution programs are widely available and offer both speed and accuracy in the solution of more complex problems.

Il. GRAPHICAL SOLUTION OF THE LINEAR PROGRAMMING PROBLEM EXAMPLE:

Let us introduce the concept of linear programming in the context of a simple problem. Suppose a small firm manufactures shelf display units for city stores and boutiques. It has the necessary plant and equipment plus a small work force who regard their labor input as being fixed at certain weekly maximum levels. The firm has tapped a market for both a standard shelf unit and a luxury shelf unit, and it has found that demand exceeds its capacity to produce either product. The firm is considering expansion of its facilities, but it is not convinced that demand will be sustained over a long enough period to justify this expansion. In the meantime, it is investigating the question of the optimal output mix between the two products, considering specialization in either the standard unit or the luxury unit or some combination of the two products. The luxury unit, which we shall call product X, involves the more complex design and has a constant average variable cost of $300. Any feasible output of the firm can be sold at the current market price of $600 per unit. The standard shelf unit, which we shall call product Y, has a constant average variable cost of

$200 and can be sold within the range of feasible outputs at a market price of $400. The firm has three processes that have limited capacity to produce both product X and Y. The first process is to cut the material to the appropriate size and configurations on the firm’s power hack saw. The power hack saw is available for only 32 hours weekly, since the operator of this machine is available for only this period. The second process is welding the materials to construct the shelf units; the availability of the welding equipment and its operator is limited to 30 hours per week. The third process involves immersing the units in the chrome bath; this facility and its operator are available for only 40 hours a week.

Linear Programming Analysis

155

Representation of the Constraints

Product X requires 8 hours per unit in the cutting process, 6 hours per unit in the welding process, and 5 hours per unit in the chrome bath. Product Y requires 4 hours of the hack saw time per unit, 5 hours of the welding time, and 8 hours of the chrome bath time. It can be seen that while model Y contributes only $200 per unit, its demands on two of the processes are less than the demands of product X. Alternatively, product X demands more time per unit for two of the three processes, yet it has a significantly higher contribution ($100 more per unit) than does product Y. Thus it is not obvious that the firm should specialize in either product X or product Y. In fact we shall see that a combination of the two products allows a maximum contribution to overheads and profits. The linear programming problem is to find the output mix that achieves the maximum contribution, given the constraints imposed on the production of these two products. Let us state the linear programming problem in symbolic form. Supposing the firm wishes to maximize the total contribution of its operations; it thus wishes to maximize an objective function of the form

1 = AX + BY

(7-1)

where 7 (the Greek letter pi) represents the total contribution to overheads and profits, X and Y are the number of units of each product to be produced, and the coefficients A and B represent the per-unit contribution expected from each of the two products. Using the per-unit price and average variable cost data outlined above, we know that the contribution per unit of product X is $300 and for

Y it is $200. Thus we can express the objective function as

am = 300X + 200Y

(7-2)

The constraints upon the maximization of contribution can be expressed as follows: Cutting Process

8X + 4Y < 32

(7-3)

Welding Process

6X + 5Y . There is, consequently, a loss equivalent to the area P,ABC,

but note that this is less than the fixed costs, which

are represented by the area EABD. It therefore pays the firm to produce: It incurs a smaller loss than it would if it closed down and still had to pay fixed costs in the short run. The area EP.CD is the excess of total revenues over total variable costs; it is known as the contribution to fixed costs. In part c. of Fig. 9-4 we show the firm’s supply curve as the irregular line OP, ABC. At prices below Po, the firm prefers to supply nothing, since price does not cover the average variable cost, and these costs need not be incurred unless to do so is profit-maximizing or loss-minimizing. Above price Py the firm minimizes losses or maximizes profits by producing where MC = MR. Hence at price P, it supplies qo; at price P; it supplies qs; and at price P, it supplies q4. At price P; total revenues equal total costs and the firm just breaks even. At prices above P;, such as P,, the firm makes a pure, or economic, profit equal to the excess of total revenues over total costs.

EXAMPLE:

Grain farmers in the prairie states and provinces of Canada are often characterised as pure competitors. There are certainly many of them, and in any given region they will grow the same kind of wheat—typically the strain that produces the highest yields, given their particular soil, drainage, and climatic conditions. Thus buyers of the grain are indifferent among suppliers, regarding their outputs as being undifferentiated. Suppose that the grain farmer anticipates a market price of, for instance, $3.50 per bushel. The farmer should plant, nurture, and harvest grain up to the point where the marginal cost per bushel is $3.50. Do grain farmers behave like this? Certainly they are responsive to changes in the market price. High prices induce them to plant more acreage, seeding their marginally profitable land. High prices also induce them to harvest more carefully

198

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

FIGURE 9-4 The Competitive Firm's Supply Curve $/q

git

and to keep only the minimum required for next year’s seed grain and animal feed. Low market prices induce the farmers to plant less wheat and put in some corn or beets as well. Alternatively, low prices may induce them to plow some part of the crop under, rather than incur the cost of harvesting it, or after harvesting feed it to their animals rather than sell it on the market. Thus the grain farmer’s supply to the market can be seen to be a direct function of the market price. The farmer acts as if he is equating his marginal costs of production with the market price. Thus the model of pure competition has predictive value, even if the farmer does not consciously calculate his MC at each output level. The Supply Curve of the Industry DEFINITION: The industry supply curve is simply the aggregate supply of all the individual firms in that industry. Note that each firm supplies up to the point where MC = MR, as long as P = AVC. Each firm has an upward-sloping supply curve as Price and Output Determination in Pure Competition

199

long as there are diminishing returns to the variable factor in the short run production function. Each firm, therefore, requires a higher price to induce it to supply more output. Clearly the aggregate supply also increases as price rises or falls as price falls. In Fig. 9-5 we show the construction of the industry (or aggregate) supply curve. We show the MC curve of one representative firm and from this deduce the amounts this firm and every other firm would supply at various price levels. Supposing all firms to have similar cost structures, with minimum AVC = Po, no firm is willing to supply output below price Po, and all firms are willing to supply output until MC = MR = P at prices above P». The industry total or aggregate supply is shown as the horizontal sum of the amounts supplied at each price level by each of the firms. Supposing there are 100 firms, then Q, represents 100 times qo. Similarly, there is 100 times q, being produced and supplied at price P,, adding to Q, in aggregate, and by the same process Q, in aggregate is supplied at price P,. FIGURE 9-5 Construction of the Industry Supply Curve

A Representative Firm

Price

Industry Total (Aggregate)

Note: Q units represent the total industry (aggregate) quantity demanded and supplied, whereas gq units represent the supply of one of many firms in that industry.

NOTE:

To complete the circle, we ask why the price settles at Py, P;, or P.? It settles at one level or the other, given the firm’s short run marginal cost curves and the resultant industry supply curve, depending on the location of the market demand curve. When market demand is represented by the curve Dy on the righthand side of Fig. 9-5, price gravitates to P), when industry supply equals market demand. Similarly, when demand is represented by the curve D,, price is P;, and the quantity Q; is supplied by the aggregate efforts of all the firms, each motivated to maximize its profits or minimize its losses. And finally, when demand

200

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

expands to Dy, price rises to Ps, and quantity supplied increases to q2 units from the representative firm (and to Q, in aggregate)

Il. LONG RUN ADJUSTMENTS In a world of changing technology and factor prices, the long run does not mean a long period of time. Rather, as discussed in Chap. 5, it is a situation in which the firm is able to vary the inputs of all factors of production and thus has no fixed factors or fixed costs as in the short run. But notice that a firm is only in the long run in a contemplative sense: It contemplates the choice among all the available sizes of plant and chooses the size of plant that allows it to maximize profits in the subsequent short run periods. Having selected a particular plant size, the firm is then committed to a short run situation, in which some inputs

(the plant, managerial salaries, and so forth) are fixed. Thus the firm never produces ina long run situation; it can only produce in short run situations when it has a plant to produce in. The long run situation, however, is important for the firm’s planning for future short run periods. While in a particular short rua situation, the firm can plan to expand or reduce the size of its plant, in order to increase its profits in subsequent short run situations.

If the firm experiences losses in the short run, it may wish to liquidate its plant and exit the industry in the long run. In a sense, this is the ultimate degree of contraction of plant size; from some finite size of plant down to zero, or no plant. The opposite situation is the entry of new firms. These firms, attracted by the existence of profits in an industry, assemble the necessary factors of production in a long run situation and begin production in a short run situation. New entrants, therefore, change their size of plant from zero to some finite level.

NOTE:

It is the existence or lack of profits that motivates the entry of new firms or the exit of existing firms. Pure, or economic, profits act as the “‘light to which the moths gather.” If existing firms are making more than normal profits, potential entrant firms attempt to enter the industry and compete for some of these profits. Alternatively, if existing firms are making less than normal profits, and if there is no other plant size that allows even normal profits, entrants are not attracted, preferring to invest their resources elsewhere. Similarly, existing firms will prefer to invest their resources elsewhere and are motivated to exit this particular industry and move to their next best alternative in order to earn a normal profit. We proceed now to examine the impact of the entry of new firms and the exit of existing firms on the industry supply curve and market price, before ex-_ amining the adjustment of plant size by existing firms. We then bring these two effects together to find the long run equilibrium price level for a purely competitive market.

Entry of New Firms

If the existing firms are making pure profits in the short run, entry of new firms occurs in the long run, given the freedom of resource mobility and the availability of the technology to potential entrant firms. In Fig. 9-6 we show a representPrice and Output Determination in Pure Competition

201

ative existing firm initially making short run profits at the market price Po, since this price exceeds the firm’s average costs at output level qo. Initially, before the entry of any new firms, industry supply is shown by the curve S in the righthand side of the figure, interacting with the market demand curve D to cause the short run equilibrium price Po. FIGURE 9-6 Entry of New Firms Causing Industry Supply to Expand and Market Price mm rar ‘ Industry/Market

A Representative Entrant Firm

A Representative Existing Firm

$/q

$/O

S

O/t

The expectation that short run profits will continue attracts the entry of new firms, which choose a plant size under long run conditions and begin to supply the product to the market. This causes the industry supply curve—the horizontal summation of the firms’ supply, or MC, curves—to shift to the right. Suppose that just enough new firms begin production, so that, in conjunction with pre-existing firms, the industry supply curve moves across to S’. Excess supply at price level Py causes price to be forced down to the new short run equilibrium price P,. At this new price, the firms each produce output level q, in order to maximize their profits. In the case shown, the firms make only a normal profit, since price now equals the firms’ average costs. The disappearance of pure profits means that no more firms are induced to enter the industry. Exit of Existing Firms

Let us now consider a situation in which the existing firms are unable to make even a normal profit and are, therefore, inclined to exit the industry in order to make at least a normal profit elsewhere. In Fig. 9-7 we show a representative firm initially producing the loss-minimizing output qo at the market price Py, given the initial industry supply curve S and market demand curve D. In the short run the firm should continue to produce and incur the loss, while planning to exit the industry in the long run. Thus the firm makes arrangements to liquidate its plant, and as soon as it is able to, it ceases production and exits the

industry. The exit of one or more firms causes the industry supply curve to shift 202

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

to the left. Suppose that just enough firms exit the industry so that the supply curve moves to that shown as S’ in Fig. 9-7. This causes excess demand at the price Po, which in turn exerts upward pressure on market price until the price P, is attained. At this price all firms remaining in the industry produce output level qi pas make normal profits again, since price now equals short run average

costs.

FIGURE 9-7 Exit of Existing Firms Causing Industry Supply to Contract and Market Price to Rise $/q

A Representative Firm

Fo%

$/Q

Industry/Market

Q, %

Q/t

Notice that once normal profits are being earned, the incentive to exit the industry disappears, since the remaining firms are making as muchas they could make elsewhere. This is so because we have reckoned the opportunity cost of all factors into our calculation of the short run average cost curves. Each factor is earning at least as much as it could in its next best alternative employment: Therefore the owner of the firm has no incentive to transfer these factors to any other industry. EXAMPLE:

The coastal fishing industry may be characterized as a group of purely competitive suppliers of a homogeneous product; e.g., mackerel. Entry to this industry is relatively easy. There is a ready supply of new hopefuls willing to buy a fishing boat and gear and enter the industry whenever it seems profitable to do so. In fact, it is a problem of the fishing industry that entry is too easy, leading to 3In order to avoid a situation in which all firms simultaneously exit the industry, then simultaneously re-enter the industry, and so on, we must postulate some reason for a differential speed of long run plant size adjustment among firms. Perhaps some firms expect demand to increase in the near future, restoring profits to normal or pure levels again. Alternatively, the demand curve for used plant and equipment would be expected to be negatively sloping, leading to progressively lower liquidation prices as more firms leave the industry. This would lower the remaining firms’ opportunity cost of these factors, until at some point it would allow firms to make normal profits at the market price, and thus halt the exodus from the industry. Price and Output Determination in Pure Competition

203

an overcrowded industry and a dangerous depletion of the fish population in some areas. Why does the fishing industry remain overcrowded? You would expect the exit of firms when normal profits are absent, and thus a decline in the number of firms. Certainly there is exit from the industry when some fishermen find themselves unable to continue and finally sell their boat and gear and take a job on shore. This is typically the very last resort, however. Fishermen subject themselves and their families to prolonged periods of penury between the good years, mortgaging all their assets and reducing their standard of living in order to stay in the fishing business. Thus, while entry\is easy, fishermen are reluctant to leave the industry, and profits seem to be chronically depressed except for an occasional season of pure profits. Observing the coastal fishing industries, one would have to conclude that the normal profit level is very low in monetary terms. The psychic income of fishermen has a monetary equivalent, however, and so many fishermen prefer to remain fishermen, rather than to earn more ’ money on shore in regular jobs. Expansion of an Existing Firm’s Plant Size A firm making pure profits in the short run may see an opportunity of making even greater profits in subsequent short run periods by expanding its size of plant to benefit from economies of plant size. The individual firm reasons that it could expand its output level without influencing market price and that it could, therefore, increase profits by producing in a plant with lower per-unit costs. In Fig. 9-8 we show the market price initially at Py) with industry supply curve S and market demand curve D. The representative firm, initially facing the cost curves MC and SAC, produces output level qy in order to maximize profits in the short run. FIGURE 9-8 Expansion of Plant Size in the Long Run

$/q

204

A Representative Firm

$/0

Industry/Market

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

While making profits in the short run, the firm contemplates its long run opportunities. It reasons that it can expand its size of plant so that its cost curves move to those shown as MC’ and SAC’. (Note that this is the optimal size of plant: No other plant size allows average costs to fall as low as they do on SAC’.) All other firms are similarly motivated to increase profits and they also change to the optimal plant size. Thus each firm’s supply curve shifts from MC to MC’, so that the aggregate industry supply curve shifts to the right, exerting downward pressure on market price. If the impact of all existing firms expanding their supply is not enough to shift the industry supply curve across to S’ in Fig. 9-8, the entry of additional firms will. Eventually enough firms will exist in the industry so that aggregate supply is as shown by S’, causing price to settle at P,. At this level, price equals average cost for all firms, and all firms are making only normal profits, each producing q, units of output. Thus each firm in a purely competitive industry will be motivated to expand its plant size until it produces in the optimal plant size. dtwill be motivated to do this by pe isa ced) poomuse of greater PEAR But notice that the firm is also forced to see e optimal plant size in order to make at least normal profits in the long run. In the example given, suppose one firm chooses to hold out at the size of plant represented by the curves MC and SAC in Fig. 9-8. The actions of other firms expanding their plant size and of new firms entering the industry causes price to be driven down below the hold-out firm’s lowest level of short run average costs. This firm is then faced with two options: Either expand plant size to SAC’ in order to obtain pure or, at worst, normal profits, or exit the industry if expansion to SAC’ would still not allow the firm to bring its per-unit costs below market price.*

The Long Run Equilibrium Price DEFINITION: The price P, in Fig. 9-8 is known as the long run equilibrium price, since there are no forces operating to change the level of price, even in a long run context. No firms are motivated to enter or exit the industry, since only normal profits are being earned. These normal profits are enough to keep existing firms in the industry, but not enough to attract the entry of new firms. Similarly no firms are motivated either to expand or contract their plant size, since it is only at the optimal size of plant that they can obtain normal profits; this is only possible at the minimum point of the optimal plant’s SAC curve. Thus there are no factors operating to shift the industry supply curve, and, given a static demand situation, there are no forces operating to raise or lower the market price level. The industry is, accordingly, in a state of long run equilibrium, where it will stay until dislodged by either a shift of the demand curve or a change in technology or factor prices. 4If several firms were slow in adjusting their plant size to the optimal size, and price had already fallen to P, as a result of other firms’ adjustments and the entry of new firms, the combined effect of the late adjusters would be to drive price below the level that allows normal profits to be attained with the optimal plant size. The existence of losses would cause some firms to exit the industry until normal profits could be earned by all firms remaining in the industry. Price and Output Determination in Pure Competition

205

If the market demand curve were to shift to the right, due to increased consumer

incomes, for example, this would cause the short run equilibrium

price to rise and allow all firms to make pure profits. These profits would induce the entry of new firms in the long run, until the industry supply curve moves far enough to the right to cause market price to fall to the long run equilibrium level, which remains at

P,, since there was no change in the cost conditions. If the state

of technology improves or if prices of some factors are reduced, the LAC and SAC curves shift downward, since any given output level could then be produced at lower cost. This allows pure profits in the short run, which would induce entry in the long run. Entry will continue until only normal profits are earned by all firms as a result of the industry supply curve shifting to the right, causing the price to fall until it is equal to the minimum level of average costs at the optimal size of plant. Thus the purely competitive industry would adjust to a new long run equilibrium price and output level in response to any change in cost or demand conditions. NOTE:

All firms must tend toward the same size of plant, using the same state of technology. That is, all firms must build the optimal size of plant, using the most efficient technology of production, in order to survive. Any firm not using the best technology in the plant size that allows minimum SAC, cannot make even normal profits in subsequent short run periods, given the profit motives of potential entrants and existing firms, the unrestricted mobility of resources, and the availability to all existing and potential firms of the necessary technology and factor price information. Now you can see why we are able to use the concept of the representative firm in our treatment of the individual firm: Since all firms are motivated to behave in the same way and are forced by competitive pressures to adopt the same cost structure, any one firm’s behavior is representative of the behavior of all other firms.

IV. ECONOMIC EFFECTS OF PURE COMPETITION

Pure competition has two major beneficial economic effects and a couple of other effects that are often claimed to be detrimental to the economic welfare of society. The beneficial effects are that there is always a strong incentive for firms to be as efficient as possible in production, and that prices to consumers tend to be lower than in any other market situation. The possibly adverse effects are that firms earning only normal profits may be forced to neglect research and development expenditures to the detriment of economic growth and future consumer welfare, and that the consumer may be faced with less variety of product offerings in a purely competitive world. We look at each of these issues in turn, and then discover that the question is probably a moot one, since this market form is not common in the real world.

206

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

Economic Efficiency in Production

We saw in the preceding section that the profit motivation of competing sellers and potential entrants, the absence of barriers to entry, and the widespread availability of information concerning the latest technology and the prices of competitors’ products, forces the individual firm to keep up to date with technology and to produce at the optimal size of plant and the minimum level of average costs. If a firm fails to incorporate the economically most efficient combination of factors, it finds itself producing at a loss, because other firms and new entrants (with the latest low-cost technology) have driven the price down to the level of minimum average costs at the optimal size of plant. In the long run the firm must either exit the industry or adjust its size of plant and technology into conformity with other firms.Thus pure competition ensures that firms always tend toward the greatest possible efficiency in production. We see in the following chapters that this is not true in other market situations. Consumer Prices

It follows from the above that the prices paid by consumers in markets characterized by pure competition tend to be lower than in any other market form. Given the time needed for long run adjustments, the entry of new firms and the movement to the optimal plant size by the new and existing firms forces the market price down to the level of minimum average costs in the optimal size of plant. Since other market situations do not force the firm to operate at this lowest possible cost level, it is clear that firms in other market situations—where prices are set at or above their average cost levels—must price at higher levels than would purely competitive firms in comparable situations. Product Development and Variety In pure competition there is little or no incentive for an individual firm to conduct research and development programs, which might lead to the development of improved products or to the development of new technologies of production. Research and development (R and D) programs typically require considerable input of time and expenditure before any significant improvements in either the product or the process of production are forthcoming. As soon as the improvements are forthcoming, however, all other firms will quickly imitate the improvements, since information flow is unrestricted in pure competition. The individual firm has to incur all the costs of the R and D, but expects to receive only a relatively small share of the benefits. When there are many firms in the market, one would expect a firm to prefer to sit back and wait for another firm to incur the R and D expenses and then simply imitate any significant improvements. If all firms did this, then none of them would be conducting R and D programs, and product improvements and technological advances would be limited to those stumbled on by chance. This has grave implications for the rate

Price and Output Determination in Pure Competition

207

of scientific advancement and the related growth of the standard of living in the economy. Arelated issue is that of product variety. The greater the variety of products available, the greater the aggregate utility (or welfare) of consumers (society) is expected to be, since each consumer may choose the product that best serves his or her needs and desires. If all products are the same or if only a limited variety of products is available, consumers must make their choices from within a more

limited set. Thus many consumers will have to choose a product that is not exactly what he or she wants, but is the product'slosest to what is wanted. In pure competition, where the incentive for R and D expenditure is re-

duced, one would expect a lesser proliferation of product types as a result. A second factor at work is that there is considerable risk of loss associated with launching a new product, since consumers may not like what the producer thought they would like. In a business environment where profits are pressed down to the normal level, firms may not be prepared to initiate the offering of new products, since this may in turn result in losses and the eventual liquidation of the firm. Thus a purely competitive market situation is likely to generate less product variety than in markets where the benefits of such innovations are enjoyed primarily by the innovating firm and where pure profits can exist in the long run, giving firms the incentive and the means to engage in R and D programs and product innovations. We shall see that these conditions are typically present in the other major market forms. The Value of the Pure Competition Model

Do purely competitive markets exist? Are there any market situations that conform to the seven assumptions outlined earlier in this chapter? The hardest conditions to meet in the real world are assumptions 1, 3, and 4: many sellers, many buyers, and identical products.’ There are certainly some markets left in our evolving socio-economic system that have many sellers, such as most agricultural markets and perhaps some manufacturing and service markets.® Many buyers is a common situation in most markets, but is surprisingly absent in some agricultural markets where a single or a few large private, governmental, or cooperative buyers operate to buy all or most of the suppliers’ output. The most difficult condition to find is identical products, or zero product differentiation. Keep in mind that zero product differentiation requires that all buyers regard all competing products as identical in all respects. Buyers cannot have personal preferences for particular sellers, nor have differing expectations ‘If there are many sellers and identical products, the behavioral assumptions of short run profit maximization, price and quantity as strategic variables, and the zero conjectural variation are likely to be appropriate. *Note that we mean many sellers in the same marketplace. There are a large number of cement manufacturers in the U.S., for example, but each one supplies only to the immediate geographical area due to the high proportion of transportation cost relative to the price of cement. In any particular market area there may be only one or several firms directly competing with each other. Thus these markets do not qualify as examples of pure competition.

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THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

of quality or after-sales service, nor find it more or less convenient to buy from one seller rather than another. The package of attributes constituting the product must be viewed as identical in all respects. Perhaps the only market in which the conditions for pure competition are fulfilled is the stock exchange, at which hundreds of buyers and sellers meet anonymously (through their agents) to buy and sell a particular company’s stock. Each share in the company has the same rights, benefits, and obligations attached to it (for each class of shares), and no buyer is likely to care about the identity of the previous owner. Agricultural and other primary industries such as coastal fishing typically do not fulfill all the requirements of the pure competition model. The problem lies not on the supply side but on the demand side. Often the small supplier does not face ‘“‘many”’ buyers, but rather a single cooperative buyer or, at best, a few oligopolistic buyers. Therefore the price is determined primarily by the buyer(s), rather than by the combined forces of market supply and demand.” If there are few—or, perhaps, only one—real world examples of pure competition, is it worthwhile studying the model at all? To answer this, recall that the purpose of models may be either explanatory, predictive, or pedagogical. The purely competitive model is an appropriate explanatory or predictive model only to the extent that the seven assumptions involved are in accord with the reality of the situation being explained or predicted. It does give useful explanations and predictions for the stock market. In fact, the theory of finance is based on the purely competitive model, because the seven assumptions underlying the model are essentially realistic in many financial markets. But for market situations that do not conform with the assumptions of the model, we should not expect correct explanations or accurate predictions to flow from the purely competitive model. The major value of the purely competitive model is clearly pedagogical: It allows the theory of the firm to be introduced in a relatively simple context, free of the complications introduced by product differentiation and the fewness of buyers or sellers. It thus forms a basis upon which we can build an understanding of more complex models or theories of the firm, which can explain and predict the behavior of real world firms in their complex environments. Moreover, the model of pure competition allows us to establish ‘“‘benchmarks,” or reference points, from which we may measure the economic effects of restrictions that exist in other market forms. Thus we will be able to show in the next chapter, on monopoly, the impact of barriers to entry on the costs of production and price charged to consumers, as compared to the pure competition situation where such barriers are absent. Similarly, in Chap. 11 on monopolistic competition, where there are no barriers to entry but products are differentiated, we can see the cost to consumers of product differentiation as compared with the undifferentiated products in pure competition. 7This is not to denigrate cooperatives, of course, which develop as a response to the damaging price fluctuations that would otherwise be common in purely competitive industries, subject to uncertain conditions on the supply side. It is simply to say that some of the predictions of the purely competitive model are not accurate for these industries (for example, prices should be very sensitive to shifts in the supply and demand curves), because the model does not accurately represent the structure of the industry. Price and Output Determination in Pure Competition

209

V. SUMMARY In this chapter we have examined the price and output determination process in markets characterized by pure competition, in both the short and long run situations. Price is determined by the forces of market supply and demand: Excess supply causes price to fall, and excess demand causes price to rise. When supply equals demand, there is no pressure on price to either rise or fall, and thus the price is an equilibrium price, at least for the duration of the short run. Profit-maximizing firms produce up to a point when marginal costs rise to meet marginal revenues, which in the case of pure competition equals price, since the firm can sell as much as it wishes at the market price. The firm’s marginal cost curve is, in effect, its supply curve, since it shows the quantity that is supplied at each price level. The industry supply curve is the horizontal sum of all individual firms’ supply curves. The purely competitive firm may make pure profits in the short run, if the market price exceeds the firm’s average cost level at its chosen output rate. Pure profits attract the entry of new firms in the long run, since there are no restrictions on the mobility of resources. The resultant increase in production causes the industry supply to shift to the right, forcing down the market price until only normal profits can be earned by the firms, all of whom are, at this point, operating at the point of minimum average cost in the optimum-size plant. When market price equals this lowest possible level of average costs, the industry is in long run equilibrium, although any change in demand or cost conditions causes the firms to jointly move toward a new long run equilibrium situation. Pure competition ensures the maximum efficiency in production, since all firms have access to the latest technology, since there are no restrictions on resource mobility, and since all existing and potential entrant firms are profit-motivated. If any firm fails to produce most efficiently and economically, it will eventually incur economic losses and be forced to exit the industry. The pressure of competition also ensures that prices tend toward the lowest possible level— the minimum level of average costs on the long run average cost curve. Pure competition may inhibit research and development expenditures and the subsequent improvement of products and production technology, but this may not be a problem in the real world, due to the scarcity of market situations approximating pure competition. The value of the pure competition model is mainly pedagogical, rather than explanatory or predictive. However, it is valuable for the study of financial markets, where its underlying assumptions are essentially realistic and its drawbacks are not applicable.

DISCUSSION

210

QUESTIONS

1.

In the purely competitive model, consumers and producers have perfect information on all the data they need. Outline the implications of this for the assumptions of the model concerning the cost and demand conditions.

2.

Can you now deduce why an upward-sloping marginal cost curve is a sufficient condition for the purely competitive model to equilibriate in both

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

the short and long run situations? What would happen, for example, if MC is horizontal or falling throughout the range of short run output possibilities for the firm. 3.

When market price is below the short run equilibrium price, why will some consumers willingly pay a higher price for the product?

4.

Explain why individual firms have a profit incentive to reduce price when there is excess supply in a purely competitive market.

5.

State and explain the rule for profit maximization in both total and per-unit terms.

6.

Explain why the individual firm’s supply curve is equivalent to its MC curve above the AVC curve, and why the industry supply curve is the horizontal summation of the individual supply curves.

7.

Explain why the existence of pure profits attracts the entry of new firms, and why earning only normal profits does not provide an incentive to exit the industry.

8.

What does the absence of all barriers to entry imply for the cost assumptions underlying the purely competitive model? Does it also have implications for the demand assumptions?

9.

Ifmarket demand temporarily shifted to the right due to the impact of some random event, why would you expect this not to induce the entry of new firms? What underlying assumption of the model ensures this?

10.

Although firms have full information on the demand and cost conditions,

it is not clear that they fully anticipate the expansion of other firms’ plant sizes and the entry of new firms. Explain the adjustment process that takes place if the expansion and entry of other firms are underestimated. SUGGESTED

REFERENCES

Economic Analysis: Theory and Application (3rd FERGUSON, C.E., and S.C. MauRIcE, ed.), chap. 7. Homewood, Ill.: Richard D. Irwin, 1978.

HIRSHLEIFER, J., Price Theory and Applications, chap. 10. Englewood Cliffs, N.J.: Prentice-Hall, 1976.

Intermediate Microeconomic Theory, chaps. KAMERSCHEN, D.R., and L.M. VALENTINE, 11, 12. Cincinnati: Southwestern Publishing Co., 1977.

KOUTSOYIANNIS, A., lan Press, 1979.

Modern Microeconomics (2nd ed.) chap. 5. London: The Macmil-

LEFTWICH, R.H., The Price System and Resource Allocation (7th ed.), chap. 10. Hinsdale, Ill.: The Dryden Press, 1979. Intermediate Microeconomics and Its Application, chaps. 9, 10. Hins, NICHOLSONW., dale, Il].: The Dryden Press, 1975.

Price and Output Determination in Pure Competition

211

ui ie ai elke eee me NS \

4 a

X

Price and Output Determination by a Monopoly

|. INTRODUCTION DEFINITION: A monopoly exists when there is only one seller of a product or service in a particular market. EXAMPLES:

‘The telephone company in your area is a monopoly, as probably are the electricity company, the liquor control board, and the cable television company. If you live in a small city, town, or rural area, your supplier of premixed cement is probably enjoying a local monopoly, protected by transport costs from the competition of suppliers from other cities or towns. If you own a Rolls Royce, a Ferrari, or a Lamborghini, your service and repair shop is also likely to be a monopoly in the market it serves, since there is rarely enough demand for these “exoticars”’ in any particular area to support more than one dealer per marque.

Reasons for Monopolies

Why monopolies? The examples above indicate several reasons. The ‘‘exoticar’’ dealer and the premixed cement supplier in many cases produce for a local market which is not large enough to support more than one seller. The telephone and electricity companies, on the other hand, serve very large markets, which could easily support several sellers in most cases. Yet the cost structure of these 212

industries is such that it is cheaper to produce in one large operation, than it is in several smaller operations. Thus if there were two firms supplying a market, it would be in their best interests to merge and become a monopoly, since they could reduce costs by producing in one large plant rather than in two or more smaller plants. This is called a natural monopoly, since the situation would automatically gravitate to a monopoly if one did not exist initially. DEFINITION: A natural monopoly situation exists when economies of plant size or firm size can be realized at output volumes that are large relative to the market demand. Graphically, a natural monopoly could be depicted by a long run average cost curve that slopes downward at least until it crosses the market demand curve. In other cases, monopolies exist by virtue of a government mandate granted to the firm allowing it to be the only seller of a particular product or service. The post office, the local liquor commission, and national defense are examples of monopolies created and protected by government mandate. Potential firms simply cannot legally acquire the right to set up a plant and operate in those markets. The rationale for the monopolies of the post office and the liquor commission is that economic and social benefit is best served by government control of these markets. The reason for the government monopoly on defense is obvious: National security is doubtless best served by a single supplier of armed force, rather than by several competitive suppliers. Other monopolies exist not because the market is too small relative to their cost structure and not because potential competitors are prohibited by law from competing, but because there are barriers to the entry of new firms.

DEFINITION: Barriers to entry are disadvantages faced by a potential entrant firm regarding the cost or availability of a resource necessary for the production of a particular product, or disadvantages faced by the potential firm in the marketing of its product. EXAMPLE:

The existing seller might control the supply of a vital raw material, or the best technology by virtue of a patented technique, or the training of skilled labor, or the best locations for production and marketing of the product. Clearly, if potential entrants cannot gain access to a necessary input, or if the price of so doing is prohibitive, then the monopoly remains a monopoly until these restrictions are removed. Consumer loyalty for the existing firm’s product also operates as a barrier to the entry of new firms. Over time these barriers do tend to crumble, as

new sources of raw materials are discovered, alternative materials are invented (for instance, synthetic rubber and plastics), technological breakthroughs are made, and consumers’ tastes and preferences change. 1Perhaps the major reason underlying government provision of national security is that national security is a public good, meaning that everyone benefits from its existence, whether or not they contribute to its cost. When left to the market mechanism, public goods are typically undersupplied; hence governments must step in and supply an adequate supply. This issue is discussed in detail in Chap. 20. Price and Output Determination by a Monopoly

213

The Seven Assumptions of Monopoly

The price and output decisions of a monopolist can be explained and predicted in a model comprised of the seven assumptions listed in Table 10-1.” Of these seven assumptions, only two are different from the seven assumptions for the model of pure competition: There is only one seller instead of many, and the product is completely differentiated instead of being undifferentiated. The product differentiation assumption bears further comment. By complete product differentiation, we mean that the cross elaaticity of demand between the

monopolist’s product and any other product is either very low, zero, or negative. This in turn means that in the particular market area under scrutiny, there are no other products of any other supplier that the buyers are willing to substitute, to any significant extent, for the monopolist’s product. Thus the assumption of a single seller of the product is inextricably linked to the assumption of extreme product differentiation. TABLE 10-1 The Seven Assumptions of Monopoly

STRUCTURAL ASSUMPTIONS

BEHAVIORAL

ASSUMPTIONS

NOTE:

1. Number of sellers 2. Cost Conditions

3. 4. 5. 6. 7.

i

Numberof buyers Demand conditions Objective function Strategic variables : ane Conjectural variation

One Cubic production function with constant factor prices. Entry of new firms is not possible. Many Product has no close substitutes Short run profit maximization Price & output levels 4 : Zero, since there are no rivals

Monopolists in the real world usually do have some peripheral competition from distant and partial substitutes. The post office experiences competition from the telephone company and from such delivery services as United Parcel Service (UPS), for some of the services it provides. The electricity company competes with the gas company in some households. Bootleggers compete with the liquor control board in some areas. In all these cases, however, the extent of substitution of these products for the monopolist’s product is quite small. Thus the cross elasticity of demand between the monopolist’s product and the distant substitutes, over the market as a whole, is quite low.

Il. SHORT RUN PRICE AND OUTPUT DETERMINATION RULE:

The profit maximization rule remains the same as it was for the pure competitor: expand output to the point where marginal costs rise to equal marginal revenues. Note, however, that the marginal revenue curve is different for the monopolist. *The monopoly model generates equilibrium short and long run price and output solutions with a variety of assumptions concerning the cost conditions. We choose one of these, the cubic production function, to demonstrate the model, without implying that this assumption is necessary for the monopoly model.

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Since this firm faces the entire market demand, the firm’s demand curve and the market demand curve are one and the same. Thus the market marginal revenue curve is the firm’s marginal revenue curve. We saw in Chap. 4 that the marginal revenue curve associated with a negatively sloping linear demand curve has the same vertical intercept on the graph and twice the slope of the demand curve. Given this knowledge, we can easily find the profit-maximizing price and output combination. The Profit-Maximizing Price and Output Levels for the Monopolist

In Fig. 10—1 we show the market demand curve (D) faced by the monopolist and the corresponding marginal revenue (MR) curve. Superimposed on these are the cost curves of the monopolist—the short run average cost (SAC) and marginal cost (MC) curves. The profit-maximizing monopolist produces up to the point where marginal costs per unit rise to meet the falling marginal revenues. This occurs at output level Q*. Notice that every unit to the right of Q* has a marginal cost greater than its marginal revenue; it therefore will not be produced. Conversely, every unit to the left of Q* costs less than it earns (marginally or incrementally); it therefore will be produced and sold. FIGURE 10-1 The Monopolist’s Price and Output Determination Price,

cost, per unit

($/Q)

P=

G

(6)

= Q

Quantity per period of time

(Q/t)

To find the profit-maximizing price, we extend a vertical line up to the demand curve at output level Q*, in order to see the maximum price the market will pay for that output level. This indicates that the monopolist should set price at P*, in order to sell the quantity Q* without causing any excess demand. (At a lower price the firm could certainly sell Q* units, but demand would exceed the amount supplied.) Average costs per unit are equal to C dollars at output level Q*, and the average profit per unit is the price per unit P* minus the average cost Price and Output Determination by a Monopoly

215

per unit C—or the vertical distance AB. Total profit for the monopolist is, therefore, AB, or P* —C, times Q*. This is shown as the shaded rectangle P*ABC. EXAMPLE:

North America’s most entertaining monopolies are, doubtless, the professional sports leagues with their component football, baseball, basketball, hockey, and more recently soccer teams. Entry of new teams is restricted in each league: It is only allowed if all existing teams agree to the expansion of the league. There is only one team per city in each league, except for very large cities like New York, which has two teams (the Islanders and the Rangers) in the National Hockey League. The teams in any one league are not competitive with each other in a profit-seeking sense; rather, their actions are coordinated, with the league acting like a monopoly firm. Profits are massive: In 1980 the average National Football League (NFL) franchise earned a profit of about $1.2 million on sales revenues of $11 million, regardless of whether it won the Super Bowl or

lost all sixteen games of the season. The game between the New York Giants and the Washington Redskins on September 13, 1980 alone generated about $700,000 in gate receipts and another $620,000 for national television rights. Television stations, thirsting for entertaining programming, in 1980 paid each team in the NFL about $5.2 million. This figure is expected to jump to $9 million in 1982. The other professional sports leagues are not as remunerative for their owners; nevertheless, they manage to extract relatively high ticket prices and lucrative television contracts as a result of their monopoly positions.? Must Monopolists Make Money?

Monopolists are often disparaged for the monopoly profits they make. Certainly the firm in Fig. 10-1 is making pure, or economic, profits in the short run situation depicted. Moreover, if there are sufficient barriers to entry and the demand situation expands or remains unchanged, this firm will continue to make pure profits in subsequent short run periods as well. But if demand shrinks or if costs rise dramatically while demand stays relatively constant, our monopolist might easily find itself incurring losses. There are certainly cases of monopolists going out of business due to the combined pressures of rising costs and shrinking demand.

EXAMPLE:

With the coming of the automotive era and the passing of the era in which horses were the primary means of transportation and horsepower, most makers of saddles, bridles, and harnesses suffered this fate. There were doubtless many saddlers and harnessmakers in towns and small cities who enjoyed a local monopoly in the early days of the automobile. But as the automobile and its cousin the farm tractor slowly but inexorably stole the hearts and minds of the populace, the demand for saddles and harnesses just as inexorably declined. 3“Monopoly Pays Off in the Business of Sports,” Business Week, October 13, 1980, pp. 146-52. Due to a somewhat obscure ruling by the Supreme Court in 1922, professional sports are exempt from the antitrust laws that oversee the activities of other monopolies.

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In Figure 10—2 we show a monopolist that has suffered a decline in demand for its product, as evidenced by the shift to demand curve D’ from demand curve D. Notice that the new demand curve D’ lies to the left of the firm’s short run average cost (SAC) curve at all output levels. Given this situation, the monopolist must make losses in the short run, but can minimize its losses by equating marginal cost (MC) with the new marginal revenue curve MR’. Thus the monopolist produces Q' units of output per period and sets price at P’ per unit, considerably below its earlier profit-maximizing price of P*. At output level Q’, average cost per unit is shown at point A’, and it exceeds the new price. The monopolist thus makes losses equal to the shaded area P'B'A'C’. FIGURE 10-2 A Monopolist Making Losses due to a Decrease in Market Demand

SAC AVC

+

0/t

Should the monopolist cease production? No, not in the short run, unless

it is forced to reduce price below the level of its average variable costs as demand further declines. The monopolist might wish to cease production in the long run, because it can then liquidate its assets and exit this industry in favor of its

next best alternative investment opportunity. There it could, by definition, earn normal profits. Alternatively, this firm might be able to move to a smaller plant, which would allow it to earn pure profits once more. We examine this in the next section.

III. LONG RUN ADJUSTMENTS IN MONOPOLY Although a monopolist is making pure profits in the short run, it may wish to change its size of plant in the long run, in order to make even larger pure profits in the subsequent short run period. If entry of new firms is impossible due to prohibitive barriers, the monopolist is able to build the size of plant that maxiPrice and Output Determination by a Monopoly

217

mizes profits from the prevailing market demand situation. If entry of new firms is not impossible and actually occurs, the market becomes an oligopoly, which we shall treat in Chaps. 12 and 13. Plant Size Adjustments to Maximize Profits

The monopolist will change its size of plant in the long run if there exists a different-size plant that offers greater profits than the existing plant. The monopolist therefore considers its long run average cost(LAC) curve, which is the envelope curve of all the possible short run average cost (SAC) curves, and contemplates moving from plant to plant, in order to find which plant size is most profitable. In this contemplative sense, the firm considers the long run marginal cost (LMC) curve, which shows the (lowest possible) marginal cost of producing one more unit when all factor inputs can be varied. This LMC curve is marginal to the LAC curve, of course, and in effect shows the impact on total

costs of producing the marginal unit of output in the plant size that produces the unit at least cost. In Figure 10—3 we show the market demand situation and the cost curves of a particular monopolist. Initially the monopolist is producing output Q* in the plant depicted by the cost curves SAC and MC. At output level Q* and price P*, the profit-maximizing condition (MC = MR) is satisfied; short run profits are shown as the rectangle P*ABC. FIGURE 10-3 Plant Size Adjustment to Maximize Profits $/Q

In the long run the monopolist is able to change the input of all factors and can thus change its plant size if a more profitable size exists. It is clear that a more profitable plant size does exist because the LMC curve is not equal to the 218

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

MR curve at output Q*. The fact that LMC < MR indicates that the monopolist should both reduce its price and expand its plant size in order to bring the MR down to equal the LMC curve. This equality, which is the long run profit-maximizing condition, occurs at output level Q**. The monopolist will therefore build the plant size represented by SAC’ and MC’, set price at P**, and earn pure profits equal to the area P**A’B'C’. Notice that these profits are larger than the earlier short run profits shown as P*ABC. At output level Q** and price P**, the monopolist is in both short and long run equilibriums: Short run marginal costs (MC’) are equal to marginal revenue, and long run marginal costs (LMC) are also equal to marginal revenue at this price-output combination. We know MC’ must equal LMC at output Q**, because SAC’ is tangent to the LAC curve at that output level. The SAC’ curve represents the plant size that can produce Q** at the lowest possible average cost and therefore must be part of the LAC curve at output level Q**. Now, since SAC’ = LAC at output Q**, MC’ must equal LMC at that output level. To see this, note that SAC’ and LAC are both declining as output is increased toward Q**. SAC’ declines faster than LAC, because MC’ lies below LMC. In each case it is the marginal cost causing the average cost to fall. At point B’, where SAC’ and LAC are tangent, both these curves are declining at the same rate, and hence both the short run and long run marginal costs must be equal. After output level Q**, as output increases, the SAC’ curve rises more rapidly than does LAC, because MC’ is pulling up SAC’ faster than LMC is pulling up the LAC curve. NOTE:

In their respective short run periods, both price P* and P** are the optimum (profit-maximizing) prices. Given the total flexibility of inputs in the long run situation, however, the firm chooses P** and plant size SAC’, since this is the optimum optimorum situation.

Plant Size Adjustments to Avoid Losses

Let us reconsider the plight of the monopolist making losses in the short run. This firm may be able to avoid losses and return to a pure profit situation, if there exists a plant size in which average costs are less than price. If the LAC curve crosses the demand curve, as in Fig. 10-4, there will be plant sizes that allow the firm to make pure profits; and the profit-maximizing monopolist can choose the plant size that maximizes the available profits. In Fig. 10-4 the monopolist is initially producing at output level Q*, in the plant size depicted by the cost curves SAC and MC. Price is P* and average cost per unit is the level C, meaning that the firm is incurring losses equal to the area P*ABC. In the long run the firm should shift to the plant size where LMC = MR. This plant size is depicted by the cost curves SAC’ and MC’ in Fig. 10-4. In this plant the monopolist can produce the optimal output level Q** at the lowest possible average cost level C’, and it can set price at P**. Profits at this priceoutput combination are shown by the area P**A’B’C’. Thus the monopolist is able to adjust to the prevailing market situation by reducing its plant size. Cost Price and Output Determination by a Monopoly

219

FIGURE 10-4 Plant Size Adjustment to Avoid Losses $/Q

per unit is reduced at output Q** (compared to output Q*), and the reduced output level can be sold at the higher price P**. Thus as the market for this product declines, the consumers must pay more per unit if the monopolist is to continue to supply the product. Notice that this long run price adjustment is in the opposite direction of the short run price adjustment in a declining market. In Fig. 10-2 we saw that in the short run, the monopolist had to reduce price in order to minimize losses in a declining market.‘ In Fig. 10-4 we see that, given time for long run plant size adjustment, the firm can raise price in conjunction with that plant size reduction, in order to restore profitability once more.

IV. ECONOMIC EFFECTS OF MONOPOLY We can find the impact of monopoly upon the price and output level by comparing what would happen if a particular market is on the one hand, monopolized, and on the other hand, purely competitive. Thus we can use pure competition as the standard by which to compare the effects of a single seller compared with many sellers. For a proper comparison we must have ceteris paribus. Thus not only should the two situations have the same market demand situation, but also the cost conditions should be identical. This necessitates the comparison of a multiplant monopolist (one owner of many plants) with many firms in pure ‘One can contrive a situation where the monopolist would increase price in a declining market in the short run, The demand curve, while shifting to the left, must become steeper, such that its inter-

cept on the vertical axis is above that of the initial demand curve. As long as the demand curve shifting to the left has a lower intercept, however, the profit-maximizing (or loss-minimizing) monopolist reduces prices in a declining market in the short run, ceteris paribus.

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THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

competition. We can thus isolate the effects of a single seller, without confusing the issue with the possible economies of plant size a monopolist might be able to derive. We investigate that possibility later. Impact on Prices and Output Levels

In Fig. 10-5 we show the long run equilibrium positions for both the purely competitive and monopolized version of the same industry. Notice that in the pure competition case (part A), the representative firm and all other firms are producing at the optimal rate of output in the optimal-size plant. Thus their perunit costs are minimized, and price has been driven down to this level by the

entry of profit-seeking firms. The final result is that all firms are earning only normal profits. FIGURE 10-5

The Effects of Barriers to Entry (Monopoly) on Prices and Output, Compared with Pure Competition

A. Pure Competition $/0

The Market/Industry

$/q

One Representative Firm

S$=ZMC

MC

LAC

d,mr

git

B. Monopoly $/Q

uM

i The Market/Firm

$/q

-_

One Representative Plant p

eR

MR

=ZMC

g/t

Price and Output Determination by a Monopoly

221

In part B of Fig. 10-5 we show the same market demand curve D, but this time show the market marginal revenue curve MR, since these are the demand and marginal revenue curves facing the monopolist who can directly change market price. The ¥ MC curve is the horizontal sum of the MC curves in all the plants operated by the monopolist.‘ A representative plant is shown on the righthand side of part B. Note that this plant has the same cost structure as the representative firm in the purely competitive case. In the long run, the monopolist, protected by barriers to entry, builds many plants, each at the optimal size, and produces the same amount in each plant. The {MC curve shows the firm’s marginal cost as each output level is produced in equal shares by all the plants shown on the right-hand side. The monopolist chooses price and output so that its marginal revenue equals its marginal cost. Therefore it sets price at P; and total output level at Q). At output level Q;, {MC has risen to the level shown as M, and in each plant MC will have risen to the level M at output level q,. Supposing there are 100 plants, then total output Q; = 100q;. The monopolist makes sure that all plants produce the same output level q,. If one produces more and another less—the total must equal Q,—the firm’s marginal cost would exceed marginal revenue, since marginal costs for the additional units in the plant producing more than q, are higher than the marginal cost had they been produced in the plant producing less than q, units. Thus in each representative plant the monopolist produces q; units at an average cost shown as C dollars per unit. Price per unit is P,, so the profit from each plant is equal to the area P,ABC. Total profits to the monopolist is the sum of this profit in all of its plants.

NOTE:

So, what are the price and output effects of monopoly? Price is higher at P, compared with Po, and total industry output is lower at Q, compared with Q,. (Price Py and output Q, are reproduced on the monopoly graph for comparison purposes.) This higher price and lower output allow the monopolist to earn pure profits compared with the normal profits in pure competition. Notice that these price and output effects of monopoly are traceable to the existence of the barriers to entry, which allow the monopoly to remain a monopoly. If entry were possible, the price would fall and output would increase in the ensuing competition, even if only a second firm entered the market.® ‘The horizontal summation of MC curves to obtain the 2 MC curve is explained in the preceding chapter in the context of pure competition. In that case the firm’s MC curve is in fact its supply curve, and the 2 MC curve is in fact the industry supply curve. In the monopoly case neither curve is the firm’s supply curve, since the monopolist equates MC with MR, which is different from price. Our purpose here is simply to find a curve (the 2 MC curve) that shows the minimum incremental cost of producing each output unit, given the availability of two or more plants. $The small triangle EFG shown in part B of Fig. 10-5, often referred to as the welfare loss triangle, is due to monopolization of an industry, as compared with the pure competition reference point. See A. Harberger, ‘‘Monopoly and Resource Allocation,” American Economic Review, May 1954, pp. 77-87, and H. Leibenstein, ‘‘Allocative Efficiency vs. X-Efficiency,’’ American Economic Review,

June 1966, pp. 392-412. Both are reprinted in E. Mansfield, ed., Microeconomics: Selected Readings, 3rd ed. (New York: Norton, 1979). See also, A. Bergson, “On Monopoly Welfare Losses,” American Economic Review, Dec. 1973.

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THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

‘ impact on Costs of Production

You may have noticed in Fig. 10—5 that the monopolist chooses not to produce at the lowest point on the SAC curve in long run equilibrium. In order to maximize profits, the monopolist produces to the left of the minimum point on the SAC curve.” Compared to the purely competitive firm, therefore, the multiplant monopolist incurs higher per-unit costs. This is a fairly restrictive comparison, however, since it depends upon the monopolist having exactly the same cost structure (in total) as the many small firms of pure competition. Economies of Multiplant Operation. Recall from Chap. 6 that we might expect a multiplant firm to benefit from certain economies of multiplant operation. For example, rather than having separate overhead structures in its many plants, the firm might be able to centralize some functions and save money by doing so. Only one set of president and vice-presidents is required and, although they are probably better paid than their counterparts in a small firm, they do not earn as much as the sum of the salaries of the many separate counterparts in aggregate. A second economy of multiplant operation concerns computerization. The firm is likely to save in aggregate by using one or several large computers for accounting, payroll, inventory control, and other systems compared with separate computers, small or underutilized, in each of its many plants. Finally, the large multiplant firm is expected to obtain pecuniary economies through bulk purchasing of raw materials and other supplies, since it may have substantial bargaining power not available to the separate small firms of pure competition. Thus we expect the multiplant monopolist to have a lower cost structure in each plant, compared with each of the purely competitive firms. This would cause the monopolist’s price to be lower than shown (P,) in Fig. 10—5. It is even possible that the economies of multiplant operation could be large enough to bring the monopolist’s profit-maximizing price down close to or below the purely competitive level.

Threshold Levels for the Incorporation of High Technology. In the considerations above we still have the monopolist as a multiplant firm. It is possible that the monopolist could achieve even greater cost savings by amalgamating its plants into one or a few much larger plants. It would do this if there was a size threshold below which it would not be feasible to use certain technology. For example, acompletely automated assembly line would not be economically feasible for a small automobile firm producing only several thousand vehicles annually. Suppose it becomes feasible when annual output exceeds 500,000 vehicles. In a market size of, let us say, one million vehicles per annum, many firms equally sharing this market would prevent any one firm from obtaining 7If the reader is really sharp, he or she should be wondering why the monopolist would build the optimal plant size at all, since the SAC curve shown in part B of Fig. 10-5 is not tangent to the LAC curve at the output level q;. You are correct if you discerned that the situation depicted is not a long run equilibrium for the monopolist. If the LAC correctly depicts the short run plant sizes available, the monopolist should build a series of slightly smaller plants, so that SAC = LAC (tangent) at the equilibrium output level for each plant. This, in turn, would shift the SYMC to the left, raising the monopoly price and reducing the monopoly supply still further. Price and Output Determination by a Monopoly

223

these economies. Similarly, a monopolist operating many plants would not obtain these economies until it scrapped its small plants and built one or more of the “super plants’’.® To the extent that there exists such an output threshold which a monopolist could attain, but to which separate competitors could not, the monopolist’s costs would therefore be even lower than the pure competitor's.

X-inefficiency and Managerial Slack. Now let us consider a force that operates to keep costs down. It is present in pure competition but is absent in monopoly. The pure competitor must be economically efficiegt inorder to survive, ifit isn't, there is the pressure of potential entrants willing and able to force it into bankruptcy. Thus the pure competitor continually updates its plant and equipment to incorporate the latest, most cost saving technology. It ensures that the day-today operation of the plant is conducted as efficiently as possible. The monopolist, on the other hand, is under no such pressure to remain at the frontiers of

technology, nor to hunt out every little inefficiency in production, such as material waste and employee loafing. It is true that the monopolist wishes to maximize profits and that reducing costs increases profits, but in the real world the monopolist may be satisfied with attaining some target profit and not consider it worth the effort (nonmonetary costs) to press for absolute efficiency in production. This tolerated inefficiency in production is called X-inefficiency, and its tolerance is known as managerial slack. The degree of X-inefficiency and managerial slack are likely to increase when business is booming and to decline when profits fall below management’s aspirations. In summary then, the monopolist is likely to be able to produce at a cost equal to or lower than a purely competitive industry due to the probable availability of economies of plant and firm size, but the lack of the threat of entry may allow the monopolist to tolerate a significant amount of X-inefficiency in production. It is unlikely that the monopolist’s costs could be low enough to have its profit-maximizing price as low as the purely competitive price. This depends on the magnitudes of the cost savings discussed above, as well as on the price elasticity of market demand. The more elastic market demand at any given price level, the smaller the profit-maximizing margin of price over average costs. Research and Development

We noted in the preceding chapter that firms operating in markets of pure competition are expected to experience a minimal incentive to engage in research and development (R and D) expenditures, since any discoveries would be imitated very quickly by competing firms. (In the simplistic model of pure competition, patents are ruled out by the assumption that all producers and consumers *The long run average cost curve in such a situation is saucer-shaped until it reaches the output threshold, where a different technology suddenly becomes feasible. At this point, it begins to rise more slowly and then falls again until the economies of size of the different technology become diseconomies. Thus the LAC curve is W-shaped instead of U-shaped. °H. Leibenstein, ‘“‘Allocative Efficiency vs. X-Efficiency,” American Economic Review, June 1966, pp. 392-412, and O.E. Williamson, ‘‘Managerial Discretion and Business Behavior,” American Economic Review, December 1963, pp. 1032-57.

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THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

have full information.) This would mean that, although a single firm might incur all the R and D expenses, it would expect to receive only a small share of the benefits of any advances it discovers. In many cases, that small share of expected benefits might not be large enough to induce the firm to undertake the costs in the first place. A monopoly, on the other hand, has to share the benefits with no one, except, of course, the tax collector. We say that the monopolist is completely able to internalize the benefits of its discoveries, whereas the pure competitor is able to internalize only a share of the increased profits, thereby creating external benefits for the other firms. Thus a monopolist would be expected to spend money on R and D whenever it expects total benefits of the R and D program to exceed expenditures, whereas the purely competitive firm would not proceed until it expected its share of benefits to exceed the R and D expenditures. For any given R and D program, it is clear that the monopolist might be prepared to undertake the expenditures, whereas an individual pure competitor might not. 1° Not only would the monopolist be more likely to want to undertake R and D expenditures, but it would also be more likely to afford these expenditures. The monopolist is likely to earn pure profits in the long run, unless the market is declining or costs are rising. Out of these pure profits, the monopolist can afford to gamble on R and D expenditures, whereas the pure competitor, forced by the entry of new firms to earn only normal profits in the long run, does not have the luxury of these excess profits in the long run. In the short run, of course, firms in

both market types might earn pure profits. Although short-lived in pure competition, these profits would be able to finance some R and D expenditures if the firm so desired.1! Thus we see that the economic effects of monopoly are something of a mixed blessing: Prices may be higher and output lower, but costs of production may be lower and research and development efforts should be greater. The general consensus is that the welfare losses associated with the first two effects outweigh the possible gains associated with the latter two effects. We thus have strong anti-monopolization provisions in the antitrust legislation.’ The middle ground is government regulation of monopoly prices (and hence outputs), which we examine in the next section.

V. TOPICS INMONOPOLY In this section we consider several variants of the basic monopoly model. In each case this involves changing one or more of the underlying structural or behavioral assumptions. We begin with the regulation of monopolies by governments, 10Fxternal benefits and costs are discussed in greater detail in Chap. 20. 11[n both the monopoly and pure competition cases, the firm may, of course, borrow to finance R and D expenditures. However, since these loans must be repaid out of future excess revenues, the firm will not borrow unless it expects to earn such excess revenues, or pure profits, as a result of the R and D efforts. 12F. M. Scherer, Industrial Market Structure and Economic Performance, (Chicago: Rand McNally and Co., 1970), chaps. 18, 20. Price and Output Determination by a Monopoly

225

for the purpose of influencing their price and output levels. We then examine

price discrimination, a situation in which a monopolist discriminates between

and among individual and groups of buyers, by charging different prices to different buyers. In Chap. 14, in the context of factor markets, we consider monopsony, the market situation in which there is a single buyer with many sellers on the supply side. Also in Chap. 14, we examine bilateral monopoly, so called because there is both a single buyer and a single seller; and thus there is monopoly power on both sides of the market. ~

\

Regulation of Monopoly Price and Output

In some cases of monopoly, the appropriate government body may feel it necessary and justifiable to regulate the price and output levels of that monopoly. Telephone and electricity prices, for example, are typically regulated, in that the government might initially establish a maximum price that the monopolist may charge, or require the monopolist to apply to the government for permission to increase price in subsequent years. Governments are motivated to regulate mo-

nopoly prices when they feel that the product or service is important to society’s welfare and that the monopolist is either pricing too high or restricting output too much in relation to society’s needs and the monopolist’s profitability. Clearly the government cannot fix the price below the monopolist’s costs, since the monopolist would cease production in the long run and society would be worse off than before. The government must fix the price at a level that ensures sufficient profit to induce the firm to stay in business and to continue R and D programs for product and production process improvements. In Fig. 10-6 we depict a particular monopoly situation, in which a single firm faces market demand curve D. Without constraints imposed upon its price and output decision, the profit-maximizing firm selects price P,, and output per period Q,, where MC = MR and profits—shown as the rectangle P,,ABC—are maximized. Suppose now that the government feels that this price is too high or the output is too low, in view of society’s needs and the level of profit being enjoyed by the monopolist. As a result of this, suppose that the government sets a price, P,, which is the maximum that the monopolist can charge. The monopolist must now decide what price and output level to set in order to maximize profits given the constraint imposed upon its maximum price.

NOTE:

Since the government has outlawed prices above price P,, the section of the demand curve above pointA’ is no longer applicable. The firm cannot set prices above P,, upon pain of prosecution and doubtless quite substantial penalties. At price P, the firm can sell its output up to the level shown as Q,, which is the maximum the market will take at that price. To sell more units of output, beyond (Q,, the firm must lower its price progressively below price P,.. Thus the demand curve now envisioned by the monopolist is the kinked line joining the points P,A'D'. The horizontal section P,.A’ is similar to the demand curve for the pure competitor: The firm can sell as much as it wishes at this externally imposed market price, limited only, in the case of the monopolist, by the market’s ability

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THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

FIGURE 10-6 Government Regulation of Monopoly Price and Output $/Q

to absorb the output at this price. The negatively sloping sectionA'D is the remainder of the market demand curve that is not outlawed. Thus the monopolist must choose between price P, or any lower price, in order to maximize profits, given the limit set on price. Profit maximization requires that MR = MC. With the setting of a maximum permissible price, the demand curve faced by the firm has been modified and, consequently, the corresponding marginal revenue curve is now different. For output units up to Q,, marginal revenue is equal to price, just as in pure competition, because each extra unit is sold at the same price level P,. For output units higher than Q,, we revert to the market demand curve and consider the sectionA 'D. The marginal revenues associated with sales at these prices below P,.are shown by that section of the market marginal revenue curve labeled EMR. Thus the firm’s marginal revenue curve is shown by the line P,A’ (coincident with the first section of its demand curve) for output levels up toQ,, and by EMR for output levels beyond Q,. Notice that marginal cost (MC) lies below marginal revenue(P,A’) up to output Q,, and it lies above marginal revenue (EMR) beyond output Q,. Thus MR = MC at output Q,, where both curves pass through point A’ in Fig. 10-6. It is therefore profit maximizing for the monopolist to produce Q,.units at price P,. Profits at this price-output combination are equal to the area P,A'B'C’ and are smaller than the profit (P,,ABC), that would be earned if the maximum price P, had not been forced upon the monopolist. The results that are of major importance for social welfare are, first, that price to consumers is lower than the monopolist prefers and, second, that this lower price has induced the monopoly to supply more units of output to the market than it otherwise would. From the government’s and society’s point of view, priceP, is the optimal price level to set. To demonstrate this we refer to Fig. 10—7, which reproduces Price and Output Determination by a Monopoly

227

the cost and demand situation of Fig. 10-6, and shows prices both higher and lower than P,. If the maximum allowable price is P;, the firm’s demand curve is

P,A,D, and the associated marginal revenue curve is P;A,E iMR. Since marginal

cost (MC) passes through the discontinuous section AE, of marginal revenue, the monopolist would maximize profits by producing Q, units of output. Profits are maximized at output Q,, given the ceiling price of P;, since Q, is as close as the firm can come to equating MC with MR. For output units before Q:, MR > MC. Therefore these units should be produced, as each one contributes marginally to profits. For output units afterQ,, MR is less than MC, so these units should not be produced. Thus with the higher ceiling price P;, the profit-maximizing monopolist produces a smaller output Q;, as compared with output Q, when the ceiling price is P,. FIGURE 10-7 Suboptimal Regulated Price Levels $/Q

Now consider price P,. This maximum permissible price causes the firm’s envisioned demand curve to be P,A,.D, with the associated marginal revenue curve P,A,E,MR. Marginal costs intersect with this marginal revenue curve at point F on the horizontal sections of the demand and marginal revenue curves. It is, therefore, profit maximizing for the firm to produce only Q, units of output at price P,, where MC = MR. Notice that this results in excess demand: Market demand at price P, is Q; units, which is directly below pointA, on the demand curve. This exceeds the quantity supplied by the monopolist—Q,. Thus, although price is lower than P,, quantity supplied is less than Q,, and some buyers will be unable to buy the product even though willing to pay the market price.

This may have such undesirable consequences as bribes and other favors to the monopolist by individual buyers wanting to ensure their supply. It could also result in the possible development of a “‘black market”, in which items in short supply are sold covertly at prices above the regulated maximum price. This 228

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

would cause the actual price paid by final consumers to move toward the price at which supply equals demand (above price P,). Thus the price P,, where the firm’s marginal cost curve intersects the market demand curve, is generally considered to be the optimal regulated price. Price is as low as it can be set without causing an excess demand situation and the subsequent undesirable economic and social effects. Quantity supplied (Q,) is as large as the firm would ever want to produce, regardless of the maximum price level set, since Q, is determined by the intersection of the demand curve and the firm’s marginal cost curve. The principle of setting price where marginal cost crosses the demand curve is known as marginal cost pricing. It is frequently used as a basis for price setting in monopoly markets regulated by government authorities.13 Price Discrimination

DEFINITION: Price discrimination is the practice of charging different prices to different buyers or groups of buyers for essentially the same product, where these price differences do not simply reflect the cost differences associated with serving different buyers or markets. The monopolist may find it both possible and more profitable to discriminate among buyers on some basis, charging a higher price to some buyers and a lower price to others, rather than setting the same price for all buyers. NOTE:

Three major conditions must exist before it is possible and profitable to practice price discrimination. First, the buyers or groups of buyers (markets) must be separable. That is, it must be possible to identify and keep separate the two or more buyers or markets, in order to prevent arbitrage selling from the lowerprice to the higher-price buyer or market. Second, the two or more buyers (or markets) must exhibit differing price elasticities of demand at any particular price level, in order to make price discrimination profitable, as we shall see below. Third, the markets must be characterized by a lack of price competition from rival firms, in order to prevent price levels being eroded from the profitmaximizing levels in each market. Clearly, price discrimination is most likely to work well in a monopoly situation, where there are no rivals to worry about, but

it is also feasible in oligopoly markets, where the firms coordinate their pricing strategies in one way or another.!4

On what basis does the monopolist discriminate? Happily it is not on the basis of skin color, language, culture, social class, sex, or age; it is rather on the basis of utility, ability to pay, and separation in space and time. Price discrimi13Marginal cost pricing as a regulatory policy should extend into the long run situation, since the firm can change its size of plant. The new rule would be: Set price equal to long run marginal costs (LMC). Marginal cost pricing runs into problems when plant size economies are so large or markets so small that the monopolist must operate on a negatively sloping section of the LAC curve. In this case, LMC

lies below LAC, and the firm cannot make a normal profit if P = LMC. See Scherer,

Industrial Market Structure and Economic Performance, chap. 22. 14We refer to the operation of a cartel, various forms of price leadership, or even conscious parallelism, all of which are discussed in Chaps. 12 and 13. Price and Output Determination by a Monopoly

229

nation, accordingly, has been categorized into three distinct types—first-, second-, and third-degree. First degree price discrimination involves First-degree Price Discrimination. forcing each buyer to pay the maximum he or she is willing and able to pay. In situations where there is no price discrimination, all buyers except the last one pay less than they would have been willing to pay, since there is only one price at which the product is offered, and the last buyer is the one who is only just willing to pay the price asked. All other buyerg—those higher on the demand curve—would have been willing to pay more, but they were not required to.1® EXAMPLE:

Suppose we have three people who have survived a plane crash. Crawling through the Mojave desert almost dead from thirst, they arrive at a lemonade stand operated by the son of a prospector. Now this enterprising son of a prospector (S.O.P., for short) realizes that the need of these survivors for his lemonade is very great. He refuses to sell until he is sure each potential buyer is paying the absolute maximum he is willing and able to. Survivor A has, let us suppose, $25 in his pockets and, seeing no alternative but death, he hands it all over for a single glass of lemonade. Survivor B has $18 and similarly parts with this sum as the price of continued survival, rather than go without and almost certainly die. Survivor C, a student, has only $0.25 and, after making absolutely sure that Survivor C is neither willing nor able to pay more, the S.O.P. sells the third glass for $0.25. Thus the buyers are each forced to pay the maximum amount they are willing and able to pay, and the S.O.P. makes more profit this way than by setting a common price, say $0.50 for all buyers. Another means of accomplishing first-degree price discrimination in practice is the ‘‘Dutch auction,” in which the price starts at a very high level and the auctioneer calls out slowly reducing price levels. The first person to accept the called price gets the product. Thus this person pays the maximum he or she is willing to pay, since he or she did not know what the second most eager buyer would have paid. Therefore he or she had to bid as soon as the price fell to the maximum level he or she was willing to pay. In the more conventional auction where price is bid upward, the successful bidder pays only slightly more than the second most eager buyer is willing to pay, rather than the maximum he or she is willing to pay. Auctions of both types require unique products, such as famous paintings or thoroughbred yearlings, for which only one person (or consortium) can be the lucky buyer. In the Dutch auction each buyer must be ready to say yes at the maximum price he or she is willing and able to pay, rather than take the chance of losing the product to the next most willing buyer. In a more general case, suppose the market demand for a particular product is as shown by D,MR in Fig. 10-8. If it is possible to sell to each buyer separately *SConsumer surplus is the name given to the amount of money the consumer would have been willing to pay over and above the price actually paid. In regular markets all buyers except the last one receive some amount of consumer surplus. With first-degree price discrimination, all consumer surplus is expropriated by the seller from every buyer, and it is added to the producer’s surplus, which is profit. For more on consumer surplus, see R. A. Bilas, Microeconomic Theory, 2nd ed. (New York: McGraw-Hill Book Company, 1971), pp. 97-107.

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and independently of other buyers, making each buyer believe he or she must take it or leave it at the maximum price he or she is willing and able to pay, the marginal revenue curve is then coextensive with the demand curve, since each incremental sale takes place separately and does not affect the prices received for other sales. In a normal market, to sell an extra unit requires a lower price that must be offered to all buyers. In the normal case, marginal revenue—the change in total revenue—is thus equal to the price of the incremental unit minus the reduction in price to all of the buyers who would have paid the slightly higher price. In the first-degree price discrimination case, where sales to individual buyers take place separately and independently of each other, the change in total revenue is simply equal to the price of the last unit sold. FIGURE 10-8 First-degree Price Discrimination

EXAMPLE:

Imagine several hundred people who wish to buy a block of land in a new urban development. Some blocks suit some potential buyers more than others, because they are closer to their place of work, for example. Now suppose the developer ranks all the potential purchasers in order of the amount they are willing to pay and allows the buyers to select their land in that order. In the market depicted in Fig. 10-8, the first buyer is willing to pay Po. The second buyer is willing to pay slightly less than Po, and so on until the last buyer pays P,. The monopolist is then unwilling to offer any more blocks for sale, since the marginal cost would exceed marginal revenues on all units sold after that shown asQ.

At output (sales) level Q, the monopolist’s average costs are shown at point B. Thus the monopolist makes total profits, shown by the shaded area P,ABC, by practicing first-degree price discrimination. Notice that these profits are substantially greater than the monopolist would have earned if it had charged the Price and Output Determination by a Monopoly

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same price to all buyers. To see this, imagine the intersection of the regular marginal revenue curve (same intercept, twice the slope as the demand curve) with the MC curve, and the subsequent price, output, and average cost levels. Discrimination may also be practiced Second-degree Price Discrimination. among groups of buyers on a time or urgency basis. Those most eager to purchase the product are willing to pay a higher price than those prepared to wait a little longer, and so on. N \ EXAMPLE:

‘The early sale of ball point pens, is an amazing example of this. The pens reportedly sold for around $30 each, because of their novelty and utility value. Later, as technology advanced, costs fell, and as the market became progressively more saturated, the price fell to the level we know today. Products that have undergone a similar reduction in price in more recent years are electronic calculators and digital wristwatches. One further example is the pricing of tickets for new movie releases. First runs in city theaters are priced substantially above second runs in suburban theaters, and so on down the line until finally the movie appears on television for virtually no charge at all. As the preceding examples suggest, second-degree price discrimination works best with new products, which have novelty value and for which there are no immediate competitors. In marketing jargon, it is called price skimming, since it is somewhat analogous to skimming the cream from the top of the milk (which those raised on homogenized milk will not remember). As time passes, the new product becomes less of a novelty, the firm gains experience in the production of the product, and it benefits from improvements in the technology of producing the product. The impact of these changes is to shift the cost structure downward’ and the demand curve to the left.17 In Fig. 10-9 we show a situation in which it is profit maximizing to reduce price over time. At first, in period t, the demand and cost situations are shown as D,, MR,, and MC,. (To simplify the figure, the average cost curve is not shown.) The profit-maximizing price is P, with output Q;, when MR, = MC,. Suppose that later, in the period t + 1, demand declines to that shown as D; + ;, and the cost structure declines, so that marginal costs are represented by MC, , ;. The profit-maximizing price and output levels are now P; , , and Q; + 4. At this output level, the new marginal cost and marginal revenue curves intersect. Thus the firm has maximized profits in each period by charging a higher price in the first period and a lower price in the subsequent period, rather than setting a single price for the two periods. ’6The reduction of average cost per unit for any given output level as time passes is related to a phenomenon known as the learning curve. As workers gain more experience with their tools and machines, and as shortcuts and improvements are discovered in the production process, costs per

unit decline. In effect, labor and management productivity increases as they learn more about the production process. ‘In the marketing discipline the product life cycle hypothesis is cited to explain the decline of demand for a product after it passes through successive stages of introduction, growth, and maturity. See P. Kotler, Principles of Marketing, (Englewood Cliffs, N.J.: Prentice-Hall, Inc. 1980) pp. 331, 347-55.

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THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

FIGURE 10-9 Second-degree Price Discrimination

$/Q

Third-degree Price Discrimination. In some cases a firm can charge different prices in two or more different markets over the same period of time. EXAMPLE:

Examples of this practice are telephone and electricity price differentials between households and business establishments, and a firm that charges a higher price for a particular product in a downtown store than in a suburban store. Telephone companies also practice third-degree price discrimination by separating their markets on the basis of the time of day and the day of the week. Long distance telephone calls during business hours cost more than during early evening hours. The cost is further reduced for calls late at night or on weekends. Business establishments are willing and able to pay the higher prices during the day, since business must be conducted when other businesses are also operating. If the prices were the same 24 hours a day, home users would write letters instead, in many cases. Recognizing the more elastic nature of home demand, the telephone company offers cheaper calls at less convenient hours, in order to increase the use of long distance telephone calls in two ways: First, it attracts buyers who would not otherwise purchase the service and second, it shifts some of the demand into the offpeak hours, which saves the company building a larger plant just to handle peak traffic. To practice third-degree price discrimination, the firm must decide what its total output should be, how it should distribute this output between or among the separate markets, and what price it should set in each market, such that profits are maximized. The profit-maximizing rule remains the same: Produce until MC = MR. But with two or more markets, there are two or more MR curves. To solve this problem, the firm should distribute each successive output unit to

the market in which that unit contributes most to total revenues—that is, has the highest marginal revenue—and continue up to the point where the marginal revenue derived from the sale of the last unit is just equal to the marginal cost of Price and Output Determination by a Monopoly

233

producing that last unit. Thus the firm continues to produce until its marginal costs have risen to the same level to which its marginal revenues (in each market) have fallen. To find this level, we need to construct a combined marginal revenue curve for all the firm’s markets.

In Fig. 10-10 are shown two market situations—A and B. Market A has the more inelastic demand situation, perhaps due to fewer competitors, higher incomes of the buyers, or simply different taste patterns of the buyers. In which market should the firm sell its very first output unit? It would certainly sell this unit in market A, at a price near Po, since the marginal revenue of the first unit is higher there than in market B. As the firm lowers its price to sell additional units, these units too will be best sold in market A, until the price P, is reached. At this point, the first buyer in market B is willing to pay P2, which offers the same level of marginal revenue as price P, in market A, and the firm should now allocate output units back and forth between markets A and B, taking care to allocate each additional unit to the market in which it derives the higher marginal revenue. The curve {MR in the figure under the heading Firm indicates the combined marginal revenue to the firm, when it is free to allocate each successive unit to the market in which marginal revenue is highest. It is found by the horizontal summation of the marginal revenue curves in markets A and B. Clearly it must begin at price level P, and kink at price level P., since below this level it is the horizontal sum of both MR curves, rather than just the one. For example, at level M, the >MR curve represents the horizontal sum of sales Q, in market A

and Q,; in market B. In Fig. 10-11 we superimpose the firm’s short run cost curves upon the MR curve. The output level that maximizes the firm’s profits is shown as SQ,

where its marginal costs rise to equal its declining marginal revenues. The interFIGURE 10-10 Construction of the Marginal Revenue Curve for Third-degree Price Discrimination

Market A

234

Market B

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

section of the MC and =MR curves defines the level at which marginal revenues in each market should be equated to the firm’s marginal costs. Extending a line at this level across to the graphs for markets A and B, we see that the firm should allocate Q, units to market A, and Q, units to market B, since marginal revenues in each of these markets at these output levéls have fallen to the level to which the firm’s marginal costs have risen. We have therefore found both the profit-maximizing total output level and the profit-maximizing allocation of this output between the two markets. Now, what price should be set in each market? Referring to the demand curve for each market, we conclude that to sell Q, in market A and Q, in market B, quantity Q, should be priced at price P, and quantity Q, should be sold at price Py. Note that

the more inelastic market is charged the higher price. The firm’s total profits may be calculated as the sum of the price-cost margin times the quantity sold in each market. That is, profits in market A are represented by the shaded area P,C x 0Q,, and profits in market B by the shaded areaP;C X 0Qs. FIGURE 10-11 Third-degree Price Discrimination

Market A

$/O

Qn

$/O

Market B

Og

= Oat Og ZO

The output level =Q and the allocation of this output between the markets as shown, is profit maximizing for the firm, because if another unit is produced, its marginal cost would exceed the marginal revenue in either market. Alternatively, if the last unit is taken from either market and sold in the other, its marginal revenue is then less than its marginal cost. Thus any different output level or allocation of output between the markets causes the firm’s total profits to be reduced. In summary, price discrimination involves charging different prices to different buyers or groups of buyers when their demand situations differ. If markets or individual buyers can be identified and kept separate, the monopolist can increase its profits by setting different prices for each one. Price and Output Determination by a Monopoly

235

VI. SUMMARY In this chapter we examined the price and output decision of a monopolist—a firm that is the only supplier to a particular market. Monopolies exist and persist due to barriers to the entry of new firms. These barriers may be natural, in that the market is not large enough to support more than one firm, or artificial, imposed by governments or by the monopolist itself. Governments give a mandate for monopoly to some firms, such as the post office, the liquor commission, and the armed forces, for reasons of social or economic benefit and national security.

The monopolist itself may erect the barrier to entry by gaining control of all viable sources of a necessary raw material, a patented technique, or the best location for production and marketing of its product. In the short run, the monopolist selects the profit-maximizing price and output levels by equating marginal costs and marginal revenues. Monopolists may make losses in the short run if market demand has decreased or if their costs have increased substantially. In the long run, the monopolist adjusts its size of plant to allow the greatest possible profits, by equating its long run marginal costs with its marginal revenues, and building the plant size associated with this equality. The economic effects of monopoly are that price is higher and output lower, as compared with the same market under pure competition. The monopolist may be able to produce at a lower per-unit cost level, however, due to economies of plant size, and pecuniary economies of firm size. Offsetting this is the lack of pressure on the monopolist to remain efficient in production, due to the absence of the entry of new firms. The monopolist is motivated to conduct research and development programs, since the entire benefits can be internalized. It is able to conduct these programs, since it can earn pure profits in the long run in most cases. The general consensus is that the net effects of monopoly on economic and social welfare are adverse; hence we see antimonopoly provisions in the antitrust legislation and government regulation of many monopolies. If the government sets a maximum price (below the profit-maximizing price) that the monopoly may charge, the monopolist is induced to expand output for the benefit of consumers and society. Price discrimination may be practiced by a monopoly if it can identify and separate individuals or segments in its overall market having differing demand elasticities. First-degree price discrimination involves separating every buyer and making each one pay the absolute maximum he or she is willing to pay. Second-degree price discrimination involves separating the market on the basis of time. The most eager purchasers are charged a higher price. The price is then reduced in subsequent periods, in order to make sales to those willing to wait for a lower price. Third-degree price discrimination is the process of charging different prices in different markets that are separated in space, time, or by type of consumer. In all cases, price discrimination allows the firm to increase its profits over what it could make with a single price for the whole market.

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DISCUSSION 1.

QUESTIONS

Monopolies persist for three main reasons. Name these reasons and explain

why they either induce or preserve monopolization of the market. If a firm is amonopolly, is its cross elasticity with every other product either zero or negative? Does this imply that there cannot be a firm on the other side of the country producing the same product? Explain. We assume that the monopolist wishes to maximize short run profits. Is there any reason why the monopolist would not wish to pursue this objective function? The monopoly model proceeded on the basis of the assumption of a cubic production function, that is, U-shaped MC and AC curves. With the aid of graphs, show the short run price and output equilibrium situation if (a) MC is constant throughout, and (b) if MC declines all the way to the full capacity output level. Does the model still work? That is, does it still produce a prediction of the profit-maximizing price and output levels? In the long run, the monopolist can change its size of plant to obtain the optimum optimorum short run price and output level. Using graphs, show a firm that is initially in the long run equilibrium situation and its subsequent adjustment to an increase in demand for the product.

Explain why you would expect a monopoly firm to set a higher price and supply a lower quantity, compared with an industry of purely competitive firms, ceteris paribus. What factors may operate to allow a monopolist to reduce its production costs down to a level below that which is possible in a purely competitive industry? Explain the terms X-inefficiency and managerial slack in terms of the impact of these phenomena on the monopolist’s cost curves.

Why is the regulation of a monopolist’s price in the best interest of consumers? What is the best price for the regulator to set? Explain. 10.

Price discrimination requires three basic conditions before it can work. What are they? Explain why each is necessary for successful price discrimination in the third-degree case. What would be the result if each one was absent, given the other two?

SUGGESTED

REFERENCES

‘Monopoly and Resource Allocation,” American Economic Review, HARBERGER, A.C., May 1954, pp. 77-87.

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Hicks, J., ‘Annual Survey of Economic Theory: The Theory of Monopoly,” Econometrica, 1935. Reprinted in E. Mansfield, ed., Microeconomics—Selected Readings (3rd ed.). New York: W. W. Norton & Co., Inc., 1979.

HIRSHLEIFER, J., Price Theory and Applications (2nd ed.), chap. 11. Englewood Cliffs, N.J.: Prentice-Hall, 1980.

KAMERSCHEN, D.R.,

‘An Estimation of the Welfare Losses from Monopoly in the Amer-

ican Economy,” Western Economic Journal, Summer 1966, pp. 221-37.

KOUTSOYIANNIS, A.,

Modern Microeconomics (2nd ed.), chaps. 6, 7. London: Macmil-

lan, 1979.

NS

LEIBENSTEIN, H., ‘‘Allocative Efficiency vs. X-Efficiency,’’ June 1966, pp. 329-415.

American Economic Review,

SCHERER, F.M., Industrial Market Structure and Economic Performance, chaps. 8, 10, 18, 20. Chicago: Rand McNally, 1970.

STIGLER, G.J.,

‘“‘The Theory of Economic Regulation,” Bell Journal of Economics and

Management Science, Spring 1971, pp. 3-21.

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oe pe Ne q

Yd

and Output Determination in Monopolistic Competition

1. INTRODUCTION DEFINITION: Monopolistic competition is characterized by many firms selling a slightly differentiated product in the same marketplace. It is different from pure competition in only one respect: The products of the competing sellers are differentiated rather than homogeneous. Recall that product differentiation can arise from perceived differences in products themselves or in differences in the various attributes surrounding products, such as a more convenient store location, better customer service and comfort, and better warranties and repair service.

EXAMPLE:

Monopolistic competition might be exhibited by several dozen food stores in a particular area, each selling the same products but each having slight differences in the total package of attributes offered to the consumer. Some have more convenient locations, some have easy parking, some also carry magazines and other merchandise, some are self-service, others provide service of varying speed and courtesy, and so forth. Similarly, monopolistic competition is formed by the people selling handcrafted shell necklaces in a Fijian market. Each necklace is different, reflecting the variety of shells available, the creative aspirations 1The monopolistic competition model of firm behavior that we discuss here originated with Edward Chamberlin, Theory of Monopolistic Competition (Cambridge, Mass.: Harvard University Press, 1933). Joan Robinson in the same year independently arrived at the same conclusions in The Economics of Imperfect Competition (London: Macmillan, 1933).

239

of the craftsperson, and perhaps a random variable. All other attributes are the same: In the crowded market no one location is superior to another, all the vendors are friendly and courteous, and the thought of warranty and repair service never occurs to you.

In such market situations, the firm must choose price knowing that the consumer has many close substitutes to choose from. If the price is too high, in view of the consumer’s perception of the value of the differentiating features of the firm’s product, the consumer will purchase a competing firm’s product instead. Thus the monopolistic competitor must éxpect a relatively elastic demand response to changes in its price level. Yet at the same time, it expects to be able to change price without causing any other firm to retaliate and, consequently, without causing a change in the general price level in the market. This is because the firm is one of many firms, and it expects the impact of its actions to be spread imperceptibly over all the other firms, giving no one firm any sufficient reason to react to the initial firm’s price change. Monopolistic competition is so called because it has elements of both monopoly and pure competition. The firm has a significant amount of monopoly power by virtue of the differentiation of its product. It can change price up and down without experiencing the extreme response of pure competition. For price

increases it will suffer a loss of sales, but this loss is not total, as it would be for the pure competitor. Like a monopoly, the monopolistic competitor can adjust the price upward or downward to the level which maximizes its profits. But like the pure competitor, the monopolistic competitor has many rivals in the short run, compounded by the free entry of new firms in the long run. We shall see that the existence of many competitors and freedom of entry causes the monopolistic competitor, like the pure competitor, to tend toward only normal profits in the long run. The Seven Assumptions of the Monopolistic Competition Model The price and output decisions of a monopolistic competitor can be explained and predicted by a model comprised of seven assumptions as shown in Table 11-1.? TABLE 11-1 The Seven Assumptions of Monopolistic Competition i

STRUCTURAL ASSUMPTIONS BEHAVIORAL ASSUMPTIONS —_—

1. Number of sellers 2. Cost conditions 3. 4. 5: 6. 7.

Number of buyers Demand conditions Objective function Strategic variables Conjectural variation

Many Cubic production function with constant factor prices. Entry is unrestricted Many Products are slightly differentiated Short run profit maximization Price and output levels Zero, since there are many firms

2As in the earlier models, the cost conditions assumed are the more general case, which gives rise to U-shaped average variable and marginal cost curves. These are not a necessary feature of the model; the price and output determination problem can be solved under a variety of cost assumptions.

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THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

As noted earlier, only one of these assumptions is different from the assumptions of the purely competitive model: Products are differentiated rather than being homogeneous across firms. This difference has major implications for the pricing and output behavior of the firm, however, since it conveys a degree of monopoly power and allows the firm to adjust price and output to the profit-maximizing levels. Notice that since there are many sellers, the products are necessarily only slightly differentiated from each other. If there were only a few sellers, their products might be located at diverse points in a multidimensional attribute space, and hence these products could be substantially differentiated yet still competing, providing essentially the same service(s) to consumers. With many firms, however, the competing products are necessarily closer to each other in multidimensional attribute space. Hence they are only slightly differentiated. NOTE:

The requirement that monopolistic competition has many firms has led some researchers to infer that monopolistic competition is unlikely to exist in the real world. The reasoning is that rarely are markets large enough to support a large number of firms, each operating at or near the optimal-size (minimum average cost) plant. Not only must markets be large in relation to cost structures, but they must be sufficiently dense to support the competition of many firms in a relatively compact area. This is because seller location is a relevant attribute in the choice decision of most consumers: If all other attributes are more or less equal, the consumer prefers the closer or more conveniently located seller’s product. Thus where seller location is a relevant attribute of the product, all competing sellers must be located in a relatively compact area, in order for the consumer to consider their products only slightly differentiated. For there to be many competing sellers of a slightly differentiated product in a particular market, it is clear that this market must be relatively large and sufficiently dense. There are some markets, such as the Fijian market mentioned earlier, where such conditions do apply.

EXAMPLE:

There are, on the other hand, several industries with a large number of producers that are not characterized by monopolistic competition, since the markets for these industries are sparsely dispersed across the nation. There may be thousands of fast-food outlets in North America, but each one caters to a local market, seldom competing with more than half a dozen other sellers in that local market. Similarly, there are hundreds of gas stations in and around a large city, but each one is in competition with the three or four gas stations nearest to it, rather than with every other gas station in the entire city. One would not expect a consumer to drive across the city to buy a tankful of gas or across the country to buy a hamburger. Rather, the consumer considers the availability of competing products within a particular geographical market area. This spatial aspect of some industries means that, rather than being monopolistically competitive, their ' markets are characterized by intersecting oligopolies, with each firm competing

directly with only a few nearby rivals.

The monopolistic competition model only explains and predicts accuPrice and Output Determination in Monopolistic Competition

241

rately if its assumptions fit the actual market situation being examined. If monopolistically competitive markets are in fact not very common, then the model’s usefulness as an explanatory or predictive device is limited to these few situations. But for pedagogical purposes, the monopolistic competition model is very useful. It allows us to discern the impact of product differentiation upon an otherwise competitive market, and it introduces several concepts of fundamental importance for the study of oligopoly markets, which are much more prevalent in the real world. ‘ In the remainder of this chapter we first examine the short run price and output decisions of the monopolistic competitor and then the long run price, output, and plant size decisions. The economic effects of product differentiation in monopolistic competition are then examined by contrast with the purely competitive situation. Finally, as special topics in monopolistic competition, we examine the impact of asymmetric product differentiation and cost conditions, as well as the use of promotional expenditures as the firm’s strategic variable for profit maximization.

Il. SHORT RUN PRICE AND OUTPUT DETERMINATION Since products are differentiated in monopolistic competition, it is conceivable that each firm could face a different demand curve compared to its rivals, since

their products appeal to different consumers in the overall market. Similarly, if products are differentiated, it is conceivable that the firms’ cost structures are different, since differentiated products are likely to have different production costs. For example, a high-quality product is likely to cost more to produce than a low-quality product, and it may face a demand situation that is more or less price elastic, depending on the income levels and preference patterns of the buyers who would prefer each. Such differences in the cost and demand conditions are prevalent in the real world. They are described as asymmetric cost and demand conditions. This asymmetry requires us to examine each firm individually, since each firm’s situation is different. Such a procedure is tedious, of course, for there are many firms in monopolistic competition. It is much more instructive to use the simplifying assumption of symmetric cost and demand conditions, in order to facilitate the exposition of the model. The model can then be extended to find the effects of asymmetric cost and demand conditions. Thus we Shall proceed on the assumption of symmetric cost and demand conditions and return to asymmetric cost and demand conditions later in the chapter. The Representative Firm: The Assumption of Symmetry

The assumption of symmetric cost and product differentiation conditions allows us to speak in terms of the representative firm, since any one firm behaves in the same way and is subject to the same stimuli as any other firm. Recall our use of the concept of the representative firm in the pure competition situation: In that market, the demand conditions are identical across firms, because products are 242

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

completely undifferentiated. Likewise, cost structures are identical in the long run, due to the pressures of new entry and competition that force all firms to adopt the most efficient technology and the optimal-size plant. Accordingly, we are able to examine the pricing and output behavior of any one firm and impute this behavior to all the other firms.

DEFINITION: What exactly do we mean by symmetric cost and demand conditions? Let us begin with the demand side. Essentially, symmetric product differentiation requires that when prices are equal, all firms share the market equally and that all © firms experience the same rate of sales gain (or loss) when they lower (or raise) © their price, with all other things equal. Thus each firm faces a negatively sloping demand curve that has the same slope and the same vertical intercept as the demand curve facing every other firm in the market. By symmetric cost conditions, we mean identical cost conditions. That is, all firms can produce any given output level at the same level of average and marginal costs. EXAMPLE:

A simple and somewhat fanciful example of symmetric product differentiation and identical cost conditions would be the market for frisbees on Waikiki Beach. Purchasers of frisbees want to buy the least common color, so that they can more easily find their own frisbee among the storm of frisbees whirling about. At equal prices, this would lead to a roughly equal proportion of frisbees of each color, presuming that all purchasers buy what they perceive to be the least common color. Now suppose that the differently colored frisbees are sold by different sellers, and that red dye costs the same as blue dye, yellow dye, or any other color dye. The cost structures of the sellers should thus be identical, since all other attributes are presumed to be the same. if there were many sellers of many differently colored frisbees along Waikiki Beach, and if the buyers of these frisbees were split equally among the frisbees at equal prices, then we could use the pricing and output behavior of any one seller to represent all the sellers.

Profit-maximizing Price and Output for the Representative Firm The representative firm in monopolistic competition faces a negatively sloping demand curve and the cost curves as shown in Fig. 11—1. Having the ability to adjust its price to achieve profit maximization, the firm chooses price P* and output Q*. At this price-output combination, marginal costs (MC) equal marginal revenue (mr). The representative monopolistic competitor’s profits are thus equal to the area shown as P*ABC in Fig. 11-1. Notice that the monopolistic competitor’s price and output decision in the short run is exactly like that of the monopolist. Without concern for rivals’ actions, the monopolistic competitor and monopolist alike employ the marginalist rule for maximum profits by choosing price and output so that MC = MR. The major difference lies in the demand situation, of course. Whereas the ne faces the entire market demand curve, the monopolistic competitor faces a demand curve reflecting the preferences of a subset of the market demand. Note ea

Price and Output Determination in Monopolistic Competition

243

FIGURE 11-1 Short Run Profit Maximization in Monopolistic Competition

Price, cost, per unit

($/Q)

Po A p*

G

Quantity per

OF

period of time (Q/)

that the monopolistic competitor’s demand curve indicates that at price Po, quantity demanded falls to zero, and at progressively lower prices, quantity demanded becomes very large indeed. This demand curve envisaged by the firm is constructed under the assumption of ceteris paribus: All other things, including the prices of rival suppliers, are expected to remain equal. There is, unfortunately, many a slip ‘’twixt the cup and the lip,”’ as we shall see. Envisaged and Expost Demand Curves in Monopolistic Competition

In the preceding price and output determination discussion centered around Fig. 11-1, we have only shown the short run equilibrium price and output levels of the monopolistic competitor. We have also shown the short run equilibrium demand curve envisaged by the firm. This envisaged demand curve is the one the firm expects to move along in the event of a change in its price level. In the short run equilibrium situation shown, the firm reaches the point it expects to, namely, at price P* and output Q*, and it thus has no desire to change price or output. In a short run disequilibrium situation, however, the firm might reach a price-output combination that it did not expect to; it would, therefore, be motivated to change price and output again. It continues to adjust price and output until it arrives at its desired profit-maximizing price-output combination. This confusion arises because the firm expects to move along its envisaged demand curve, but it actually moves along an unanticipated demand curve. The envisaged demand curve is the firm’s expected demand curve, given ceteris paribus. But in some situations, other things do change, and thus the ceteris paribus demand curve is inappropriate. In particular, if other firms are simultaneously 244

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

changing their prices, then the firm’s envisaged (ceteris paribus) demand curve becomes inappropriate. Considering that the representative firm behaves in the Same way in response to the same stimuli as does any other firm, it is not surprising that competitors’ prices do change when our representative firm changes its price. If the representative firm does not move along its envisaged demand curve, where does it move when all firms change price concurrently? It moves, instead, along an unanticipated demand curve called the mutatis mutandis demand curve. DEFINITION: Mutatis mutandis in Latin means taking into account all concurrent changes. Thus the mutatis mutandis demand curve shows the price-quantity combination that prevails after other firms similarly adjust price. The firm fails to anticipate this because it expects its behavior to go unnoticed and to not cause any reactions from rival firms. In fact they are not reacting: they are simply acting in the same way as the representative firm. In Fig. 11-2 we show both the envisaged demand curve, d, and the unanticipated demand curve, D. Suppose the representative firm is initially setting price Py and selling output Qo. Next, suppose that, due to a change in cost conditions, the firm wishes to change price to P;, so that marginal cost equals marginal revenue (not shown) at output level Q,. The firm expects to sell Q, units at price P,, because it expects ceteris paribus to prevail. It does not expect its changing price to cause anything else to change. But all other firms are similarly motivated and simultaneously adjust their prices to P,, each expecting to sell Q, units of output. It is clear that all firms cannot expand their sales to Q,, since this was possible only when ceteris paribus. Each firm that reduces price expects to move to pointA ’, largely as a result of gaining customers from its rivals, who are expected to maintain their own prices at Py. When all firms reduce price to P;, however, no one firm will gain FIGURE 11-2 Envisaged and Unanticipated Demand Curves in Monopolistic Competition

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Price and Output Determination in Monopolistic Competition

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sales from any other firm, since all prices are once again equal at the new level. Each firm increases its sales to Q’, however, as a result of new buyers entering the market at the lower price or as a result of existing buyers purchasing more units, as predicted by the law of demand and consumer behavior theory. Market demand has thus increased at the new (lower) price, and each firm benefits by receiving a share of this increase in market demand. Note that since product differentiation is symmetric, and since all firms initially set price Py and then price P,, quantities Q, and Q’ must represent equal shares of the market demand at each of those prices. Thus the mutatis mutandis demand curve is in reality the firm’s share-of-the-market demand curve. If there are n firms, this curve traces out 1/n” of market demand at each price level, presuming that all firms change prices independently and concurrently to the same extent. In summary, then, the individual firm changes price from P, to P;, expecting to expand sales from Q, to Q, by gaining sales from other sellers who are expected to maintain their price at Po. Instead, these other sellers, facing the same cost and demand conditions, also reduce price to P;, and quantity demanded expands only to Q’ as a result of the increase in market demand at the lower price. Thus the individual firm expects, ex ante, to move along the ceteris paribus demand curve, but instead, ex post, moves along the mutatis mutandis demand curve, simply maintaining its share of the market. Short Run Adjustment to a Shift in Demand To demonstrate the process whereby firms in monopolistic competition adjust prices and outputs, let us suppose that the short run equilibrium situation is disturbed by a reduction in market demand. This leftward shift of the demand curve may be due to a reduction in consumer’s incomes or to a change in taste and preference patterns away from the product in question. If market demand is reduced, then the demand

for each firm’s product, in the symmetric case, is

reduced by the same proportion. In Fig. 11-3 we show an initial equilibrium in part (a). Notice that both the ceteris paribus demand curve, dd, and the mutatis mutandis demand curve, DD, pass through the coordinates of the representative firm’s price and quantity (P), Qo). In part (b) of the figure, we show the DD curve shifting back to its new location shown by D’D’. The representative firm’s quantity demanded at price P) falls to Q’, and, in contemplating a price adjustment, the firm now envisages the ceteris paribus demand curve d’. In part (c) of Fig. 11-3 we see that the firm selects price P; on the demand curve d’, since the firm expects to expand output to Q,, where marginal revenue (mr’) is equal to marginal costs (MC). But the firm’s expectations are not fulfilled, since ceteris paribus does not hold. Instead of moving from point B to point C, the firm moves to point D on the mutatis mutandis curve, selling only Q’, at price P,. In part (d) of Fig. 11-3 we see that the firm now envisages the d” curve for price adjustments, and adjusts price to Py, expecting to move to point E, which would allow marginal costs to equal marginal revenues. Once again the firm’s expectations are not fulfilled, since all other firms concurrently changed their prices as well. Each firm moves instead to point F, gaining only its share of 246

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

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the increased market quantity demanded, rather than the sales it expected to steal away from its rivals. And so the process continues, with the price adjustments becoming progressively smaller as the price level converges on the new equilibrium price P*, shown in part (e) of Fig. 11-3. The new equilibrium price-quantity coordinate is characterized by the firm’s ceteris paribus and mutatis mutandis demand curves intersecting at the same output level where the firm’s marginal costs equal the envisaged marginal revenues. This occurs at point G. Prior to this, the MC = mr output level was to the right of the output level at which the two demand curves intersected. Part (f) of Fig. 11-3 shows the comparative statics of the adjustment process. Point B is the firm’s price-output coordinate just prior to the first price adjustment. Instead of moving out to point C, the firm, in effect, slides down the D’'D’ curve with each subsequent price adjustment. This causes the envisaged demand curve to be relocated each time, with the result that its marginal revenue curve intersects the marginal cost curve at progressively smaller output levels. Finally, at point G the firm (and the market) is in equilibrium again, since MC = mr’’”’ (at output level Q*). Thus no firm has any incentive to change price from the equilibrium level P*. We now turn to the long run adjustment process, where, in addition to the price adjustment process described above, the firm may choose to adjust its size of plant, and new firms may enter the market.

II]. LONG RUN ADJUSTMENTS IN MONOPOLISTIC COMPETITION

In the monopolistic competition model, as in the pure competition model, we assume the free mobility of resources or the absence of barriers to the entry of new firms. This means that the existence of pure profits in the short run induces

the entry of new firms in the long run, each with its own slightly differentiated product. Oppositely, if existing firms make losses in the short run, some of these firms exit the industry in the long run. Alternatively, existing firms may choose to reduce or expand their plant size in the long run, in order to increase their profits or to avoid losses. In the following we look first at the entry and exit of firms and then at the adjustment of plant size necessary for all firms to attain long run equilibrium. Entry of New Firms

The existence of pure profits in the short run causes new firms to establish a plant and subsequently enter the market. Given a market of a particular size, more firms in the market means smaller market shares to all existing firms. In the

symmetric case, the entrant firm attracts customers away from all existing firms

in the same proportion, immediately capturing an equal share of the market. It is evident that the mutatis mutandis, or share-of-the-market, demand curve for the 248

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

representative firm must shift to the left as a result of the entry of new firms. All firms then proceed to adjust prices downward in the manner described in the preceding section. The adjustment process is visualized in the same two stages: The DD curve shifts to the left, due to entry of new firms, and the ceteris paribus demand curve slides down the new DD curve until there is no further profit incentive for firms to adjust prices. New firms stop entering the industry when they see that pure profits can no longer be earned. In the long run context, this means that there is no price and output combination that allows an excess of price over average costs. Long run equilibrium in the monopolistic competition model is depicted in Fig. 11-4. Notice that the firm’s envisaged demand curve dd is just tangent to the long run average cost curve (LAC) at pointA. Therefore all possible prices either above or below P* are less than the corresponding average cost level. For this to be the equilibrium price, the DD and dd curves must cross at price P*, otherwise the firm would continue to adjust price as shown in the preceding section. Thus long run equilibrium is attained when just enough firms enter the industry to cause the location of the DD curve to be such that the intersecting dd curve is tangent to the LAC curve at the equilibrium price level. FIGURE 11-4 Long Run Equilibrium in Monopolistic Competition

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In the long run the firm must build the plant size which has its SAC curve tangent to the LAC curve at pointA. This is the only plant size that allows normal profits to be made, since any other SAC curve would lie completely above the envisaged demand curve dd, and hence average costs would exceed price at every output level. Since the SAC curve is tangent to the dd curve and the LAC curve at point A, short and long run marginal costs must equal marginal revenues at that output level. Thus the short and long run equilibrium conditions are fulfilled— SMG = LMC = MR and SAC = LAC = P. Price and Output Determination in Monopolistic Competition

249

Exit of Existing Firms

Suppose that too many firms enter the industry or, alternatively, that market demand fell, so that the market share curve for the representative firm is curve DD in Fig. 11-5. Suppose further that the price gravitates to level Po, as a result of firms myopically adjusting prices along their ceteris paribus demand curves, and moving prices down the mutatis mutandis demand curve instead. At price P, the representative firm sells Qo, and its lowest possible average costs are shown at point C. Since the firm’s entire envisaged demand curve dd lies below the LAC curve, there is no price that allows a profit. In the short run the firms choose the loss-minimizing price where marginal revenue equals marginal costs. In the long run some firms leave the industry, and the share-of-the-market curve gradually shifts toward D’D’ until the remaining firms attain point A where normal profits can be earned. FIGURE 11-5

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Exit of Firms Leading to Long Run Equilibrium in Monopolistic Competition

To summarize, entry takes place in the long run, if pure profits exist, until the market share of each firm is sufficiently reduced to allow each firm to earn only anormal profit at its preferred price and output levels. Conversely, exit from the industry takes place in the long run, if losses exist, until each firm attains normal profits. When there are exactly the right number of firms in the industry for the given demand situation, the long run equilibrium situation prevails. Plant Size Adjustment to Avoid Losses

Implicit in the preceding discussion is the adjustment of all firms to the same size of plant in the long run. Since entry is not restricted, entrant firms cause existing firms to incur short run losses if the latter do not operate the appropriate 250

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

size of plant. The downward progression of prices, which follows entry of new firms, might cause the firm’s envisaged demand curve to fall completely below its SAC curve. Incurring losses, the firm must then adjust its size of plant to the one that allows normal profits—the one with its SAC curve tangent to both the LAC curve and the dd curve at the point where the DD curve intersects, as shown in Fig. 11—4 above. Both entrant firms and existing firms must build and operate this size of plant, if they are to survive under long run conditions.

IV. ECONOMIC EFFECTS OF MONOPOLISTIC COMPETITION We can compare the long run equilibrium situation in monopolistic competition with that of pure competition and ascribe any differences we detect to product differentiation, since this is the only difference between the two models of firm behavior. We shall see that there is a cost of product differentiation, which is

borne by the consumer. The Cost of Product Differentiation

For any valid comparison, we must have ceteris paribus, so let us suppose that the products are differentiated in monopolistic competition simply by differing locations of the individual sellers. Thus, in this simple case, the products are otherwise identical, but buyers prefer to buy from the most convenient, or nearest, seller, given equal prices. The firm’s cost structure can, therefore, be assumed to be the same, whether it is operating under pure competition or monopolistic competition. Market demand is assumed to be the same, but the individual firm’s demand situations are different: The firm’s demand is completely elastic under pure competition, but less than perfectly elastic under monopolistic competition. In Fig. 11-6 we contrast the long run equilibrium solution for each market situation. FIGURE 11-6 Comparison of Long Run Equilibrium Prices and Outputs for Firms in Pure Competition and Monopolistic Competition

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Price and Output Determination in Monopolistic Competition

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Under conditions of pure competition, the representative firm’s price and

output levels tend, in the long run, toward those shown as P, and Q,. Price equals the minimum level of long run average cost (point A), and the firm produces at

the most efficient level of output in the optimal-size plant. By contrast, in monopolistic competition under long run conditions, the firm’s price and output

levels tend toward those shown as P, and Q,. Price and average costs are equal at

the point A’, where the firm’s envisaged demand curve is tangent to the LAC curve; the firm builds and operates the plant size that has its SAC curve tangent at the same point. ata

NOTE:

The conclusion is unambiguous: Price tends to be higher and output from each firm lower under monopolistic competition compared with pure competition. The number of firms is greater under monopolistic competition (given the same total market demand situation), with each firm operating a smaller, less-efficient plant, compared with the optimal-size plant of the pure competitor. This example, using seller location as the differentiating variable, demonstrates that consumers are forced to pay for the extra convenience they prefer to have by purchasing from a nearby supplier.

EXAMPLE:

Suppose that another product, for instance, a particular style of raincoat, is produced only in grey by every firm under pure competition and in every conceivable color under monopolistic competition. Suppose also that product differentiation is symmetric, that is, that the market is equally divided over all firms—each producing a different color raincoat of the same design and material—when prices are equal. Thus consumers have to pay more for the colored raincoat of their choice compared with the grey raincoat of pure competition. Thus consumers must, and demonstrably do in the real world, pay higher prices in order to have a variety to choose from and to have the opportunity to select the most preferred variant from among those offered. From the consumer’s point of view, such higher prices may well be worth the extra product variety offered. It should be kept in mind that society has an opportunity cost of such variety, since the additional resources being used to produce this variety could be employed elsewhere to produce other goods and services for social and private benefit.

V. TOPICS INMONOPOLISTIC COMPETITION In this section we extend the simple model of monopolistic competition by relaxing two of the simplifying assumptions. First, we remove the assumption that product differentiation and cost structures are symmetric. The more general asymmetric case, in which market shares differ and firms face different price elasticities, and in which cost structures may differ, allows considerable insight

into the observed pricing behavior of firms in actual business environments. Second, we relax the assumption that price (and associated output variations) is the firm’s only strategic variable. By replacing this assumption with the assump252

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

tion that firms may adjust both price and promotional expenditures simultaneously, we considerably enrich the descriptive and predictive powers of the monopolistic competition model. Asymmetric Product Differentiation and Cost Structures

In order to fully understand what is meant by asymmetric product differentiation, let us first restate what is meant by symmetric product differentiation. Symmetric product differentiation means that all firms face the same demand. situation: Hence the representative firm’s ceteris paribus and mutatis mutandis demand curves have the same slopes and the same intercepts as for any other firm. Any one firm changing its price expects to experience the same price effect and price elasticity as would any other firm. As a consequence, in both short and long run equilibrium situations, all firms will set the same price level and each will have the same share of market demand. DEFINITION: Asymmetric product differentiation means that consumers do not divide equally among sellers when prices are equal, nor do they respond to independ- * ent price changes to the same degree for every seller. Thus firms may have dif- * fering shares of the market and face ceteris paribus demand curves of differing slopes. For example, a firm with several very close substitutes for its product might face a flatter ceteris paribus demand curve than another firm with only a few very close substitutes to contend with. In the asymmetric case, consumers are not distributed evenly over the multidimensional spectrum of tastes and preferences, and neither are the products of the competing firms. A relatively large number of firms may contest one area of the market, whereas relatively few may contest another. In both cases, they compete primarily with firms offering .; the closest substitutes and only peripherally with firms offering more distant. substitutes. 3 Given asymmetric product differentiation, it is reasonable to expect differences in the cost structures of the firms. High quality products may be expected to cost more, for any given output level, than low-quality products. Products with more features might cost more to produce than products with less features. Alternatively, some firms may have locational advantages, which are manifested in lower raw material costs or lower labor costs than are available to other firms. Thus we depict the firms as having different short and long run cost structures to reflect the differences in their products and their resource costs. Let us examine the price and output determination problem for the firms in an asymmetric monopolistic competition situation. Since there is now no representative firm, we should depict each firm separately and show the individual price and output adjustments of each and every firm. This would be tedious, of course, since there are many firms in monopolistic competition. Instead we shall look at a few selected firms and imagine the behavior of the others. In Fig. 11~7 we show three firms selected from among the many operating in the market. Notice that each firm has different ceteris paribus and mutatis mutandis demand curves and different marginal cost curves. Firm 1, for example, has a Price and Output Determination in Monopolistic Competition

253

relatively small share of the market (curve Dy), a relatively steep envisaged demand curve (curve dy), and a relatively high-cost structure (curve MC). The other cost curves have been omitted here for simplicity. FIGURE 11-7 Selected Firms in Asymmetric Monopolistic Competition: Short Run Equilibrium

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The firms represented in Fig. 11-7 are shown in a short run equilibrium situation. The marginal cost curve of each firm intersects the firm’s envisaged marginal revenue curve at the same output level where the mutatis mutandis and ceteris paribus demand curves intersect. You are asked to imagine similar equilibrium situations for the remainder of the firms in the market. Some might have higher prices and smaller quantities demanded, others might have lower prices and larger quantities demanded. Still others might have higher prices and larger quantities demanded, and some might have lower prices and smaller quantities demanded. Each firm’s equilibrium price and output level depends on the location of its own demand and cost curves. The widely-appreciated product of a firm with certain cost advantages might hold a relatively large market share at a relatively low price. Alternatively, a high-cost, high-quality product appealing primarily to the tastes of relatively few consumers might hold a small market share at a relatively high price. In response to a disturbance of the short run equilibrium situation, the firms would adjust prices the same way as in the symmetric case. Each would equate its expected marginal revenues (from its envisaged, or ceteris paribus, demand curve) to its marginal costs. Finding itself at an unanticipated priceoutput combination, due to the concurrent actions by other firms, each firm would continue to adjust prices until it ended up where it expected to end up. If these price adjustments were downward, due to a reduction in market demand or a decrease in raw material costs, for example, the ceteris paribus demand curve would, in effect, slide down the mutatis mutandis demand curve until the marginal cost and revenue equality is obtained at the same output level at which the two demand curves intersect. Oppositely, if the price adjustments were upward, due to an increase in market demand or an increase in resource costs, the 254

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

ceteris paribus curve of each firm would slide up the mutatis mutandis demand curve until the same equilibrium conditions prevail.

NOTE:

What is the impact of relaxing the symmetry assumptions? For the first time in our study of the theory of the firm, we see price and market share differentials in equilibrium. Firms selling more popular products can set higher, profit-maximizing prices and obtain larger market shares, ceteris paribus. Firms with lower cost structures can set lower, profit-maximizing prices and obtain larger market shares, ceteris paribus. Firms with a combination of a more popular product and lower costs have larger market shares and a price that is above or below the average price, depending upon whether the product differentiation or cost advantage is dominant. Firms with a less popular product and high costs have smaller market shares and a price that is higher or lower, depending upon which disadvantage dominates. In every case the price and market share differentials are the direct result of the differences in the cost and demand conditions faced by the firm. Following the same myopic price adjustment procedure as in the symmetric case, the firms continue to adjust prices until they have no profit incentive to further adjust prices. Each firm’s equilibrium price and quantity demanded is likely to be different precisely because their cost and demand conditions are different. Long Run Adjustments in the Asymmetric Case. In the long run, entry of new firms is induced if the firms are making pure profits in the short run. Entrant firms establish a plant and begin production of a differentiated product. Unlike the symmetric case, however, the new entrants need not gain sales equally from all existing firms. Rather they gain sales largely from firms whose products are most closely similar to their own product. As long as any firm makes short run pure profits, there will be an entrant firm ready to enter with a closely similar product, until finally no firm makes pure profits and the industry is in long run equilibrium. In Fig. 11-8 we show three selected firms in long run equilibrium.

FIGURE 11-8 Selected Firms in Asymmetric Monopolistic Competition: Long Run Equilibrium

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Price and Output Determination in Monopolistic Competition

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Due to the differences in product differentiation and cost conditions, there will be price and market share differentials in the long run as well. But note that since price equals average cost in long run equilibrium, low-cost firms have lower prices but not necessarily larger market shares, since entry of new firms into the more profitable segments of the market cause the demand to be shared among more firms. The individual firm’s share of the market in the long run depends entirely upon its long run average cost curve and its envisaged, or ceteris paribus, demand curve: The tangency point of these two curves defines the long run equilibrium price and quantity demanded for each firm. Enough new firms enter until the share-of-the-market, or mutatis mutandis, demand curve moves far enough to the left to intersect the other two curves at their tangency point.

Thus, the flatter a firm’s envisaged demand curve, the lower its price and the larger its market share, since the tangency of that curve with the LAC curve occurs further toward the lowest point on the LAC curve. (Compare firm 28 with firm 63 in Fig. 11-8.) Oppositely, firms with similar price effects, that is, the same slope on their envisaged demand curve, have higher prices and smaller market shares the higher their cost structure. (Compare firm 3 with firm 63 in Fig. 11-8.) Remember that differences in cost structure are due to differences in the product and differences in resource costs, not to differing efficiencies in

production. An inefficient firm is soon forced into losses by an efficient entrant buying resources at the same cost and producing a similar product. Thus asymmetry of product differentiation and cost conditions allow price and market share differentials to prevail in both short and long equilibrium in the monopolistic competition model. Not even the unrestricted entry of new firms in the long run can completely remove these differentials, since the asymmetry of product differentiation and cost conditions are unaffected by that entry. Entry will cause only the pure profits to be squeezed out until all suppliers earn only a normal profit.

Promotional Expenditures as a Strategic Variable Up until this point we have assumed that price and consequent quantity variations are the firm’s only strategic variables. By adjusting price, the firm obtains the price-output combination that it believes will maximize its profits. All other factors influencing demand were assumed to be constant by the ceteris paribus assumption of the demand curve. In this section we relax part of that assumption by allowing the firm to have another strategic variable, namely, promotional expenditures.3 3We follow the treatment first shown by N. S. Buchanan, “Advertising Expenditures: A Suggested Treatment,” Journal of Political Economy, August 1942. Reprinted in W. Breit and H. M. Hochman, eds., Readings in Microeconomics (New York: Holt Rinehart and Winston, 1968). An alternate treatment of the issue is given by R. Dorfman and P. O. Steiner, “Optimal Advertising and Optimal Quality,”” American Economic Review, December 1954, pp. 826-36.

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THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

DEFINITION: By promotional expenditures we mean all those expenditures intended to inform consumers about the existence and the merits of the product and to influence consumers’ taste and preference patterns and subsequent buying behavior. Promotional expenditures thus include such diverse elements as commercials on radio and television, advertisements on billboards and in newspapers and periodicals, point-of-purchase displays in retail outlets, promotional contests, free samples, and so forth. Promotional expenditures are a shift parameter of the demand curve, as we saw in Chap. 4. Increased promotional efforts are expected to shift the firm’s demand curve to the right, whereas reductions in these efforts cause the demand curve to shift to the left. Promotional expenditures must be regarded as a fixed cost, since they are typically independent of the current level of output and sales.* Thus the average promotional expenditures, or, more broadly, average selling costs, are graphed as a rectangular hyperbola against the output level. In Fig. 11-9 we show the average selling cost (ASC) curve for a particular level of promotional expenditures, given a particular demand and production situation. The intersection of the marginal cost and marginal revenue curve indicates that the profit-maximizing output level is Qo, to be sold at price Py. The relevant point on the average selling cost curve is the point labeled Ao, since this is the average selling cost level at output level Qo. FIGURE 11-9 The Average Selling Cost Curve $/Q

There is nothing in Fig. 11-9 to indicate promotional expenditure. Larger promotional to shift to the right and the average selling cost right. To find the optimal level of promotional

that ASC, is the optimal level of budgets cause the demand curve curve to move upward and to the expenditure and the profit-maxi-

i budgets on past sales levels or expected current sales leve 1s,: but this omotional ften b 4F ij must =ictse dasaniiyseilvaieeit to current production levels, of course. Promotional expenditures which case they be treated as a fixed cost, unless they vary directly with current output levels, in but are sellwould then be variable costs. Note that promotional expenses are not production costs, ing costs.

Price and Output Determination in Monopolistic Competition

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mizing price, we must know to what extent additional promotional expendi; tures will shift the demand curve. l promotiona of level the increasing of In Fig. 11-10 we show the results level, l promotiona initial the from expenditure by two distinct steps, starting ASC, which gave rise to the optimal quantity and price levels Qo and Pp». Suppose that this expenditure is increased to the level indicated by the hyperbola ASC,. This causes the demand curve to shift from do to d,. The marginal cost

curve remains in the same place, of course, and intersects the new marginal revenue curve mr, at the output level Q,, indicating a new profit-maximizing price level shown by the point P;. At this output level, A; indicates the average selling cost per unit. FIGURE 11-10 Optimal Prices for Successive Levels of Advertising Expenditures

Suppose now that promotional expenditures are again increased, this time to the level shown by ASC,. This in turn causes the demand curve to shift to d, and the related marginal revenue, mr, to intersect the marginal cost curve at output level Q,. The profit-maximizing price for this output level is shown by Po, and the average selling cost at this output level is shown by the point A». Clearly by continuing this process, we could trace a series of optimal price points and a series of average selling cost points. The locus of optimal prices for various levels of promotional expenditure is shown as curve LOP in Fig. 11-10. The locus of the average selling costs for various promotional and demand levels is shown as curve LASC. Note that the general curvature of these curves reflects the presence of diminishing returns to promotional expenditures. The LOP curve and the LASC curve in Fig. 11-10 are each the locus of a variable that represents an average—average revenue, or price, and average sell-

258

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

ing cost. Each of these average curves has a curve that is marginal to it. In Fig. 11-11 we show the LMR curve (locus of marginal revenue) as the curve that is marginal to the LOP curve, and we show LMSC (locus of marginal selling costs) as the curve that is marginal to the LASC curve. Notice that the shape and placement of these marginal curves follow the general principles of the relationships between average and marginal curves. The decision-maker’s problem is to have the marginal increase in selling costs just equal to the marginal change in revenues. Thus the intersection of the LMSC curve with the LMR curve indicates the output level at which the increment to revenues is just equal to the increment to selling costs. The optimal output level is shown as Q* in Fig. 11-11. The point on the LOP curve at that output level must lie on the optimal demand curve, which we show as d*; the

optimal price level is thus P*. The optimal level of promotional expenditures can be found from the LASC curve to be ASC*, which represents A* dollars per unit of output at the optimal output level. FIGURE 11-11 Establishing the Optimal Price and Advertising Levels

Thus we have seen that the firm may adjust both price and promotional expenditures to the point where profits are maximized. If all firms are simultaneously adjusting price and promotional expenditures, the individual firm’s expectations are not fulfilled at first, since ceteris paribus does not hold. We have seen that the price adjustment process converges on an equilibrium level in the simple case, and the same applies here. In this case, both the firm’s price and promotional expenditure levels converge upon the equilibrium levels, at which point the firm will realize the price and output levels it expected to realize; thus it will have no further incentive to adjust either price or promotional expenditures.

Price and Output Determination in Monopolistic Competition

259

VI. SUMMARY In this chapter we examined the price and output determination problem for the monopolistic competitor, a firm which is small relative to its market and which produces a product slightly differentiated from those of its rivals. In the symmetric case, where products are, in effect, equally differentiated, and costs are identical, all firms set the same price and share the market equally. In the long run, new firms enter the market and squeeze out,any pure profits. The price adjustment process is characterized by the firms’ myopia: Each firm expects to obtain a price-quantity coordinate on its ceteris paribus curve, but instead ends up after each price adjustment on its mutatis mutandis demand curve. The firm’s expectations are not fulfilled, because it does not recognize that all other firms are similarly motivated to change price. As the firm myopically continues to adjust price, however, the anticipated result and the actual result converge, until finally the firm ends up where it expected to, and is thus in equilibrium, having no incentive to adjust price further. In the long run, entry of new firms causes the same adjustment process until each firm finds its envisaged demand curve tangent to its short and long run average cost curve. This is the long run equilibrium condition, since no firm wants to adjust price either upward or downward, no new firm wants to enter, and no firm wants to leave the

industry. The difference between monopolistic competition and pure competition is simply that there is product differentiation in the former and product homogeneity in the latter. This difference has a profound impact on the behavior of firms, however. Product differentiation causes price to be higher and plant size to be smaller and less efficient, as compared with pure competition. Thus the cost of product differentiation is borne by the consumer. As a special topic in monopolistic competition, we relaxed the assumption of symmetric product differentiation and cost conditions. We found that this caused price and market-share differentials to exist in both short and long run equilibrium situations. Finally, we allowed the firm to adjust both price and promotional expenditures simultaneously to demonstrate that, up to a point, additional promotional efforts allow the firm to raise its price and expand its quantity demanded.

DISCUSSION

QUESTIONS

1.

Which of the seven assumptions of the monopolistically competitive model do you think is the most critical for the real-world application of the model? Why?

2.

Explain why the assumption of symmetry is necessary for the concept of the representative firm in monopolistic competition.

3.

Define the mutatis mutandis demand curve. Why is it, in effect, the firm’s share-of-the-market demand curve? Why doesn’t the firm perceive this curve?

260

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

4.

Verbally explain the firm’s adjustment procedure in response to a reduction in market demand in the short run.

5.

What are the equilibrium conditions for the firm’s price and output levels in the short run monopolistically competitive market?

6.

In the long run, new firms enter the market if pure profits exist in the short run. What happens if too many new firms enter?

7.

Whatare the long run equilibrium conditions in the monopolistically competitive market situation?

8.

Explain the assertion that the cost of product differentiation is borne by the consumer. Do consumers want to pay extra to obtain differentiated products?

9.

What is the impact on the monopolistically competitive model of introducing asymmetric cost and demand conditions? Why does this endure in the long run?

10.

Explain the optimal level of promotional expenditure in terms of the required marginal equalities.

SUGGESTED

REFERENCES

BUCHANAN,N.S., ‘Advertising Expenditures: A Suggested Treatment,” Journal of Political Economy (August 1942). Reprinted in W. Breit and H.M. Hochman, eds., Readings in Microeconomics. New York: Holt, Rinehart & Winston, 1968. HAMBERLIN, E.,

Theory of Monopolistic Competition. Cambridge, Mass.: Harvard Uni-

versity Press, 1933.

Dewey, D.,

The Theory of Imperfect Competition. New York: Columbia, 1969.

DORFMAN, R., and P.O. STEINER.,

‘Optimal Advertising and Optimal Quality,” Ameri-

can Economic Review (December 1954) 826—36.

HIRSHLEIFER, J., Price Theory and Applications (2nd ed.), chap. 12. Englewood Cliffs, N.J.: Prentice-Hall, 1980. KOUTSOYIANNIS, A.,

Modern Microeconomics

(2nd ed.), chap. 8. London: Macmillan,

1979.

ROBINSON, J.,

The Economics of Imperfect Competition. London: Macmillan: 1933.

SAMUELSON, P., “The Monopolistic Competition Revolution,” in Monopolistic Competition Theory, ed. R. Kuenne. New York: John Wiley, 1967. SCHERER, F.M., Industrial Market Structure and Economic Performance, chap. 14. Chicago: Rand McNally, 1970.

Price and Output Determination in Monopolistic Competition

261

Price and Output Determination in an Oligopoly

1. INTRODUCTION DEFINITION: Oligopolies are markets in which there are only a few sellers. (The word oligopoly is derived from the Greek word oligos, meaning few and the Latin | small enough such that the actions of any one firm have a noticeable impact on the demand for each of the other firms. In oligopolies, a reduction in the price or

a change in any other strategic variable by any one firm causes that firm to gain sales and causes rival firms to suffer a noticeable loss of sales, as consumers switch across to the firm that has made the change in its strategic variable.

EXAMPLE: In the real world the great majority of market situations are oligopolies. Prominent examples are the automobile, steel, aluminium, and chemical industries.

These are national and, in some cases, international oligopolies. In your local or regional area, you will notice many more oligopolies. There are probably a few universities competing for the students coming out of the secondary school system. There are probably half a dozen new car dealerships competing for your expenditure on anew automobile (after you graduate and get a high-paying job!). Similarly, there are only a few sellers in a multitude of other lines of business in your area, and these qualify as oligopolies if the actions of any one seller have an impact on the sales of any other seller. The essential difference between oligopoly and monopolistic and pure 262

» competition is that in oligopoly, the sales gain resulting from the action of one firm is atthe expense of fewer firms, whereas in monopolistic competition and pure competition, the effect is spread imperceptibly over a large number of rivals. Oligopolists, therefore, should be expected to react to the actions of their rivals, rather than ignore them, as in the other two cases. In turn, this implies that a firm contemplating an adjustment in its strategic variable should anticipate the reaction of its rivals when estimating the impact of that adjustment on its sales and profits. Since the actions of any oligopolist have a direct impact on each of its rivals and might be expected to provoke a reaction, we say that the actions of the firms are interdependent, or mutually dependent.

Recognition of Mutual Dependence in Oligopoly Models of firm behavior under oligopoly may be dichotomized according to whether or not the firms recognize their mutual dependence. In simple models where the firms do not recognize this fact, the conjectural variation assumption is zero. These models characterize the oligopolist as being incredibly myopic, adjusting prices on the assumption that there will be no reaction from rivals. When rivals do react by adjusting their prices, the oligopolist again adjusts its price, again oblivious to the fact that rivals will react, and so on. These myopic models do not have very strong explanatory or predictive power, since most oligopolists in the real world have long since discovered that imprudent price cuts can lead to damaging price wars, just as ill-considered price increases can lead to substantial losses of market share. Such models are useful, however, for pedagogical purposes, since they illustrate very forcefully the implications of myopia in oligopolistic markets. When oligopolists do recognize their mutual dependence, there are a variety of different conjectural variations they might make. In the following section we examine several models, each with different assumptions concerning the firms’ conjectural variations. We then examine long run adjustments and the economic effects of oligopoly, following the pattern established in the preceding chapters.

ll. SHORT RUN PRICE AND OUTPUT DETERMINATION

|

The first model we consider is not a model of price and output determination, since this takes as its starting point the firm’s current price and output levels. The kinked demand curve model, however, does illustrate several very important features of oligopoly markets in which mutual dependence is recognized. Later in this section we see how prices and outputs are determined in several 1In short, failure to recognize mutual dependence leads to the downward progression of prices toa price floor, as in the Cournot model, or to the fluctuation of prices between a price floor and a price ceiling, as in the Edgeworth model. A particularly thorough treatment of these classical models of duopoly (two sellers) under conditions of unrecognized mutual dependence is found in A. Koutsoyiannis, Modern Microeconomics, 2nd ed. (London: Macmillan, 1979), pp. 216-33. Given the space constraints of this textbook, however, I prefer to bypass these models in favor of other models of oligopoly behavior that not only have pedagogic value but explanatory and predictive value as well. Price and Output Determination in an Oligopoly

263

other models, including those depicting price leadership and cartel pricing situations. The Kinked Demand Curve Model

the oligopolist enThe kinked demand curve (KDC) model is so-called because

visages ademand curve that is kinked at the current price level.” This envisaged kink occurs because the firm has a two-part conjectural variation. When contemplating price increases, the firm expects no reaction from rivals, since the other firms are expected to be content to sit back and receive extra customers who switch away from the firm raising its price. For price reductions, the firm expects rivals to react by exactly matching the price reduction in order to maintain their shares of the market. The seven assumptions for the KDC model of oligopoly are listed in Table 12-1. TABLE

12-1

The Seven Assumptions of Oligopoly-The Kinked Demand Curve Model

1. Number of sellers 2. Cost conditions

STRUCTURAL ASSUMPTIONS

BEHAVIORAL ASSUMPTIONS

‘ 3. 4. 5. 6. 7.

Number of buyers Demand conditions Objective function Strategic variables Conjectural variation

Few Cubic production function with constant factor prices. Entry of new firms restricted Many Product differentiation Maximize short run profits Price and quantity Zero for price increases, unity for price de-

creases

Since the firm’s conjectural variation for price increases is zero, it envisages aceteris paribus demand curve at all prices above the current level, this curve being more or less elastic depending primarily upon the degree of substitutability between its product and rival products. In contemplating price reductions, however, the firm envisages a mutatis mutandis demand curve, meaning that it takes into account all reactions induced by or concurrent with the firm’s price adjustment. In this case the firm expects all other firms to exactly match its price reduction. Thus it expects its quantity demanded to expand only because total market demand will be greater at the lower price level. Rather than steal customers away from rivals, the firm expects to expand sales only as a result of getting its share of the new buyers attracted into the market by the lower price level.

NOTE:

Thus the mutatis mutandis section of the firm’s demand curve represents a constant share of the total market for the product in question. The ceteris paribus ?This was initially proposed separately by R. L. Hall and C. J. Hitch, “Price Theory and Business Behavior,” Oxford Economic Papers, May 1939, pp. 12-45, and by P. M. Sweezy, “Demand under Conditions of Oligopoly,” Journal of Political Economy, 47 (August 1939), 568-73. The kinked demand curve is also suggested by incomplete information. See J. E. Stiglitz, “Equilibrium in Product Markets with Imperfect Information,” American Economic Review, 69 (May 1979), 339-45.

264

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

demand curve is appropriate for independent action by a firm not expecting reactions, and the mutatis mutandis demand curve is appropriate forjoint action by firms, taking rivals’ reactions into account. The ceteris paribus section of the firm’s demand curve (for price increases) is relatively flat, reflecting the relatively elastic demand response expected as consumers switch away from the firm’s product. The mutatis mutandis section (for price decreases) is relatively steep, reflecting the relatively inelastic demand response expected as its sales increase. This increase is only a share of the increase in total market quantity demanded. In Fig. 12—1 the firm’s current price and output levels are shown as P and Q. For prices above P, it envisages the relatively elastic ceteris paribus demand curve shown by line dA. For prices below P, it envisages the relatively inelastic mutatis mutandis demand curve shown by line AD. The demand curve facing the firm is, therefore, dAD, being kinked at the current price level. The marginal revenue curve appropriate to this demand curve has two separate sections. The upper section, shown as dB in Fig. 12-1, relates to the ceteris paribus section of the demand curve, and therefore shares the same intercept and has twice the slope of line dA. The lower section, CMR, relates to the mutatis mutandis section of the demand curve. It is positioned so that it has twice the slope of line AD; if it is extended up to the price axis, it would share its intercept point with line AD when similarly extended. FIGURE

12-1

The Kinked Demand Curve Model of Oligopoly

MR

You will note that there is a vertical discontinuity in the marginal revenue curve, shown as the gap BC in Fig. 12-1. Given the foregoing, it is apparent that the length of this gap depends upon the relative slopes of the ceteris paribus and mutatis mutandis demand curves, which in turn are related to the elasticity of Price and Output Determination in an Oligopoly

265

demand under the two conjectural variation situations.? If the firm is a profit maximizer, its marginal cost curve passes through the gap BC. If P and Q are the profit-maximizing price and output levels, this implies that outputs to the left of Q have marginal revenues exceeding marginal costs, whereas outputs to the right of Q have marginal costs exceeding marginal revenues. This is only true if the MC curve passes through either point B, C, or some point in between.* While MC does not equal MR when the MC curves passes through the gap in the MR curve, it comes as close as it can to equalling MR, since it is converging on MR up to output level Q and then diverging from MR after output level Q. The oligopolist’s profits are shown by the rectangle PAEF in Fig. 12-1.

Price Rigidity in the Kinked Demand Curve Model. The KDC model is not a complete theory of price determination, because it is unable to tell us how the firm arrives at the initial price and output levels. Given this starting point, however, the model is able to tell us several things that are important to our understanding of oligopoly markets. First, it offers an explanation of the widely observed rigidity of prices in the face of changing cost and demand conditions.

Recall that in each of the models of firm behavior we have examined so far, the firms set price where marginal costs equal marginal revenue. If either costs or demand conditions change, one of these marginal curves shifts, and a new price level is required if the firm is to maximize profits under the new conditions. In the KDC case, however, the marginal cost and marginal revenue curves may shift to a considerable degree without a new price level becoming appropriate, as we shall see. Second, the KDC model tells us when prices do change in oligopoly markets. If cost or demand changes are too large to be absorbed at the present

price level, the firm adjusts price to the new profit-maximizing level, regardless of what it expects rivals to do. Modified versions of the KDC model allow other pricing behavior of oligopolists to be explained and predicted. Let us first examine price rigidity in oligopolies.

In the KDC model, the firm does not wishto change price as long as the marginal cost curve passes through the gap in the marginal revenue curve. Thus costs could increase so that the MC curve moves upward until it passes through point B in Fig. 12-2, without the present price becoming inappropriate. Oppositely, if variable costs fall, the MC curve could sink downward until it passes

through point C, and price P would remain the profit-maximizing price. As long as marginal revenue exceeds marginal costs for higher prices and is less than marginal costs for lower prices, the present price remains the optimal price. Of course, profits are smaller when costs are higher, but profits are maximized when the MC curve passes through the MR gap. Now consider changes in the demand situation. In most real world market situations, quantity demanded at the prevailing price level fluctuates up and down over time as the result of seasonal, cyclical, or random influences on the factors determining demand. But as we show in Fig. 12~3, demand at price P 9G. J. Stigler, “The Kinky Oligopoly Demand Curve and Rigid Prices,” Journal of Political Economy, vol. 55, October 1947. DESY, Smith, and W. C. Neale, “The Geometry of Kinky Oligopoly: Marginal Cost, the Gap, and Price Behaviour,” Southern Economic Journal, 37 (Jan. 1971), 276-82.

266

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

FIGURE

12-2

Price Rigidity despite Changes in Cost Levels in the Kinked Demand Curve Model

could fluctuate over the range Q, to Q;, without causing the MC curve to pass outside the relevant MR gap. At quantity Qo, the MR curve is shown by d'B’C’MR’, and the MC curve passes through point C’. This is the extreme leftward point to which the demand curves could shift and yet still allow the MC FIGURE

12-3

Price Rigidity despite Shifts of Demand in the

Kinked Demand Curve Model

Q/t

R”

Price and Output Determination in an Oligopoly

267

curve to pass through the gap. The extreme rightward shift of demand, which allows P to remain as the profit-maximizing price, is found when the MC curve passes through point B”, as it does at output Q;. Thus demand could fluctuate over the relatively wide range Q, to Q, at price P, without the firm wishing to change its price. Profits are lower when demand is lower, but are maximized at price P as long as the demand shift is not so large as to cause the MC curve to miss the gap in the appropriate MR curve. Price Adjustments in the Kinked Demand Curve Model. Let us look briefly at a cost change that will lead to a change in price. As implied above, if the change is such that the new MC curve no longer passes through the MR gap, then the firm will want to change price. In Fig. 12-4 we show a shift of the marginal cost curve from MC to MC’, causing it to intersect the MR curve at point B’. The initial

price P is no longer the profit-maximizing price, since marginal cost exceeds marginal revenue for all the output units between Q’ and Q. The new profitmaximizing price is thus P’, where the MC’ curve intersects the MR curve. The firm therefore raises its price to P’ and experiences a reduction in its quantity demanded from Q toQ’. FIGURE

12-4

A Profit-maximizing Price Change in the Kinked Demand Curve Model

Notice that the firm raised its price independently, with the expectation that no other firm would follow its price increase; consequently, it lost part of its market share. Since the firm’s price-output coordinate is now point A’, it must envisage the new mutatis mutandis demand curve, A'D’, for any contemplated price reduction. Thus the firm’s share-of-the-market demand curve has effectively shifted to the left as a result of its independent price increase. But the firm, being a profit maximizer by assumption, would rather increase profits than worry about market share, and hence prefers the higher profit situation at price P’, given the cost increase that upset the initial equilibrium situation. 268

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

Alternatively, we could show the demand curves shifting to the right to such an extent that the firm prefers to raise price (and lose part of its market share), in order to maximize profits. Oppositely, we could show the marginal cost curve falling sufficiently or the demand situation declining sufficiently, causing the MC curve to cut the lower section of the marginal revenue curve.’ In either of these two cases, the firm would cut its price, notwithstanding its expectation that rivals would immediately follow suit, because cutting price allows profits to be maximized. Since all rivals match the price reduction, all firms maintain their market shares at the lower price level. Thus the KDC model predicts that firms will hold price steady, despite the fluctuations of variable costs or demand over a significant range of cost or output

levels. Outside the limits set by the requirement that the MC curve pass through

the gap in the MR curve, the firm will be motivate to change d price. It will raise or lower price to the new profit-maximizing level, whether or notit expects

rivals to do likewise. Conscious Parallelism

DEFINITION: The simultaneous adjustment of prices with the expectation that rivals will do likewise has been called “‘conscious parallelism.’ The firms consciously act in a parallel manner given their expectation that all other firms are motivated to act in the same way. Under some conditions, the firm’s expectation may be that other firms will want to increase prices at the same time. Such a situation might arise when a cost increase applies to all firms, such as an increase in the basic wage rate or an increase in the cost of an important raw material. In the case of cost increases that apply to all firms, the individual firm might reasonably expect that all firms would like to maintain profit margins by passing the cost onto consumers. Especially if there is a history of this practice in the industry, the firm’s conjectural variation for a price increase, up to the extent necessary to

pass on the cost increase, will be unity. Thus the relevant demand curve for this type of price increase is the mutatis mutandis demand curve. As indicated in Fig. 12—5, the kink in the demand curve moves up the mutatis mutandis section to the new price level chosen. It kinks at the level that passes on the increase in average costs, because the firm expects that any further price increase will not be matched by rivals. The firm, therefore, expects to experience a more elastic demand response above that price level. The firm’s conjectural variation is unity up to the price level that is expected to be agreeable to all firms, and it is zero for price levels above that.’ 5The lower section of the MR curve may lie completely below the horizontal axis, of course, in which case the MC curve could not intersect it, since MC cannot be negative. 6W. Hamburger, “Conscious Parallelism and the Kinked Oligopoly Demand Curve,” American Economic Review, 57 (May 1967), 266-8.

7The extent to which price is raised depends on the extent to which the firm expects other firms to raise prices simultaneously; it may be more than, less than, or equal to the cost increase. It would be (joint) profit maximizing to raise price all the way to the point where the MC curve cuts the mutatis mutandis MR curve (extended upward). But if some firms are not expected to raise price that far, the demand curve will kink, and that MR is thus inappropriate. Price and Output Determination in an Oligopoly

269

FIGURE

12-5

Conscious Parallelism in the

Kinked Demand Curve Model of Oligopoly

Since all firms are expected to act jointly, each firm expects to maintain its share of the market at the higher price level, and, by passing on the cost increase to consumers, each firm expects to maintain its profit margin per unit (the difference between price and average costs). In the next chapter we see that the prevalent practice of markup pricing allows firms to practice conscious parallelism in the real world, even when they don’t know how their demand curves slope away from the present price level. Price Leadership

A number of oligopoly models rely on the notion of price leadership to explain the upward adjustment of prices in oligopoly markets. The major difference between conscious parallelism and price leadership is that in the former situation, all firms take the initiative in adjusting prices, confident that their rivals will do

likewise; whereas in the latter situation, a particular firm leads the way, and within a relatively short period all or most of the other firms adjust their prices toa similar degree. The price leader is the firm willing to take the risk of being the first to adjust price. But as we shall see, the leader usually has good reason to expect that the other firms will follow suit. The risk involved here relates particularly to price increases, since if the firm raises price and is not followed by other firms, it will experience an elastic demand response and a significant loss of profits before it can readjust its price to the original level. Conjectural variation for the price leader is unity, since this firm expects all rivals to adjust prices up or down to the same degree as it does. For the price followers, conjectural variation is zero for self-initiated price increases, since price followers do not expect the other firms to follow their price increases. For price decreases, the price follower expects all firms to follow suit to protect their market shares, and so the conjectural variation is unity for price reductions. It 270

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

should be immediately apparent to the reader that the price follower faces a kinked demand curve. There are three major types of price leaders—the barometric price leader, the low-cost price leader, and the dominant-firm price leader. The Barometric Price Leader.

Asthename implies, the barometric price leader

possesses an ability to accurately predict when theclimate is right for a price change. Following a generalized increase in labor, material costs, or demand, the barometric firm judges that all firms are ready for a price change and takes

the risk of sales losses by being the first to adjust its price. If the other firms trust that firm’s judgment of market conditions, they will follow the leader’s price change. If they feel the increase is too much, they might adjust prices to a lesser degree, and the price leader may bring its price back to the level seemingly endorsed by the other firms. If the other firms fail to follow the price change, the firm initiating the price change may change its price back: It finds that it is no longer the price leader. For this and other reasons, such as better information about the market, the price leadership role may shift from firm to firm and will rest with the firm that has sound knowledge of market supply and demand conditions, the ability to sense a consensus among the firms, and the willingness to take the risk of sales losses if its judgment on these issues is faulty.®

Low-cost Firm Price Leadership.

The low-cost price leader is a firm that has a

significant cost advantage over its rivals: That is, itscost curves lie lower for all levels of output. It inherits the role of price leader largely due to the other firms’

reluctance to get involved in a price war witha low-cost firm. If their price cuts were more these price price

to start a price war, the high-cost firms would incur greater losses and be prone to the risk of bankruptcy than would the low-cost firm. In view of dangers, the other firms may prefer simply to follow the low-cost firm’s adjustments. Alternatively, it might be said that the low-cost firm is the leader, because it has the least to lose if the other firms refuse to follow its

lead. We can show graphically the determination of price in such a situation. The most simple situation is an identical-product case involving two firms. In Fig. 12-6 we show the demand curve D as the curve faced by either firm when each firm sets price at the same level. This curve is thus a mutatis mutandis demand curve, being predicated upon the simultaneous adjustment of the other firm’s price to the same level. In price leadership situations, price adjustments are more or less concurrent, and the demand curve D in this case represents a constant (half) share of the total market at each price level. The marginal cost curves of the two firms are shown as MC, for firm A, the low-cost firm, and MC, for firm B, the high-cost firm. The low-cost firm maximizes its profit from its share of the market by setting price P and output level Q. Firm B follows the lead and also sets price P. 8Barometric price leadership was first proposed by J. W. Markham, “The Nature and Significance of Price Leadership,” American Economic Review, Dec. 1951, pp. 891-905. For further discussion of barometric price leadership, see F. M. Scherer, Industrial Market Structure and Economic Performance, (Chicago: Rand McNally & Company, 1970), chap. 6. Price and Output Determination in an Oligopoly

271

FIGURE

12-6

Low-cost Firm Price Leadership: Simple Case

O (Market demand)

D (Firm’s demand)

Qf’

Given that it sets price P, what output level should the high-cost firm produce? Being a profit-maximizing firm, by assumption, it will simply choose the output level that maximizes profits, subject to the (self-imposed) constraint that its price will be the same as the price leader’s. The demand curve facing firm B, in this simple identical-product case, is the kinked line PAD, since if firm B sets its price above P, all consumers will purchase from firm A at the lower price. If firm B sets its price below P, the other firm will match this price reduction to avoid having its sales fall dramatically. The marginal revenue curve associated with demand curve PAD is the disjointed line PABMR, with a horizontal section

relating to the horizontal part of the demand curve faced by firm B, and with section B MR relating to prices below the price P. Firm B should therefore choose output level Q, since below this output level marginal revenue exceeds marginal costs, and above this level, marginal costs exceed marginal revenue. The firms thus share the market equally at the price level chosen by the low-cost firm.

The Differentiated Products Case. The simple model above allowed us to introduce the low-cost price leadership model. With little difficulty the model can be made more realistic by changing the assumptions concerning the degree of product differentiation and the number of sellers. The following verbal treatment should be intuitively clear. When products are differentiated, the price followers face a kinked demand curve, in which the upper section is not horizontal but nevertheless quite elastic, as in Fig. 12-5 in the preceding section. Where there are more than two firms, the mutatis mutandis section of the demand curve represents the particular firm’s share of the total market when all prices are at a similar level. If product differentiation is symmetric among the products of the various firms, the shares of all firms are equal, as in the identical272

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

products case. If we let n represent the number of rival firms, then the mutatis mutandis demand curve represents 1/n"" of the total market demand at each price level. If the market divides unequally among the firms when all prices are at a similar level, product differentiation is asymmetric, and the mutatis mutandis demand curve represents a market share that may be greater or less than 1/n of the total demand at each price level. When product differentiation is asymmetric, we should expect a range of prices among rival firms, reflecting the different cost and demand situations facing each firm. Price leadership in this situation requires one slight modification to the above analysis. The price leader might adjust its price by a certain amount, and the price followers will adjust their prices by the same percentage as is represented by the price leader’s price adjustment. Thus the relative price

differentials that prevailed prior to the price changes are unchanged, and no firm expects to gain or lose sales from or to a rival. The price leader simply initiates an upward or downward adjustment in the entire price structure of that particular market. In Fig. 12—7 we show a situation in which three firms produce asymmetrically differentiated products. Firm A is the acknowledged price leader and sets price P,, selling Q, units. Firms B and C are price followers. They do not wish to initiate price adjustments, in case this precipitates active competition or a price

war, in which the low-cost firm A would have a definite advantage. Firm B’s price is above the price leader’s price, and firm C’s price is below the other two prices. Firm B’s product may be a higher quality item desired by a relatively small segment of the market. This firm’s higher cost level may be the result of higher quality inputs and more hand finishing of the product, for example. Firm C’s product is both lower priced and more expensive to produce, as compared FIGURE

12-7

Low-cost Firm Price Leadership: Two or More Firms, Asymmetric Case

$/Q

FirmA (Price Leader)

Firm C (Price Follower 2)

Firm B (Price Follower 1)

Of

Price and Output Determination in an Oligopoly

273

with the price leader’s product. The lower price might be due to the market’s

perception of an inferior location, or absence of other attributes, whereas the

higher costs may be the result of more expensive sources of inputs, inefficiencies in production, or a plant size too large or too small in view of the present output level. NOTE:

The price followers face the kinked demand curves shown because they expect no reaction from rivals for price increases, but.expect the price leader and the other price follower to match any price reductions. The price leader’s demand curve is simply the mutatis mutandis demand curve: The price leader expects the other firms to follow both price increases and price reductions. If the price leader’s costs increase, for example, it adjusts price upward along the Ds, curve. The price followers, who have probably incurred a similar cost increase, follow the lead and adjust prices upward. But for this particular price increase, they do not expect ceteris paribus; they expect (or have seen) the other firms to simultaneously adjust their prices upward. As stated earlier, the firms are likely to adjust price upward by a similar proportion, in order to maintain their relative prices and hence their market shares. In this case, however, the proportion is decided by the price leader. We see in Chap. 13 that the common business practice of markup pricing allows firms to adjust prices to cost increases by a similar proportion. We turn now to the third type of price leader.

The Dominant-Firm Price Leader. As the name implies, thedominant firm is large, relative to its rivals and its market. The smaller firms accept this firm’s price leadership perhaps simply because they are unwilling to risk being the first to change prices, or perhaps out of fear that the dominant firm could drive them out of business if it wanted to. The dominant firm could, for example, force raw material suppliers to boycott a particular small firm, by threatening to take its own (very large) orders elsewhere. In such a situation, the smaller firms accept the dominant firm’s choice of the price level; they simply adjust output to maximize their profits. In this respect they are similar to pure competitors, who can sell as much as they want at the market price. Like pure competitors, they want to sell up to the point where their marginal cost equals the price (equals marginal revenue). The dominant firm recognizes that the smaller firms behave in this manner and must, therefore, choose price to maximize its profits with the knowledge that the smaller firms will sell as much as they want to at that price.

The Supply Curve for the Small Firms. The first task of the dominant-firm price leader is to ascertain how much the smaller firms will want to supply at each particular price level. Since each of the smaller firms wants to supply up to the point where MC = MR, and since MR = P in a situation where the individual firm is so small that it does not influence market price, each of the smaller firms views its MC curve as its supply curve. At each price level the firms supply the amount for which marginal cost equals price.Itfollows that a horizontal aggregation of these curves indicates the total amount the smaller firms supply at each price level. In Fig. 12-8 we show three small firms and the marginal cost curves 274

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of each. The aggregation of the smaller firms’ marginal cost curves is depicted by SMG, To derive curve =MG,, we start by supposing that the dominant firm sets price P,. Each of the small firms subsequently expand supply to the point where its MC curve rises to the price level P,. A similar pattern is followed when the dominant firm sets lower prices, such as P, and P;. Summing the supply of the three firms at each price level, we obtain the MC, curve in the right-hand part of the figure.

The Residual Demand for the Dominant Firm.

Knowing how much the smaller

firms supply at each price level, the dominant firm can subtract this from the market demand to find how much demand is left over at each price level. This residual demand can be measured as the horizontal distance between curve MC, and market demand curve D at each price level. It is shown as the demand curve dz in Fig. 12-9. Only at prices below P, is there any demand left for the dominant firm after the smaller firms have supplied their desired amounts. At price P, there is an excess of market demand over the supply of the smaller firms, shown as the horizontal distance R, between the }MC, curve and the D curve. Similarly, the residual demand at price P, is shown by the distance R,. Shifting these residual amounts across to the price axis, we find that the dominant firm’s residual demand curve is dz. This residual demand c ount that the dominant firm can be assured of selling at each price level, since the smaller firms have sold as much as they wanted to and since thére are still buyers willing to purchase at those price levels. FIGURE

12-9

Construction of the Dominant Firm’s Residual Demand Cun

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profits from this assured, or residual, demand. The marginal sociated with the residual demand curve is shown as the

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The dominant firm’s marginal cost curve is MCp. The dominant firm, therefore, selects price Pp and output Q, in order to maximize its profits. Faced with the price Pp, each of the smaller firms produces up to the point where its marginal costs equal that price. Hence the smaller firms in aggregate produce output level Q,. Since the residual demand curve is constructed to reflect the horizontal distance between the XMC, and D curves, the total amount supplied to the market, XQ, is equal to the market demand, and an equilibrium situation exists.

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An interesting long run implication of the dominant firm price leadership model is that, if the chosen price allows the smaller firms to earn pure profits, then the dominance of the large firm is eroded over time. This is so, because in the long run the small firms expand their plant sizes in search of even greater profitability, and new firms enter the industry in search of this profitability, if the barriers to entry can be overcome. In any case, the residual demand remaining for the dominant firm, with market demand static or growing relatively slowly, must be reduced, and the price leader is thus forced to set a lower price and accept a reduced market share. Eventually, of course, the dominant firm is no longer dominant, and the system of market price determination presented above gives way to some other form of price leadership, or conscious parallelism, or independent price setting.

EXAMPLE:

A case in point is theAmerican steel industry. for 65% of American ingot U.S. Steel accounted high prices allowed entrantsto flourish.By 1915 it continued to fall to 28% in 1960 and to 21% in

According to Scherer, although , capacity in 1901 its relatively its share had fallen to 52%, and ofthis decline, result As a 1968.

Price and Output Determination in an Oligopoly

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U.S. Steel’s dominant-firm price setting behavior gave way to what appears to have been barometric price leadership and conscious parallelism.® Cartel Price and Output Determination

DEFINITION: A cartel is a group of firms acting as one, taking their orders for price or output levels from a central administering body. Cartels are illegal in most Western countries, but a couple of major international cartels continue to exist, immune from national legislation. EXAMPLE:

The International Air Transport Association, IATA, dictates airfares and many elements of non-price competition to its members, such as types of meals, beverage prices, and in-flight movie prices. During the 1970s, higher levels of excess capacity due to the advent of jumbo jets, as well as the vigorous competition of third-world airlines, reduced IATA’s market control to a significant degree. The Organization of Petroleum Exporting Countries, OPEC, undoubtedly the most powerful cartel in the late 1970s, was able to elevate the prices of petroleum products dramatically as its members jointly raised prices to the levels agreed upon. A cartel may be either profit maximizing or market sharing. The profitmaximizing cartel attempts to maximize the joint profits of the firms. The firms then take a share of the total profits as determined by prior agreement or as actually earned. The market-sharing cartel establishes rules that allow each firm to maintain its predetermined or historical share of the market. We examine here each type in turn. The Profit-maximizing Cartel. The profit-maximizing cartel has exactly the same price and output decisions to make as does the multiplant monopolist. The cartel is like the monopolist except that it does not own each of the plants; it simply controls their pricing and output decisions. As well as choosing the price and the total output level, the cartel (or multiplant monopolist) has one additional decision to make, namely, how it should divide its total output among the participating firms or plants in order to maximize total profits. The standard profit-maximizing rule—that marginal costs equal marginal revenue—is still applicable, but our interpretation of the marginal cost curve must reflect the fact that marginal costs now derive from two or more production sources. The relevant marginal cost curve must show the marginal cost for each incremental unit produced, when the cartel is free to nominate which of the firms will produce each incremental unit. Clearly the cartel will always nominate the firm that can produce the incremental unit at the lowest marginal cost. Fig. 12-11 demonstrates a simple means of ensuring this result. For simplicity we assume there are two members in the cartel. In order to make the exercise non-trivial, we assume differing cost structures for the two firms: Firm A has a higher cost structure than firm B, due perhaps to its location °F. M. Scherer, Industrial Market Structure and Economic Performance, (Chicago: Rand McNally,

1970), p. 217.

278

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

FIGURE

12-11

Price and Output Determination by a Joint Profit-Maximizing Cartel

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in an area having high land values, to some other cost disadvantage, or to the inability of this firm to achieve the same degree of production efficiency compared with firm A. The marginal cost curves of A and B are summed horizontally to find curve {MC shown in the part of the figure labelled cartel. This curve shows the combined marginal costs of the cartel; that is, for a particular output level, some part of the output is produced in firm A, and the remainder in firm B, taking care always to select the incremental unit from the firm that can produce it at the lower marginal cost. From this it follows that at any particular total output level, the marginal cost from each plant should be approximately equal. If this is not true, the last unit might be taken away from the firm with the higher marginal cost and produced instead by the firm with the lower marginal cost, thus reducing the marginal cost of the last unit produced to the cartel as a whole. The =MC curve thus shows the marginal cost to the cartel of each successive output unit, given the ability of the cartel to have that unit produced by the firm that can produce it most efficiently. The cartel’s profits are maximized at the output level where the combined marginal cost just equals the marginal revenue. This is shown as output level >Q in Fig. 12-11. The demand curve indicates that the cartel should set price P. The intersection of the SMC and MR curves indicates the level at which marginal costs are equal to marginal revenue. If we extend a line at this level across to the cost curves of firms.A and B, we see how total output {Q should be divided between the two firms. In firm A marginal costs come up to this critical level at output Q,, and in firm B they come up to this level at output Q2. Outputs Q, and * Q, together add up to XQ, by virtue of the method of construction of the curve =MC. Thus when the output =Q is divided among the firms in this way, the marginal cost of firm A equals the marginal cost of firm B. Both of these equal the marginal revenue of the final unit sold. The cartel’s profit is shown as the Price and Output Determination in an Oligopoly

279

sum of the two rectangles PABC (from firm A) and PEFG (from firm B). These rectangles show the per-unit profit margin times the number of units produced, in each of the two firms. Side Payments and the Incentive to Undercut the Cartel Price. The two member firms may agree to keep the profits they have each earned. Alternatively, there may be a prior agreement that the more-profitable firm B must give some of its profits to the less-profitable firm A. This side payment may be thought necessary to help firm A resist the temptation to undercut the cartel price and temporarily, at least, enjoy an elastic demand response for its product. In fact, both firms face the temptation of large sales gains and higher profits, if they can secretly undercut the cartel price. If either firm can set a price below the cartel price, while the other firm continues to set the cartel price, the price-cutting firm will face a relatively elastic ceteris paribus demand curve, on which there will be a lower, more-profitable price. Let us illustrate, using firm A as the price cutter in Fig. 12-12. FIGURE

12-12

The Incentive to Undercut the Cartel Price

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Initially, firm A is setting the cartel price P and producing Q, units of output. When contemplating independent price adjustments, the firm envisages the ceteris paribus demand curve shown as d. Associated with that curve is the marginal revenue curve, mr, which intersects the firm’s marginal cost curve, MC,, at output level Q’. Profits at the lower priceP’ are equal to the area P’A’B’C’ and are considerably larger than the profits PABC available to the firm as a member of the cartel. Thus there is considerable profit incentive to leave the cartel and price independently. Firm A might require a side payment equal to the difference in these two profit rectangles in order to keep it in the cartel. But notice that the firm would only earn these extra profits as long as ceteris

paribus prevailed. As soon as the other firm noticed its loss of sales and ascertained that firm A was ‘‘chiseling” the cartel price, it would probably match A’s 280

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

price reduction in order to maintain its share of the market. Alternatively, it might undercut A’s price to teach it a lesson, and a price war might ensue. The extra profits are available to firm A only as long as the price reduction remains unknown to firm B. If A is able to give customers secret discounts, and if sales normally fluctuate considerably in any case, firm B might not discover the duplicity for several weeks or months, during which time A can earn extra profits, which may be worth the risk of setting off a price war or facing other disciplinary action by the cartel. The more firms there are in a cartel, the more difficult it is, ceteris paribus, for the cartel to control prices or outputs of individual firms. The more firms the more difficult it is for cartel members to find out that they are being undercut, since the ‘‘chiseler’s’”’ sales gain is comprised of proportionately smaller sales losses for each firm. There is thus a greater inclination for individual firms to undercut the cartel price. In actual business practice, the life of cartels has usually been short and stormy, ending with a rapid decline in prices after the disA covery that one or more firms were secretly undercutting the cartel price. The Market-Sharing Cartel. In some instances, oligopolists may wish to come to an agreement regarding their share of the market as a primary objective, rather than allowing this to be the outcome of their price-fixing agreement, as in the preceding discussion. Firms that are geographically dispersed, for example, may feel that they have a right to sales in their own territory and will want to preclude encroachment by rivals into that territory. In this case, the total market would be shared on the basis of the firms’ locations and the density of population (and consequent demand) in each territory. Alternatively, firms with large output capacities may feel that they deserve a larger share of the market than would be allocated to them under a joint profit-maximizing cartel agreement. The other firms may be willing to allow these firms to take more than their (joint profitmaximizing) share, rather than risk a breakdown of the cartel’s price agreement. The agreement on market share may be quite an explicit arrangement (firm A gets 15% of industry sales) or an implicit, generally understood feeling among the firms concerning each one’s annual output levels (firm A has a quota of about 200,000 units annually). We immediately see that problems arise in business situations, since these agreements involve an estimate of annual market demand. Different conceptions of the market, different projections as to the coming year’s demand, and different perceptions of the same phenomena are likely to lead to disagreements about what constitutes a 15% share, for example. Compromises on these issues may leave some firms feeling less happy than others and perhaps more likely to violate the agreement at a later time. Similarly, agreements on the boundaries of each firm’s geographical territory may be hard to arrive at and may be quite fragile when finally made. Market-sharing agreements represent a constraint on profit maximization for all firms whose agreed market share is less or greater than the profit-maximizing market share. Firms desiring a share larger than profit-maximizing presumably want the larger share more than they want the larger profit. We saw briefly in Chap. 8 and we will see in more detail in the next chapter, that short run sales maximization, given a satisfactory level of short run profits, may lead Price and Output Determination in an Oligopoly

281

to profit maximization over the longer term. This is preferable for firms with longer time horizons. Firms whose market shares are smaller than the profitmaximizing shares receive both lower profits and smaller market shares as a result of the agreement. We might reasonably expect these firms to become disgruntled and think about cheating on the agreement. When business is booming, firms have little time or reason to think about how the market-sharing agreement puts them at a disadvantage. When market demand slackens in periods of recession or depression, however, firms are expected to be considerably more inclined to undercut the cartel price or encroach into another firm’s territory and compete for sales. Such price cutting, probably in the form of secret discounts, generous trade-in allowances, or additional goods and services for the same price, soon comes to the attention of other firms. The cartel agreement would be expected to break down as other firms begin to take defensive measures to avoid losing any more of their market shares. ‘Cartel price and market-sharing agreements might be expected to work a lot better if the participant firms have similar cost structures and either identical or symmetrically differentiated products. In such cases, a single market price and equal market shares is likely to be a relatively palatable solution to the uncertainty faced by oligopolists. When cost structures are different and products are asymmetrically differentiated (this being more likely the case), many firms may feel considerably constrained by cartel agreements; these agreements are not likely to last very long. 7

Ill. LONG RUN ADJUSTMENTS IN OLIGOPOLY With sufficient time to vary the input of all factors of production, the oligopolist may wish to adjust its size of plant to one that is more profitable, given the prevailing market demand situation and the competitive conditions in that market. Also in the long run, new firms may be attracted to enter the industry by the existence of pure profits, and will do so if they can overcome the barriers to entry, which typically exist in oligopoly markets. In oligopoly situations, the barriers are often more accurately described as ‘“‘hurdles,”’ since they do not necessarily make it impossible to enter an industry, but they merely limit the number of firms that are able to enter. Overcoming the hurdles typically involves additional operating costs, which means that many potential entrants will not enter, since they cannot foresee being able to operate profitably. The firms that presently exist in the oligopolistic market may be able to make long-term pure profits in the shelter of these hurdles. This is not to say that oligopolists always make pure profits. In declining markets, for example, firms may incur continuing losses, forcing them to exit the industry in the long run. Barriers to Entry in Oligopolies

Potential entrants to an oligopoly market face similar barriers to entry as do potential entrants to monopoly markets. There are two important differences of degree, however. First, the barriers to monopoly markets are usually insupera282

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

ble, whereas oligopoly markets can usuallybe entered if the potential entrant has the necessary information, skills, other resources, and sufficient financial support to overcome the barriers facing it. Second, potential entrants to oligopoly markets typically face a muchstronger product differentiation barrier. By this we mean the tendency of consumers to conclude that the products of the established firm(s) are probably of higher quality, more durable, more securely guaranteed, more likely to have available replacement parts and service facilities, and so on. That is, consumers are likely to distrust the new firm’s ability to provide these attributes until it has been in the industry for long enough to prove it can consistently provide them. Potential entrants to monopoly markets face this same barrier, of course, but it is likely to be mitigated by the desire of many customers for a variety of product offerings. Many customers would try the new firm’s product for the sake of variety and, in so doing, judge for themselves whether its quality, durability, guarantee, and service compare favorably with the established firm. In oligopolies there are already several different product offerings, and consumers might be more inclined to get variety by shopping around among the established sellers and by adopting a wait-and-see attitude toward the new firm. While they are waiting, of course, the new firm might go bankrupt and exit the industry, or, if it has not yet entered, it may have the prior expectation of doing so. J. S. Bain found such product differentiation barriers to be particularly strong in oligopoly markets.1° EXAMPLE:

In the North American automobile industry there has been no successful domestic entrant into the mass market for decades. The Bricklin automobile did enter the specialty market that was largely occupied by the Corvette in 1974, but the company failed in 1977 after selling only a few thousand units, many of which were sold in an incomplete state due to shortages of the necessary parts. Demand did exist for this automobile, however, largely because of its exclusivity. The failure of the firm may have been primarily due to lack of management skills. The De Lorean automobile, an even more expensive specialty sports car assembled in Northern Ireland, entered the U.S. market in 1981. This company may prove to have learned from the mistakes made by Bricklin. If new firms are able to achieve entry intc oligopoly markets and survive the initial period of probable losses while they establish themselves as a reputable, reliable firm, they then become one of the established firms and may wish

to expand their plant size as acceptance of their product grows. We turn now to the plant-size adjustments of existing firms under long run conditions. Plant-size Adjustment to Maximize Profits

Under oligopoly market conditions, the firm contemplating an adjustment of its plant size should consider the impact of this upon rivals and the consequent reactions of rivals. When firms recognize their mutual dependence, they expect 107, S. Bain, Barriers to New Competition (Cambridge, Mass.: Harvard University Press, 1956).

(July 1977), “1P, Bedard, “John De Lorean Builds a Sports Car: The DMC-12,” Car and Driver, 23 37-46. Also, D. Sherman, “De Lorean,” Car and Driver, 26 (May 1981), 41-48. Price and Output Determination in an Oligopoly

283

rivals to either react or not react to a price change that may be necessary for profit maximization, given the new cost structure associated with a new plant. In the kinked demand curve model, the firm may wish to adjust to the plant size that produces its current output level at minimum per-unit cost. If either upward or downward price adjustments are rendered undesirable by the probable reactions of competitors, the firm may elect to leave price undisturbed and maintain its market share. It should, however, attempt to produce that output at lowest possible cost. In Fig. 12-13 we show the plant-size adjustment for a particular firm tad facing a kinked demand curve. FIGURE

12-13

Plant-size Adjustment in the Kinked Demand Curve model

We depict the firm as initially setting price P and producing output level Q in the plant shown as SAC. The average cost per unit is shown as the point E. This is not the minimum cost of producing output level Q, because this point does not lie on the long run average cost (LAC) curve. By building the plant size that has its short run average cost curve tangent to the LAC curve at output Q, the firm can minimize its average cost of producing that output level. We show the optimal plant size as SAC*, where per-unit cost is reduced to that shown by the pointE’. Notice that the associated marginal cost curve (MC*) passes through the gap (BC) in the MR curve. Thus the present price and output level are still profit maximizing. In other cases it is profit maximizing to change plant size and subsequently change price as well, notwithstanding the reactions of rivals. In Fig. 12-14 we show such a case. Suppose the firm initially sets price P and produces Q units of output. When contemplating the adjustment of plant size, the firm notes that the LMC curve does not pass through the gap in the MR curve, shown as BC. Instead, 284

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

the LMC curve intersects one of the solid portions of the MR curve at point C’ at output level Q’. By building the plant that minimizes the cost of producing Q’ (represented by curve SAC*) and by reducing its price to P’,the firm can increase | its profits substantially. Notice that this happens regardless of the fact that all rivals are expected to match the price reduction fromP to P’, in order to maintain their shares of the market. FIGURE

12-14

Plant-size Adjustment and Subsequent Price in the Kinked Demand Curve Model

Thus the oligopolist under long run conditions chooses the plant size for which long run marginal cost equals marginal revenue, or comes closest to equalling it when MC passes through the MR gap. In some cases, perhaps most, this does not necessitate a price adjustment, if the LMC curve already passes through the MR gap. If the LMC curve cuts a solid part of the MR curve, the firm adjusts its plant size and price so that the LMC curve passes through the gap. If this causes other firms to match the price adjustment, as in the example above, then the general price level changes, but market shares remain the same. If other firms do not follow the price adjustment, then the firm changing price experiences a change in its market share.

DEFINITION: The full capacity output rate is usually considered to be that rate where short run average costs are minimized.!? 12The firm can produce up the right-hand side of its SAC curve, of course, and is then said to be producing at a rate above full capacity. Inability to supply any more output is reached when the SAC curve becomes vertical on the right-hand side. Long before this, however, the SMC curve would have been vertical and would probably have necessitated a price increase to stem demand to profit-maximizing levels. Price and Output Determination in an Oligopoly

285

Operation at Less than Full Capacity. One can predict that oligopolists will wish to build plants that operate at less than full capacity. Notice that in both Figs. 12-13 and 12-14, the firm moved to a plant size that it operated at an output rate less than that which would minimize unit costs for that plant. That is, it operates the plant at an output rate to the left of the lowest point on the SAC* curve. Hence the firm has constructed excess capacity in building the plant size that maximizes profits in the long run. Oligopolists are expected to want this excess capacity for the following reasons. First, giyen the time lag involved in changing plant size, excess capacity allows the firm to respond to shifts in the demand curves or to match rivals’ price cuts without losing market share due to its inability to expand output further. Second, the firm prefers to have excess capacity in case of a breakdown or other work stoppage, in which case it can produce at or above full capacity in order to replenish its inventories, catch up on its orders, and so forth, rather than lose these sales to rivals.

We could continue to show the plant-size adjustments for oligopolists operating under other assumptions regarding their conjectural variations, but this is not necessary, since most of these cases follow quite readily from the kinked demand curve case. Anyway, I am sure that by now you can do it by yourself.

IV. ECONOMIC EFFECTS OF OLIGOPOLY The economic effects of oligopoly that have an impact on the welfare of society are essentially the same as those of monopoly and monopolistic competition; the differences are largely of degree. We saw that monopoly causes price to be higher, total output to be lower, and costs to be higher, as compared with the pure competition situation. We saw that monopolistic competition requires con-

sumers to pay more for differentiated products, which are produced in smaller, less-efficient plants by more firms, although total output would be less, as compared with pure competition. In monopoly the adverse effects are the result of

barriersto entry, whereas in monopolistic competition the adverse effects result from product differentiation. In oligopoly wetypically have both, with few firms

protected by at least partial barriers to entry and with products that are typically

differentiated. It is the combination of these features that is responsible for the

economic effects of oligopoly. The Effects of Fewness

In an oligopoly market the firms are few in number, tending toward the monopoly end of the spectrum in terms of the number of competing firms. Like a monopolist, oligopolists are able to set price above average costs in the long run due to barriers to the entry of new firms. How much the price may be held above average costs depends upon the height of the barriers to entry and the ability of the firms to coordinate their actions. The height of the entry barriers can be measured by the per-unit cost advantage that existing firms would have over entrant firms if the latter were to enter. Existing firms may set price above their costs to the extent of this cost advantage without attracting new firms. 286

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

But notice that oligopolists can only set price above costs when they share an understanding to avoid price cutting for short-term gain. If the firms completely coordinate their actions, they may set price all the way up to the monopoly price. Recall that a cartel is a group of firms acting like a monopoly. Lesser degrees of coordination, such as price leadership and conscious parallelism, may also allow the price to be raised to the monopoly level. In all likelihood, however, the firms would be uneasy about such a high price level, since the incentive for individual price cutting would be great. Most firms tend to prefer stability and reduced uncertainty to instability and increased uncertainty, and would therefore be willing to forego some margin of profits for the greater likelihood of price and output stability at a price below the monopoly price level. Oligopoly, therefore, allows firms to raise price to or near to the monopoly price level, if the barriers to entry are high enough and if the firms are willing to coordinate their actions in order to maximize joint profits, rather than attempt to maximize individual profits. The fewer are the oligopolists, the easier it should be for these firms to arrive at and maintain a collusive price-fixing agreement. Although such price-fixing agreements are typically illegal, it is often difficult to prove that an agreement exists. Oligopolists practicing price leadership (and followership) or conscious parallelism, for example, are unlikely to have any explicit agreement concerning the coordination of their behavior. Rather, these firms are likely to have an implicit understanding about each others’ “‘appropriate” behavior. The fewness of oligopolists thus has a direct impact on the prices of goods and services and an indirect cost to society, as a result of the resources allocated to the surveillance of oligopolies by individuals and agencies, in order to ensure that these firms adhere to the legislative requirements concerning their pricing and other market behavior. The Effects of Product Differentiation

In the next chapter we see that oligopolists often turn to nonprice competition as a strategic variable, since price adjustments may be expected to start price wars and to increase uncertainty about market shares and profits. Since oligopolists allocate resources toward differentiating their products and toward informing and persuading consumers that their products are different, we should ask whether this activity has any negative implications for society’s welfare. We saw in the case of monopolistic competition that product differentiation imposes a cost on consumers, as compared with undifferentiated products. The same holds true for oligopoly. There are additional costs to society or resources being wasted, due to their mutually offsetting impacts in the market place. It can be argued that oligopolists tend to spend excessive amounts on advertising and promotional efforts in the short run. These expenditures may be excessive in the sense that some part of these expenditures is wasted, being offset by the expenditures of rival firms. As oligopolists bombard their markets with messages about their products, the claims and counter claims of the firms tend to nullify each other to some extent, and may add nothing to the consumer's Price and Output Determination in an Oligopoly

287

understanding of the products’ virtues (or vices). To the extent that these efforts to differentiate the products do offset and nullify each other, resources are being wasted. These resources have an opportunity cost to society, since they could have been used elsewhere for public or private benefit. Even if the oligopolist recognizes that some part of its product differentiation efforts are wasted from a social viewpoint, it will not wish to reduce its expenditures in this area unless all rival firms similarly reduce their own product differentiation expenditures. To do so unilaterally would cause the oligopolist to lose part of its market share, since Such expenditures are a shift parameter in the firm’s demand function. Reducing promotional expenditures, for example, allows rival firms’ messages to gain an advantage, and some consumers would switch over to rival products. Thus the oligopolist is in the situation where it must waste resources in order to maintain its market share and profitability. This, unfortunately, imposes a cost upon society, which is traceable to the differentiation of products and to the fewness of firms in oligopoly. Other Effects of Oligopoly To a large extent the oligopolist is free from the intense day-to-day pressure of competition faced by the firm operating under pure or monopolistic competition. We have seen that this pressure, supported by the threat of entry in the long run, forces firms to be as efficient as possible. We noted that the monopolist might allow X-inefficiency to persist, due to the absence of this pressure. Oligopolists may similarly be permitted to indulge in a little X-inefficiency. Thus the cost of production might not be pressed to the absolute minimum for each output level; workers may be permitted some discretion concerning working hours and conditions, and managers may make expenditures on items that are not essential for production, but that do contribute to the comfort or prestige of management. This X-inefficiency imposes an opportunity cost on society, since the resources used inefficiently may have been used elsewhere in society for greater social benefit. On the positive side, oligopolists are likely to undertake substantial research and development expenditures, with subsequent beneficial impacts on employment, production efficiency, economic growth, and consumer satisfaction. Oligopolists typically are financially able to undertake R and D programs, since they are usually able to earn pure profits in both the short and long run. Moreover, oligopolists are highly motivated to undertake R and D programs, as a result of their mutual dependence in their markets. Since price competition is potentially dangerous in oligopoly, the firms tend to compete in nonprice areas. One area of nonprice competition is product design. R and D expenditures assist the firm in discovering the wants and needs of consumers and in designing and manufacturing new and improved products. R and D expenditures may also allow firms to discover new production processes and raw materials, which would reduce the firm’s cost of production, a critical factor in profitability when price adjustments are constrained. Thus oligopolists are motivated to conduct R and D programs and these, in turn, are expected to produce economic benefits for the oligopolist itself and for society as a whole. 288

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Whether or not oligopolies are beneficial or detrimental to social welfare is an academic issue, since the great majority of markets are oligopolies, and it would appear impossible to convert them to a more socially desirable structure, even if such a structure could be ascertained unambiguously. It is, however, important to see that each market structure does have positive and negative implications for several economic variables, these including, in particular, the price level, per-unit costs, production efficiency, and technological improvements.

SUMMARY In this chapter we discussed the mutual dependence of oligopolists in their markets and noted that the recognition of this mutual dependence necessitates a change in the conjectural variation assumption. The kinked demand curve model explains price rigidity and subsequent price adjustments on the basis of the two-way conjectural variation that rivals will ignore price increases but match price reductions. Joint action by oligopolists, through conscious parallelism, price leadership (and followership), and cartel pricing, allows the firms to raise their prices without sacrificing market share. Conscious parallelism is the joint adjustment of prices in response to some common stimuli, with the expectation that all rivals are to proceed similarly. Price leadership may be of the barometric, low-cost, or dominant-firm type, and

it involves one firm taking the initiative and the risk of independently adjusting its price, with the expectation that competitors will follow suit. A cartel, which is a group of oligopolists acting like a monopolist, may attempt to maximize joint profits and share these profits in some way or, alternatively, share the market in some predetermined way. Cartels, which are illegal in most Western economies, may be seen in international business. They tend to have a short and turbulent life, due to the inherent conflicts of members. Long run plant-size adjustment in oligopoly and the economic effects of oligopoly were examined. For the most part, this discussion is a simple extension of the reasoning expounded in earlier chapters in the context of other market forms. The economic effects of oligopoly are similar to those arising in monopoly and monopolistic competition and are, similarly, a result of barriers to entry and product differentiation.

DISCUSSION

QUESTIONS ®

1.

Discuss the impact that recognition of mutual dependence has upon the conjectural variation assumption in oligopoly models.

2.

Ifthe kinked demand curve model is not a theory of price determination, what is it a theory of?

3.

Explain the mutatis mutandis demand curve. Why does it, of necessity, have a steeper slope than the ceteris paribus demand curve? Price and Output Determination in an Oligopoly

289

4.

What factors determine the length of the gap, or vertical discontinuity, in the marginal revenue curve? Construct a graph in which the gap extends below the horizontal axis. Then explain why you would expect this firm never to wish to reduce price, regardless of how much costs fell per unit.

5.

Explain the notion of conscious parallelism. Categorize this in terms of price leadership and price followership—which firms are price leaders and which (if any) are price followers?

6.

Discuss the concept of barometric price leadership. What qualities is the barometric firm likely to possess?

7.

Why are the other firms likely to follow the price leadership of a low-cost or dominant-firm price leader? Is it solely due to the threat of reprisals if they don’t? Does price followership save the firms anything?

8.

Explain the residual demand curve that is faced by the dominant-firm price leader. How is it constructed?

9.

Discuss the operation of a profit-maximizing cartel. Why are side payments often necessary? How large do these side payments need to be?

10.

Explain graphically the long run plant-size adjustment decision for a dominant firm price leader. (Suppose that the dominant firm is able to foresee the entry of new firms at the time of making its decision.)

SUGGESTED BAIN, J.S.,

REFERENCES ‘‘Price Leaders, Barometers, and Kinks,” Journal of Business, 33 (July 1960),

193-203.

BAIN, J.S.,

1956).

Barriers to New Competition (Cambridge, Mass.: Harvard University Press,

FELLNER, W.,

Competition among the Few. New York: Knopf, 1949.

HALL, R.L., and C.J. Hircu, ‘Price Theory and Business Behaviour,’ Oxford Economic Papers, May 1939, pp. 12—45. HAMBURGER, W.,

‘‘Conscious Parallelism and the Kinked Oligopoly Demand Curve,”

American Economic Review (May 1967), pp. 266-8.

KOUTSOYIANNIS, A.,

Modern Microeconomics (2nd ed.). London: Macmillan, 1979.

MarKHAM, J.W., “The Nature and Significance of Price Leadership,” American Economic Review, Dec. 1951, pp. 891-905. SCHERER, F.M., Industrial Market Structure and Economic Performance, Chicago: Rand McNally, 1970.

chaps. 5, 6.

SMITH, D.S., and W.C. Neate. ‘‘The Geometry of Kinky Oligopoly: Marginal Cost, The Gap, and Price Behavior,” Southern Economic Journal, January 1971, pp. 276-82. STIGLER,G.J., ‘“The Kinky Oligopoly Demand Curve and Rigid Prices,” Journal of Political Economy, October 1947. SWEEZY,P.M.,

‘‘Demand under Conditions of Oligopoly,” Journal of Political Economy,

1939, pp. 568-73. Augus t

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THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

Further Topics in Oligopoly Markets

|

1. INTRODUCTION In this chapter we examine three special topics concerning the behavior of firms in oligopoly markets. First we consider several models of oligopoly behavior that depend on different assumptions concerning the firm’s objective function. The traditional objective function—maximization of short run profits—is particularly inappropriate for oligopolists, since these firms should be sensitive to the impact of their pricing policy upon existing rivals and potential rivals (new entrants). The profit-maximizing price in the short run could lead to a substantial reduction in market share and induce the entry of new firms in the long run. We should expect oligopolists to be concerned with profits over a longer period than the short run. Let us, therefore, examine long-term profit maximization as the firm’s objective function. Under this heading we look at several short run objective functions that provide an operational means of approaching the goal of long-term profit maximization. These include the maximization of net present worth,

sales maximization,

limit pricing, growth maximization,

maximization of managerial utility, and ‘‘satisficing.”’ The second major topic of this chapter concerns oligopoly pricing under uncertainty. Without full information as to the slope and placement of its cost and demand curves, the firm has, in effect, two choices. One, it may incur search costs to obtain this information and then proceed with its pricing and other competitive strategies on the basis of its estimated cost and demand functions. 291

Alternatively, if it feels that the cost of the information is likely to exceed the extra revenue to be generated as a result of full information, it will use an alternative decision rule for its pricing decision. A commonly used decision rule is markup pricing, whereby a percentage markup is added to some measure of costs to obtain the selling price. Although a crude means of determining the price level, it does avoid search costs and is simple to apply. When you consider that many firms have literally hundreds or even thousands of different products, it should not be surprising that firms decide to avoid the search costs of estimating hundreds (or thousands) of separate demand and cost situations and instead opt for the more expedient markup pricing rule. We shall see that the markup can be adjusted to be profit maximizing and, moreover, that it serves as a means of coordinating price changes and adjusting for the effects of inflation. The third major topic of this chapter is nonprice competition. By this we mean the utilization of strategic variables other than price, but particularly advertising and promotional efforts. Adjustments to these strategic variables cause a shift in the demand curve, and thus allow the firm to sell more units of its product at the prevailing price level. Oligopolists, aware of the dangers of price wars in their mutually dependent market situations, often prefer nonprice competition, since it provides a less dangerous outlet for their competitive urges. Advertising and promotional competition, unless it is offensive in some way, is expected only to shift the demand curve to the right. It does not involve the risk of loss of sales revenue or market share. Each oligopolist in the market is motivated to engage in nonprice competition as an aggressive strategy to increase sales at the current price level. But there is a defensive element in nonprice competition as well. The consumer is bombarded with informational and persuasive messages about the products of each firm, and if one firm were to reduce its nonprice efforts, at least some consumers would switch to rival products as the result of the continued advertising and promotional efforts of rival firms. Thus the oligopolist may find itself on an advertising and promotional treadmil1: It must keep running to stay in the same place. We shall consider whether oligopolists should explicitly recognize this problem by agreeing to coordinate their advertising and promotional efforts. We shall also investigate the benefits of these efforts as an investment in the future and as a means of raising the barriers to entry.

Il. LONG-TERM PROFIT MAXIMIZATION The assumption of short run profit maximization is appropriate for cases of pure competition and monopolistic competition, where entry of new firms is unrestricted, and also for pure monopoly, where entry is typically impossible. In oligopoly, however, while entry is not unrestricted, neither are the barriers to entry insurmountable. Hence if oligopolists set too high a price, this may induce entry of firms that expect to make profits at that price level. After entering, these

292

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

firms will take a share of the market in all future periods. This in turn dilutes future profitability of the established firms. If the time horizon of oligopolists extends beyond the current time period, we should expect them to wish to prevent this dilution of profits by setting prices that do not attract new competition. We do have reason to expect oligopolists to be concerned with their profitability in future periods. By definition, these firms are large relative to their markets, and in most cases this makes them large in absolute terms as well. This in turn usually leads to their taking on corporate form, in order to raise sufficient capital as they expand and to allow individuals to avoid the risk of having “all their eggs in one basket.”’ The diversity of ownership involved in most corporations means that the control of the firm is typically entrusted to a small group of managers who are responsible only indirectly to the owners. The managers receive salaries and only have a direct interest in profits to the extent that they are also shareholders or that they receive bonuses that depend on profits. But the future of the managers depends to a substantial degree upon the future of the corporation. If it prospers and grows over time, their reputations and salaries would be expected to grow commensurately. If its market share dwindles due to the incursion of new firms, then the reputation and tenure of the managers is placed in jeopardy. It is thus reasonable to expect that, especially where there is separation of ownership and control, oligopolistic firms will forego short run profit maximization in favor of their continued existence and profitability over the longer term. Long-term profit maximization does not mean the maximization of the absolute number of dollars profit from now to eternity. First, we need to establish what is meant by long term: Here it means the period of time from the present to the end of the firm’s time horizon. The firm’s time horizon is the end of the firm’s planning period, the point in the future after which the firm does not consider the outcomes of its current decisions. For example, a firm might contemplate expansion and base its decision on its estimates of demand and competition from rivals in each of the next ten years, ignoring the eleventh and subsequent years’ outcomes. That firm’s time horizon is thus ten years. Other firms may have a twenty- or thirty-year time horizon, whereas some firms, for various reasons,

may plan over only the next three or five years. Second, we should recognize the time value of money. When considering profits earned at various points in time, it is important to distinguish between profits received immediately and those received at some later date. A dollar received today is worth more than a dollar received next year, which in turn is worth more than a dollar received the following year. The reason for this is that a dollar held today may be deposited in a bank or used to purchase an interestearning security. At the expiry of one year it will be worth the original dollar plus the interest earned on that dollar. Hence if the interest rate is, let us say, 10%, a dollar today will be worth $1.10 one year from today. Looking at this from the reverse aspect, a dollar earned one year from today is worth less than a dollar that is held today. Hence future profits must be discounted by the interest this money could have earned had it been held today. When considering the dis-

Further Topics in Oligopoly Markets

293

counted value of a sum of money to be received in the future, we call this discounted value the present value of that sum of money.’ DEFINITION: Thus long-term profit maximization should be interpreted to mean the maximization of the present value of the firm’s profits over the period extending from the present to the firm’s time horizon. Maximization of Net Present Worth

a

\

Maximizing the present value of profits effectively maximizes the firm’s net present worth. The firm’s net worth is the excess of its assets over its liabilities. Extending this concept over the firm’s time horizon, during which assets are acquired and liabilities retired, means that the firm’s net worth, in present-value terms, is maximized when the present value of the firm’s profit stream is maximized. Now how does the firm set about doing this? In theory, the firm would consider various price levels for each time period up to its time horizon and form an expectation of demand at each price level for each period. This would need to take into account the loss of sales to new entrants, which may occur at some price levels, and the impact of expected changes in other variables, which are expected to influence the sales of the firm’s products in future periods, such as population, incomes, consumer preferences, and prices of competing products. On the cost side, the firm must estimate changes in relative factor prices and in the state of technology, such that it can estimate its marginal cost of production at all output levels in each future period. After carefully estimating each possible revenue situation and the associated cost position, the firm would (for each future period,) choose the prices, outputs, and cost structures that would allow the maximization of net present worth or the excess of revenues over costs, each in present-value terms. It is immediately evident that long-term profit maximization requires a crystal ball to allow the future cost and demand situations to be foreseen and estimated. Even if it were possible, the costs of gathering the required information and data under real world constraints would likely too far exceed the benefits of having the data. In fact, business firms often adopt a concrete short run 1The formula to calculate the present value of a future sum of money is PV =

FV

(1 +r)!

Where PV is present value, FV is future value (the sum to be received), r is the opportunity rate of interest (the opportunity discount rate), and t is the number of years hence that the sum is to be received, In Chaps. 16 and 17 we deal with this concept in considerable detail in the context of investment decisions involving cash flows in the present and future time periods. ?Net present value or net present worth is the sum of all future revenues in present-value terms, less the sum of all future costs in present-value terms. It can be expressed as NPV

=

ices a

R; rs C;

where R,, C; are revenues and costs in the t® period, and > symbolizes the sum of the variables over

all pPenlodsyb =) 12 onnmemn

294

nn:

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS ¥

policy which they anticipate will lead to the approximate maximization of their net present value, without the attendant search costs and day-to-day surveillance necessary to achieve their objective completely. Such ‘‘proxy”’ policies for long-term profit maximization are usually simple to administer and involve Little search cost. We turn now to one of the most commonly used proxies for longterm profit maximization—sales maximization in the short run, subject to a minimum profit requirement. Sales Maximization with a Minimum-profit Target

W. J. Baumol has suggested that the appropriate objective function for many firms is the maximization of sales in the short run, subject to the attainment of a certain minimum-profit level. First let us consider the minimum-profit requirement, which is necessary for two main reasons. A certain minimum profit must

be forthcoming to allow payment of dividends sufficient to prevent shareholders from becoming disgruntled and voting for a new board of directors. Secondly, the value of the firm’s shares on the stock exchange depends, in part, on the current profitability of the firm, since the expectation of dividend payments has a positive influence on the market value of the shares. If, due to low current profits, the shares become undervalued in view of the firm’s longer term prospects, the firm may be subject to a takeover bid by another firm, which again involves the risk that managers might lose their jobs. Hence managers are motivated to keep profits at a level sufficient to stave off these two possibilities, while making sure that profits are not so large as to attract the entry of new firms. Once having determined the minimum acceptable, or target, level of profits, the firm’s objective is to maximize its sales subject to this profit constraint. We can show the sales maximization decision on the same graph as for short run profit maximization. In Fig. 13—1 are displayed the familiar total revenue and total cost curves, with the profit curve indicating the excess of total revenue over total costs at each output level. Suppose that the minimum profit constraint is the vertical distance indicated by O07*. The profit constraint is satisfied anywhere between output (sales) levels Qo and Qs, but sales are maximized, subject to this constraint, at output level Q,. It is clear that this output level is larger than the short run profit maximizing output level Q,, and that it must be offered at a lower price than the short run profit maximizing price, since the firm faces a negatively sloped demand curve. But why is the maximization of sales in the short run a proxy for the maximization of longer term profits? The lower price level compared with the short run profit-maximizing price, has three major implications for future profits. First, it tends to inhibit the entry of new firms, whose costs may exceed that price level due to the extra expenses associated with overcoming the barriers to entry. Second, it introduces more customers to the product and thus operates to gain more repeat sales in future periods, due to the goodwill and brand loyalty that 3W.J. Baumol, Business Behavior, Value, and Growth, (New York: Harcourt Brace Jovanovich, Inc.,

1967).

Further Topics in Oligopoly Markets

295

FIGURE 13-1 Short Run Sales Maximization Subject to a Minimum Profit

develops over time as customers use the product. This cultivation of consumer loyalty and goodwill acts to raise one of the barriers to entry, since a potential entrant firm would need to spend even more on advertising and promotion to induce customers to try their product. Third, increased sales in the short run provide a larger base for complementary sales over the longer term. EXAMPLE:

This is particularly important in the market for some durable consumption goods, such as automobiles and cameras, where apparently quite lucrative markets exist for specialized replacement parts and accessories. A policy of sales maximization in the short run thus operates to inhibit the entry of new firms and to generate future sales of the firm’s product(s). The resultant profit stream probably comes reasonably close to that which could be attained by the present-value calculation for long-term profit maximization, given that there are likely to be considerable search costs associated with obtaining the information necessary to make that calculation. Sales maximization is a relatively simple and inexpensive rule-of-thumb procedure that can be applied in each period. It thus obviates the cost, effort, and uncertainty associated with the continual recalculation of a price that would maximize the present value of the expected profit stream. The sales-maximizing price is always lower than or, at the worst, equal to the profit-maximizing price. From Fig. 13—1 you will appreciate that quantity demanded Q, must be priced at a lower level than quantity Q,, because it represents a point farther along the TR curve and hence farther down the demand curve. In Fig. 13-2 we show the same initial situation, but also indicate that there has been a shift in the demand curve causing the TR curve to fall to TR’. Given the same cost curves, the profit-maximizing output level falls to Q*, at which point profits are just equal to the minimum-profit requirement or target

296

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

profit. In this case, the sales-maximizing price (subject to the attainment of the target profit) is the same as the profit-maximizing price. FIGURE

13-2

Sales Maximization When the Target Profit is Also the Maximum Profit Attainable

$

NOTE:

Thus as long as the profit curve, 7, rises above the profit target line (7*), the sales-maximizing price is lower than the profit-maximizing price. In the event that the target profit is just barely attainable, the two prices are the same. Moreover, if the target profit is not attainable due to current demand or cost conditions, the two prices are still the same, because the firm’s profit-maximizing price (where MC = MR) minimizes losses and therefore allows the firm to come as Close as possible to the target profit. In effect, the firm’s priority shifts to attaining the target profit, and sales volume (or market share) becomes a secondary consideration.

Limit Pricing to Deter Entry DEFINITION: The limit price is the price that is not quite high enough to induce the entry of new firms. Limit pricing is a second policy that may be regarded as a proxy for long-term profit maximization. In many cases an entrant firm is expected to have higher costs than existing firms, due both to its probable smaller scale of operation and the additional product differentiation expense it must incur to offset consumer loyalty to existing products. Thus the established firms, perhaps at the suggestion of a price leader, choose a price that does not allow the potential entrant to earn even a normal profit at any output level. In Fig. 13—3 this price is shown as P,, which is lower than any point on the potential entrant’s short run average cost curve, SAC,. The demand curve D should be interpreted as the

mutatis mutandis, or share-of-the-market, demand curve of one existing firm. Further Topics in Oligopoly Markets

297

Given that the existing firm does not wish to set a price above P,, it faces, in

effect, the kinked demand curve P, AD. Its profit-maximizing output, subject to the self-imposed constraint, is thus Q, where marginal cost and marginal revenue come nearest to being equal. The marginal revenue curve (not shown in Fig. 13—3) would be coextensive with the line P,A up to output level Q, and would then show a vertical discontinuity to below the quantity axis, since it relates to the section AD of the demand curve for output levels greater than Q. *

\

FIGURE 13-3 Limit Pricing to Deter the Entry of a High-cost Firm $/O

D (Mutatis mutandis)

Since the price set by the existing firms is less than the expected minimum per-unit cost of potential entrant firms, new firms will not enter, and the existing firms’ future market shares and profitabilities are therefore protected from incursions, from this quarter at least. Pursuit of a limit-pricing policy is therefore— like sales maximization—a relatively simple short run means of approximating a long-term objective. This is not to say that entry will not occur, since there may well be entry of a new firm if existing firms incorrectly estimate the costs of the potential entrant, if the new firm employs the latest technology while existing firms continue to use older, less-efficient plants, or if the entrant firm is prepared to take a loss for a protracted period while gaining a foothold in an expanding market. Deterring Entry of a Low-cost Firm. There is another limit-pricing model for the case in which the potential entrant has access to the same technology and factor markets and hence is expected to have the same or lower cost structure, compared with each of the existing firms. In this case, there is no point in pricing below the new entrant’s costs, since all firms would make losses. Instead the firms should choose a price such that the extra quantity supplied due to the entry of another firm would cause the market-clearing price to be depressed below the level of cost for all firms. The prospect of losses thus prevents the potential en298

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

trant from actually entering, unless it expects market demand to expand over time or expects existing firms to reduce their output levels so that price is not depressed below costs.* In Fig. 13-4 we demonstrate the limit price that deters entry of a potential entrant that has costs equal to or lower than existing firms. The market demand curve is shown as D, and the potential entrant firm’s long run average cost curve is shown. To simplify the figure, the existing firms’ mutatis mutandis and ceteris paribus demand curves are not shown. Suppose that the existing firms follow a price leader and establish the market price shown as P,. At this price they collectively supply =Q units to the market. Note that this means that all buyers willing to pay at least price P, for the product (that is, those above pointA on the demand curve) have been able to obtain the product. FIGURE 13-4 Limit Pricing to Deter the Entry of a Low-cost Firm $/Q

LAC

(entrant firm)

D (Market demand)

Q

The strategy for deterring entry requires the existing firms to make known the threat that, if a new firm enters, the existing firms will maintain their output levels at the current levels, or £Q in aggregate. Thus the new firm’s output would be additional to =Q and could only be sold at a lower price. In effect the new firm would be looking at the market demand curve below pointA. This is the residual demand left for the new firm after the existing firms have supplied XQ units to the market. Shifting this residual section (AD) of the market demand curve over to the vertical axis, we have the demand curve dr that is faced by the potential entrant firm. Now we see why P, is the limit price: There is no part of the residual demand curve dr that lies above the potential entrant firm’s LAC curve. Thus the entrant could not make a profit at any output level.

NOTE:

The limit price to deter the entry of a low-cost (or lower cost) firm is, therefore, the price that causes the residual demand curve to lie everywhere below the 4F. M. Scherer, Industrial Market Structure and Economic Performance, (Chicago: Rand McNally,

1970), pp. 225-30.

Further Topics in Oligopoly Markets

299

potential entrant firm’s LAC curve. There is then no plant size the entrant can select that would allow normal profits. Notice, however, that the deterrent to

entry is simply the threat that existing firms will maintain their output levels and let the new firm’s output cause the market price to fall to a lower level until demand equals supply. But at this lower price level, existing firms do not make profits either, since they have no cost advantage over the entrant. It is clear that if the new firm actually does enter the market, the established firms would be better off to reduce their output levels (and market shares) and have the price leader choose a price that would allow all firms to make at least normal profits. Thus if a potential entrant firm ‘‘calls the bluff” of the existing firms and does enter the market, the firms would be better off to reduce their output levels,

despite their earlier threats, and to follow their price leader to a new price level that is acceptable to all. The potential entrant who foresees this and who, in any case, expects to incur losses initially, might not be deterred at all. Other Objective Functions: Growth, Managerial Utility, Satisficing

More recently there have been developed several managerial and behavioral models of business firm behavior, following Baumol’s break with the traditional profit-maximizing assumption with his sales-maximization hypothesis. Following Baumol’s managerial emphasis, it has been postulated that managers of firms wish to maximize the rate of growth of the firm or, alternatively, that they wish to maximize managerial utility. The behavioral model of the firm depicts the firm as simultaneously monitoring several different objectives and being satisfied to attain predetermined targets in each area. Each of these models can in some way be related to the basic objective of maximizing profits over the longer term. Let us look briefly at these models in turn.

Maximization of the Rate of Growth. Considerable attention has been directed to the theory of the firm under the assumption that the firm wishes to maximize the rate of growth of its assets or net worth.’ In pursuit of this objective, the firm reinvests its profits or borrows in order to expand its facilities, to takeover or merge with rivals or firms in other industries, and to expand in one way or another its market share and capital base. Since the major part of a firm’s new investment funds come from internal sources—primarily undistributed profits—growth maximization requires a ready supply of profits. But since growth is desired over a protracted period, longer term profits are preferred over profits that may be short-lived. High short-term prices and profits tend to attract price competition from rivals and the entry of new firms. Since a constant or increasing market share is important to support the growth of the firm, prices and profits should be kept below the short run profit-maximizing level, in order to preserve or increase the firm’s market share and ensure a continuing stream of profits over the longer term. It can be argued, therefore, that pursuit of growth maximization, SE. Penrose, The Theory of the Growth of the Firm, (Oxford: Oxford University Press, 1959), and R. hela “A Model of the Managerial Enterprise,”’ Quarterly Journal of Economics, 77 (May 1963), —209.

300

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

under some conditions at least, results in an outcome similar to what would be

achieved by attempting to maximize long-term profits.®

Maximization of Managerial Utility. Another objective function proposed in an oligopoly model is that firms operate to maximize the utility of the managers.’ Managers may derive utility from a quiet life, high managerial salaries, material comforts, the goodwill of customers and the general public, and other factors. The firm’s continuing existence and market standing require continuing public goodwill. The preference of some managers for the quiet life may inhibit the firm’s propensity to be continually seeking higher profits in the short run, which may induce entry. In effect, firms do what they do in the short run, because they expect their present actions to enhance profits some time in the future. A firm that makes a charitable donation, contributes to a political campaign, installs antipollution equipment voluntarily, or refrains from a price rise at the suggestion of government officials is no doubt thinking of the public relations impact of its actions, which in turn will influence the future profitability of the firm. Satisficing. Perhaps the most empirically supportable contention is that the objective of the firm is not to maximize any single variable, but rather to achieve satisfactory levels of performance, or targets, in a number of variables, which include the production, sales, market share, profits, and inventory levels. This “satisficing’’ theory of the firm® is based on the proposition that firms face considerable uncertainty as to costs and demands even in the short run, and that

firms adjust prices, promotional expenditures, and other variables whenever it appears that one of their targets is not going to be attained. Once the profit target is met, for example, managers apply their efforts to satisfying the next constraint that has not yet been met, on the basis of their imperfect information systems and their imperfect expectations of the impact of the adjustments they make. In effect, satisficing managers appear to act by short run criteria designed to ensure the continued existence and maintained market standing of the firm they control. The satisficing model of firm behavior is, in effect, an extension of Baumol’s sales-maximization model, if we accept that a minimum-profit target is the firm’s first objective. After attaining this minimum-profit level, the firm might pursue a target market share. Having attained this target, it might pursue a target inventory to sales ratio, and so on. In fact, all these targets are simultaneously monitored and attention is directed primarily to whichever of these targets might seem to be in jeopardy at any particular time. The targets themselves, or aspiration levels, are set by management consensus and usually reflect past achievements plus an additional margin to act as an incentive for improved performance. Thus the targets, or aspiration levels, may be consistently revised up6J.H. Williamson, “Profit, Growth, and Sales Maximization,” Economica,

33, no. 129 (1966), pp.

1-16.

7H.A. Simon, “Theories of Decision Making in Economics and Behavioral Science,” American Eco-

nomic Review, 57 (March 1967), pp. 1-33. 8R.M. Cyert and J.E. March, A Behavioral Theory of the Firm (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1963). Further Topics in Oligopoly Markets

301

ward, as the firm becomes more and more efficient in its operation. R. H. Day has

argued quite plausibly that this continued revision of aspiration levels can mean that a satisficing strategy eventually converges on the long-term, profit-maximizing strategy.

Agency Costs and the Theory of the Firm

The most recent major development in the theory of the firm involves the incorporation of elements of agency theory, the thebdry ‘of property rights, and the theory of finance.!° The firm is viewed not as a single entrepreneurial risk-bearing entity, but as a nexus of contracts among shareholders, managers, workers, suppliers and customers. Each group within the firm can be expected to have differing objectives. Agency costs are incurred when one group must monitor or require a bond from another group toensure that the behavior of the latter serves the interests of the former. EXAMPLE:

Agency costs arise due to the separation of ownership and control, whereby managers act as agents for the shareholders. Managers may wish to maximize managerial utility, or sales volume subject to a profit constraint, while shareholders may want to have the value of the firm, or shareholder wealth, maxi-

mized. Shareholders must incur monitoring costs to limit managerial behavior which would not maximize shareholder wealth. Managers must incur bonding costs to guarantee that they will not undertake certain actions that reduce shareholder wealth. Similar agency costs are incurred by parties to the other contracts involved in the firm (for example, warranties given to customers, delivery schedules agreed to by suppliers, and work conditions agreed to by labor) to ensure that all parties honor their commitments and obligations. There are markets for each of the contracts involved in the modern firm. The market prices for the various contracts, for example managers’ salaries, employees’ wages and the prices of the firm’s products, are influenced by the performance of the managers, workers, and products respectively. The market value of an individual manager, worker, or product adjusts up or down to reflect past performance. These markets therefore operate to encourage greater efficiency and performance from all members of the firm. Unfortunately, the managerial and behavioral theories of the firm, and the latest variant incorporating agency costs, can be treated here only briefly due to the constraints of a single textbook at the intermediate level. Nevertheless these issues are of great importance and represent the new frontiers in the theory of the firm. I hope you will be able to take a more advanced course in microeconomics and study these models in more detail. In the meantime, if the reader’s °R.H. Day, “Profits, Learning, and the Convergence of Satisficing to Marginalism,” Quarterly Journal of Economics, May 1967. 10M.C, Jensen and W.H. Meckling, ‘‘Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure,” Journal of Financial Economics, 3, 1976, pp. 305-360.

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THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

appetite is sufficiently whetted, he or she can refer to a more advanced textbook treatment and the recent literature.12

Il. OLIGOPOLY PRICING UNDER UNCERTAINTY In the preceding discussion, pricing theory was considered in an environment of certainty, in which firms are assumed to know the shape and location of their cost and demand curves. On the basis of these curves, the firms choose price in

order to obtain their desired objective. In the real world business environment, however, firms are not aware of the exact shape and location of their cost and revenue curves. In many cases it may be reasonable to expect that the search costs of obtaining estimates of the MC and MR relationships will exceed the extra revenue that might have been obtained using these estimates. Before attempting to obtain the additional information, the decision-maker must expect that the additional revenues to be earned as a result of making the optimal decision (as compared to the revenues expected from the decision to be made on the basis of existing information) will exceed the cost of obtaining that information. Clearly in many business situations, the decision-maker has no such expectations. Thus it is not surprising that business decision-makers, notwithstanding the elegant models of the economists, tend to adopt simple rule-of-thumb procedures when setting or changing prices.

Rules-of-Thumb and Markup Pricing Rule-of-thumb pricing procedures should be viewed as shortcut decision-making methods that economize on search costs and the decision-maker’s time. These procedures usually result in a suboptimal decision being taken when that decision is compared with one which might be taken if full information were available. In terms of profits gained by the firm, however, the rule-of-thumb decision-making procedure may be optimal, since although it may never lead to the optimal decision in any particular instance, consistent decision-making by rule-of-thumb procedure may approximate the same net profit levels over the longer term. The inefficiency of rule-of-thumb decision procedures arises from the fact that some amount of profitability is lost because the optimal decision in particular instances is not taken. But to know what the optimal decision is requires additional information, which in turn requires search costs. Hence all that is required by rule-of-thumb pricing procedures is that they lose less than the information would cost. The most common rule-of-thumb pricing procedure is known as markup, or cost-plus, pricing. Under this pricing method, the decision-maker ascertains 11A, Koutsoyiannis, Modern Microeconomics, 2nd ed. (London: Macmillan, 1979) Chaps. 13-18; R. Marris and D. Mueller, “The Corporation, Competition, and the Invisible Hand,” Journal of Economic Literature, 18 (March 1980), pp. 32-63; E.F. Fama, “Agency Problems and the Theory of the

Firm,” Journal of Political Economy, 88 (April 1980), pp. 288-307.

Further Topics in Oligopoly Markets

303

the average variable costs of the product and adds to this a percentage markup to determine the price level. Thus,

P = AVC + X% (AVC)

(13-1)

whereX is the markup percentage chosen. Markup pricing is often thought to be simply cost-based, but it is evident that the amount by which price can be marked up is highly dependent on the demand conditions facing the firm. When asked what factors determine the size of the markup percentage, businesspeople often respond that they choose the markup ‘“‘with an eye to what the market will bear’ or “in order to meet the competition”.12 These are statements that carry an implicit message about the demand conditions facing the firm. Hence the size of the markup is both costand demand-based, contrary to the naive view that markup pricing depends upon cost alone. Since firms tend to use markup pricing in practice, does this mean that they are ignoring the marginalist principles of pricing? Before we are able to answer this question, we must investigate whether markup pricing is necessarily inconsistent with the marginalist principles. In fact, the marginalist and markup pricing approaches can be reconciled, which we now demonstrate. Reconciliation of Markup and Marginalist Pricing To reconcile the markup and the marginalist approach to price determination we must incorporate the MR = MC rule into Eq. (13-1). We start by finding an expression for marginal revenue. Recall from Chap. 4 that total revenue is the product of price and quantity:

TR =P-Q

(4-5)

Marginal revenue is the first derivative of total revenue with respect to output. Using the chain rule, since P also depends on Q, we have

MR = P + Q—

(13-2)

We now perform a manipulation on Eq. (13—2) which will allow a substitution. Multiply and divide the last term by P such that we obtain

QP MR = P+—.Ry

dP — dQ

-3 aa

dP — a)

i

Factoring out P we obtain

Q MR=P{1+—-: ( i

12A, Silberston, “Price Behavior of Firms,” Economic Journal, vol. 80, Sept. 1970.

304

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

4

Note that the second term in the brackets is in fact the reciprocal of the expression for price elasticity we found in Chap. 4, which is restated here:

need apg h

(4-11)

Substituting from Eq. (4-11) into (13—4) we obtain

MR = P(1 +2) (13-5) € Having derived this expression for the relationship between marginal revenue, price, and elasticity we are now ready to perform the reconciliation. Marginalist pricing requires MC = MR. Setting MC equal to the above expression for MR we have

mc =P(1+2)€

(13-6)

Expressed in terms of price, this may be restated as

€ eS mc (— :)

(13-7)

In business situations, average variable costs are often constant—or they are viewed as constant—over the relevant range of outputs. Under such circumstances, marginal cost is equal to average variable cost. Hence we may restate Eq. (13-7) as € P= ave (— :)

(13-8)

Let us now substitute into Eq. (13—8) an arbitrary value for elasticity, say « = —5. In this case, -—5 P = AVC (= z )

P = AVC (5/4) or P = AVC + Y%4(AVC) or P = AVC + 25%(AVC) Thus a 25% markup on average variable cost is the profit-maximizing markup percentage when the elasticity value is 5. Let us repeat this calculation for some other values of elasticity. For e = —3,

P = AVC (3/2) = AVC + 50% (AVC) and for e = —9,

P = AVC (9/8) = AVC + 12%% (AVC) Further Topics in Oligopoly Markets

305

It is apparent from the above that there is a level of the markup percentage profit maximizing, and that this level varies inversely with the value of is that price elasticity. Products with higher price elasticities of demand should be expected to have relatively lower percentage markups, in order to make the maximum total contribution to overheads and profits.13 From Chap. 4 you recall that the greater the number of substitutes and the greater proportion of income spent on that particular product, the higher the price elasticity. In practice we know that markups on individual items of groceries, for example, tend to be low, whereas markups on gift items tend to be hight, in keeping with the preceding analysis. NOTE:

Do firms choose their markups with an eye to the value of price elasticity? Certainly most do not. Rather, they find their best markup by trial and error or by adopting the same markup that is applied by other firms or by the price leader in their industry. This is not to say, however, that marginal analysis is of limited usefulness to the decision-maker. Although firms may not use marginalist analysis in choosing price levels, they may act as if they do. Marginalist analysis may thus predict the pricing actions of firms, even if in practice they use a markup pricing procedure. To the extent that they choose the size of the markup with reference to market conditions, and to the extent that they wish to maximize

the contribution to overheads and profits, the markup price level may closely approximate the price that would be indicated by marginalist procedures. Markup Pricing under Inflationary Conditions

A markup pricing policy applied to increasing levels of per-unit variable costs leads to a commensurate increase in the price level. In Table 13—1 we show a situation in which average variable costs have increased over a particular period by 10%. The 40% markup, when applied to that cost base at the beginning of the period, resulted in a price of $8.40. The 40% markup, when applied to the higher average variable cost figure at a later date, resulted in the size of the markup, or the contribution margin, being increased also by 10%. Since both components of price have increased by 10%, it is not surprising that price itself has also increased by 10%. Table 13-1 Markup Pricing with Inflation

Before

After

($) ($) a eee ee Average variable costs 6.00 6.60 40% markup 2.40 2.64 Price 8.40 9.24

Change

(%) 10 10 10

‘Note that the formula only works for « > 1. For e < 1, MR < 0. Hence we cannot have MC = MR since MC must be nonnegative.

306

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

Thus markup pricing under conditions of inflation tends to pass the cost increase along to the consumer of the product. Notice, however, that the increase in average variable costs was $0.60, whereas the increase in the price amounted

to $0.84. The difference arises, of course, because the absolute amount of the contribution has risen by $0.24. Since this contribution has risen by 10% and the cost level has also increased by 10%, the contribution at the end of the period of inflation has the same purchasing power as the contribution had at the beginning of the period of inflation: It will now take $2.64 to purchase what previously was purchased for $2.40. Thus markup pricing, as well as passing the cost increase along to the consumer of the product, also serves to maintain the purchasing power, or real value, of the firm’s contribution to overheads and profits.

NOTE:

If during this regime of inflation, consumers’ or purchasers’ incomes have also gone up by 10%, then this product still requires the same proportion of their incomes as it did before the inflation. Thus the 10% change in the price level is not areal price change, in the sense that it does not cause consumers’ purchasing power to be reduced. It is a simple monetary price change resulting from the depreciation of the monetary unit. Such a price increase may not be regarded by purchasers as causing the product to become more expensive in terms of their incomes, and hence their quantity demanded need not necessarily fall as a result of the monetary price increase. This depends of course on the coincident raising of prices of the substitute products for the product in question. If one firm chooses to absorb the increase in average variable costs or to take a lower markup on those increased costs, then this firm is likely to gain sales at the expense of those firms that do apply the simple markup pricing policy to the increased cost base. If the markup percentage closely reflects the price elasticity of demand, so that at any point in time the firm is setting a price level very close to the profitmaximizing level, then markup pricing policy allows the maintenance of the status quo and saves recalculation of the optimal price each time there is a cost increase.

Markup Pricing as a Coordinating Device

We know that a crucial element in the oligopolist’s decision-making procedure is to know whether or not rival firms are likely to adjust prices at the same time and by similar magnitudes as are being contemplated by the decision-maker. To the extent that price changes are coordinated among firms, their market shares are likely to remain stable. On the other hand, if one firm raises price and rival firms do not, we expect that firm to suffer an elastic demand response and subsequently lose some part of its market share. Similarly, if all firms raise prices, yet one firm raised price by a significantly larger amount, that firm is expected to lose part of its market share. The existence of an established markup pricing policy in a particular industry acts as a coordinating device when price changes become necessary. All Further Topics in Oligopoly Markets

307

firms are likely to be faced by similar changes in their cost structure, since they purchase labor and raw materials in the same or similar markets. If they each apply the same markup percentage to these average variable costs, their prices will rise by a similar percentage. Hence the relative prices of the firms remain undisturbed at the new general level of prices. Markup pricing policy and a common markup percentage allow a common and predictable strategy for price

increases. Whether under conditions of conscious parallelism, price leadership, or independent action, the firm expects that other firms will raise their prices to the extent of the familiar markup proportion oft the change in unit costs. Thus when a cost component changes, the firm may confidently adjust its price upward in the expectation that all rival firms will do likewise. An established markup pricing procedure within a particular industry thus allows the decisionmaker to predict, with a high degree of certainty, responses of rival firms to changes in cost conditions. Markup Pricing and Longer Term Objectives

The markup percentage may not be chosen with a view to maximizing short run profits or contribution to overheads and profits. As we noted earlier, the firms may wish to maximize longer term profitability and maintain present price levels somewhat below the short run profit-maximizing levels, in order to inhibit the entry of new firms. We noted that short run sales maximization and limit pricing were policies that the firm may follow to achieve these longer term objectives. In these cases the markup and the price level are somewhat lower than for the case of short run profit maximization, since longer term price elasticity of demand is typically greater than short run price elasticity, due to the time lags involved in consumer and producer adjustment to price changes. For example, some consumers ignore a price reduction at first and later switch their patronage, whereas producers adjust prices or attributes of their offerings at varying intervals in the future. The size of the markup that maximizes sales, subject to a profit constraint, or limits the entry of new firms, is chosen by the price leader or by the collective consensus of firms operating under conditions of conscious parallelism. Once a level of the markup is found that seems to achieve these objectives, this markup percentage becomes institutionalized in the industry and becomes the standard percentage applied by the firms, as long as the objective functions and general market conditions do not change significantly. This is not to imply that competing firms must necessarily markup their average variable costs by exactly the same percentage figure. Firms with higher cost structures may have to use lower markup percentages to bring their price into the same general area as other firms’ prices. Firms with higher quality products may use higher markups. But once each firm establishes the markup level, it can continue to adjust prices to cost increases using that markup, secure in the knowledge that rivals are doing likewise. Hence market shares should remain relatively stable.

308

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

IV. NONPRICE COMPETITION Price competition in oligopoly markets has been seen to have its disadvantages. Itis easy, perhaps too easy, to adjust prices, but the consequences may be mighty. Rivals may ignore your price increase, causing a substantial and perhaps irretrievable loss of market share. Oppositely, your price reduction may be interpreted as a hostile act, and it may precipitate several rounds of price cutting and perhaps a prolonged and damaging price war. It is not surprising, therefore, to find that oligopolists tend to adjust prices only when absolutely necessary and to use other strategic variables for their major competitive thrusts. This nonprice competition may take the form of product design changes, new products, advertising, promotion, free samples, prizes, and so forth.

Under conditions of oligopoly, the firm should recognize that its nonprice competition will have a noticeable impact on the sales and profits of rivals, unless the other firms are simultaneously carrying out similar campaigns. Unlike price adjustments, however, nonprice competition requires a significant lead time in which advertising campaigns must be planned and coordinated with the availability of time and space from the various advertising agencies and media channels. This means that if a firm is “‘caught napping” by a competitor’s new advertising campaign, there will be a significant lag before it can produce its own retaliatory campaign. During this time it may lose a significant share of its market, which may prove difficult or impossible to retrieve. The existence of this lag thus motivates firms to have an ongoing involvement in promotional activity. If there is always a new campaign in the pipeline, the firm does not expect to be caught napping to the extent that it would be if it had waited for a competitor to launch an advertising or promotional campaign. The Interdependence of Promotional Efforts Given that firms tend to have continual advertising and promotional strategies,

changes in market shares should only be expected to occur when the relative advertising and promotional effectiveness of firms are suddenly made different by an increase in the relative size of a particular firm’s advertising budget or in the relative effectiveness of a firm’s advertising expenditures. EXAMPLE:

Suppose two large firms share the major part of a particular market and each budgets approximately $4 million toward promotional expenditures each year. In Table 13—2 we show the payoff matrix for interaction of the firms’ advertising strategies.14 When both firms spend $4 million, the net profits to each firm are $10 million. By convention, A’s payoffs are shown first (followed by B’s payoffs) for each combination of promotional expenditure strategies. Suppose now that 14The payoff matrix is an expositional device borrowed from “game theory.” The vertical and horizontal dimensions of the matrix indicate the alternative strategies of the players in the “game.” The interior coordinates of these strategies show the “payoffs,” or profits, in this case, to each of the players. See R.D. Luce and H. Raiffa, Games and Decisions (New York: John Wiley, 1957).

Further Topics in Oligopoly Markets

309

Firm A contemplates increasing the promotional budget level to $6 million. If Firm B maintains its promotional budget at $4 million, this will cause A’s profits to rise to $12 million, while B’s profits will fall to $6 million. This indicates, of course, that A’s additional $2 million promotional expenditure causes a sub-

stantial proportion of the market to switch from Firm B’s products to Firm A’s products, with associated changes in the firms’ relative profitabilities. Table 13-2 Payoff Matrix for Advertising Strategies Firm B’s Advertising Budget $4 million

Firm A’s

$4 million

10:03

Advertising Budget

$6 million

12.0,

$6 million

VOl07/26:0) 9 1220 SHO) | tehG7/e

8.7

Conversely, if Firm B increases its advertising budget to $6 million and if Firm A holds its advertising constant at $4 million, Firm B would benefit from

the change in market share. If both firms increase advertising to the new higher advertising levels, the result is as shown in the lower right-hand quadrant of the payoff matrix. Note that profits are reduced, compared with the earlier levels of advertising expenditures. This is the result of the firms’ competing messages to consumers tending to offset each other’s effectiveness, by creating “‘noise” in the communication process between the sellers and prospective consumers. Since oligopolists are usually risk averters and since there is a significant lag before any firm could retaliate to an increase in advertising expenditures by other firms, we might expect each firm to protect itself by not being caught napping and increasing its advertising expenditure to the higher level.15 If both firms in the above example independently increase their expenditures in pursuit of private gain, they will instead find that the result is inferior to that which was enjoyed at the earlier promotional levels. The Prisoner’s Dilemma

DEFINITION:

The firms are subject to what has become known as the prisoner’s dilemma.

This arises when two or more adversaries are motivated to behave in a self-serving manner and when they assume that their rivals or adversaries will act similarly.1¢ If each rival pursues private gain, both will become worse off. *5In game theory jargon, the firms would adopt the maximim strategy, opting for the strategy having the maximum of the minimum (best of the worst) outcomes. This behavior may be typical of conservative, risk-averse decision-makers. See M. Shubik, Strategy and Market Structure (New York: John Wiley, 1959). 16See Luce and Raiffa, Games, pp. 94-102, and F. M. Scherer, Industrial Market Structure and Eco-

nomic Performance (Chicago, Ill.: Rand McNally, 1970), pp. 142-5, 335-7.

310

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

EXAMPLE:

This situation is called the prisoner’s dilemma after the supposed instance of two bank robbers caught with the proceeds of a robbery, but with no more than circumstantial evidence of being involved in that robbery. Interrogated in two separate rooms, they are each told that if they confess and implicate the other, they will go free as a “‘state witness,” whereas their accomplice will receive a substantial term in prison. Each robber knows that if they both refuse to confess, they will receive only a short prison term for possession of stolen goods. However, if they both confess, neither will be allowed to turn state witness, and both will receive relatively long jail sentences. Since the robbers cannot communicate with each other, and since they both dislike time spent in jail, they will both be motivated to avoid the worst possible outcome. Since the worst possible outcome is not to confess while the other does confess, the best strategy for each prisoner is to confess. Since each prisoner confesses, they each end up with a relatively long jail sentence, whereas if they had been able to communicate and coordinate their strategies, they would have been sentenced to the relatively short prison term for possession of stolen goods. The essence of the prisoner’s dilemma thus applies to firms in situations of advertising rivalry. A lack of communication and coordination between parties with conflicting self-interest can lead to a situation in which both parties are worse off compared with the outcomes which would have been obtained had there been communication and coordination between them. Referring back to Table 13—2, had the firms agreed to limit their advertising expenditures to $4 million, their net profits would have remained at $10 million each. In pursuit of independent profit gains, however, and without knowing whether or not the other firm is simultaneously planning an increase in the promotional budget, both firms find themselves at a reduced level of profit.

NOTE:

Notice that when both firms have increased their promotional budget to $6 million, there is no incentive for either firm to independently reduce the advertising budget, since this would lead to a loss of market share and net profits. Similarly, larger promotional budgets promise increases in net profit levels if they are undertaken independently. When each firm fears that the other might undertake a further increase in promotional expenditures, we have the prisoner’s dilemma all over again. Thus both firms are motivated to spend the additional amount on promotion in order not to be left standing still when the other’s promotional campaign is launched.

Coordination of Advertising Expenditures

Will firms be motivated to coordinate their advertising and promotional expenditure levels? While firms may achieve an implicit agreement not to-escalate advertising budgets beyond present levels, it is unlikely that they will achieve agreement to reduce budget levels to a point that would seem to be more efficient in terms of total profitability. This is in part probably due to the distrust that a firm might feel concerning the reduction of its own advertising expenditures, when rivals may not in fact reduce theirs. Given the lead time required to prepare Further Topics in Oligopoly Markets

311

additional promotional campaigns, a firm that doublecrosses its rivals could gain a market share advantage that might be impossible for the other firm to regain. A second factor militating against the coordination of advertising and promotional competition is that these activities are seen as an appropriate forum for the competitive instincts of rival firms and that this avenue for civilized competition should not be closed to the firms. Promotional competition requires skill and planning and the services of talented people. Price competition, on the other hand, requires little planning and not much skill on the part of the instigator, yet the impact upon the profitabilities of all firms may be significantly adverse. To avoid active competition shifting to the price arena, firms may prefer to compete on a promotional level, where gains in market shares and profits are the rewards for exceptional abilities on the promotional side.

Advertising as an Investment

The impact of a particular advertising campaign may not be felt simply in the period of that expenditure, but should be expected to have a residual impact, which gradually attenuates over subsequent periods. Potential buyers may be only partly convinced by a particular campaign, but this may build a necessary base for future persuasion. Alternatively, the campaign may convince consumers to switch to this product, but only after they deplete their personal inventories of rivals’ products. Thus a dollar spent on advertising now may lead to revenues in the same period, plus a stream of revenues in future periods. In this respect advertising can be regarded as an investment project, and it should compete for funds within the firm on the same basis as other investment projects with multiperiod revenue streams. The conditions for optimal promotional expenditure considered in Chap. 11 were generated under the implicit assumption that the total impact of the expenditure would be felt in the same period. This analysis remains sufficiently accurate if the residual impact of advertising expenditure is very low or if the time period used for analysis is long enough to include the greater part of any residual impact. If there is a significant residual impact of advertising expenditures in subsequent periods, the present value of the future revenues generated must be included in the decision-making process. Current advertising expenditures may exceed the short run, profit-maximizing level to the extent of the present value of the future revenues generated, before we could say that the firm’s objective of long-term profit maximization was not being served. Advertising to Raise Barriers to Entry

It is widely supposed that advertising and promotional efforts operate to raise or maintain barriers to the entry of potential competition.17 Repeated messages 17Following J.S. Bain, Barriers to New Competition (Cambridge, Mass.: Harvard University Press, 1956) many economists have argued along these lines. For a recent view and a comprehensive bibliography, see D. Needham, “Entry Barriers and Non-Price Aspects of Firms’ Behaviour,” Journal of Industrial Economics, 25 (Sept. 1976), 29-43.

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THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

concerning existing firms and their products are said to increase consumer loyalty to existing products and cause consumers to be reluctant to switch to the products of new entrant firms.18 In order to convince consumers that their products have comparable quality, reliability, and other desirable features, the entrant firms may need to spend more on advertising and promotion over at least the first few years, compared with the existing firms. The prospect of these additional expenses in an uncertain market for their products is argued to cause potential entrants to decide against entry because of the low or negative level of expected profits. Thus high levels of advertising by existing firms in a particular industry might be expected to allow those firms to continue to earn higher than normal profits, since entry is not attempted or successfully accomplished, due to the expectations or actuality of significantly higher cost structures for entrant firms. Various studies have been reported in which tests were made for the empirical relationship between levels of advertising and levels of profitability. The results of these tests tend to be ambiguous.’9 A more recent and probably much more fruitful avenue of inquiry concerns advertising’s function of imparting price and

quality information, which can be expected to increase, rather than inhibit, competition.?°

In summary, advertising and promotion decisions within the firm are an important adjunct to the firm’s pricing decision and in some cases become the firm’s primary strategic variable. In oligopoly situations, the level of advertising and promotional expenditures may be taken to excess, due to the uncertainty concerning the simultaneous actions of rivals. Even when the future impact of advertising expenditures is taken into account, oligopolists, unable or unwilling to coordinate their advertising strategies, may be expected to spend beyond the point where profits (short- or long-term) are maximized. They must continue to run in order to stay in the same place, since any unilateral reduction in advertising expenditures would cause them to lose some part of their market share and presumably reduce the present value of their future profit stream. Advertising and promotional expenditures tend to generate a stream of future revenues as new customers return to purchase more units in the future. Such nonprice com-

petition may be considered as an investment in future revenues and is, therefore, an apppropriate strategy for firms wishing to maximize long-term profits.

V. SUMMARY In this chapter we examined three major topics in the theory of the oligopolistic firm. Our first topic was the departure from the traditional assumption of short run profit maximization as the firm’s objective function. Since oligopolists are 18Notice that this argument involves the residual effects of past advertising and promotional efforts. It is the sum of these residual effects that operates to enhance consumer loyalty to existing firms’ products. 19/W.S. Comanor and T.A. Wilson, “Advertising, Market Structure, and Performance,” Review of Economics and Statistics, 49 (Nov. 1971), 423-40. Also, R. Schmalensee, “Advertising and Profitability: Further Implications of the Null Hypothesis,” Journal of Industrial Economics, 25 (Sept.

1976), 45-54.

54. 20**A New View of Advertising’s Economic Impact,’’ Business Week, December 22, 1975, pp. 49,

Further Topics in Oligopoly Markets

313

likely to have time horizons (or planning periods) longer than the short run, we considered various means of attaining or approximating profit maximization over the longer term. In principle, long-term profits are maximized by pursuit of a short run policy of maximizing net present worth or the net present value, of the firm’s profit stream over the planning period. In practice, the search costs involved in obtaining the demand and cost information required are likely to disqualify this as a viable short run objective. A proxy policy for long-term profit maximization is the short run maximization of sales volume (or market share), subject to the attainment of a minimumprofit target. Increasing sales in the present period above the profit-maximizing level has revenue and hence profit implications over the longer term. Limit pricing to deter the entry of new firms can also be viewed as a long-term- profitmaximizing strategy, since it is intended to keep out new firms, which otherwise would enter and take a share of future profits. Essentially, the firms should practice limit pricing if they expect the net present value of their profit streams to be greater as a result of this strategy. The more recent managerial and behavioral theories of the firm were briefly examined. Maximization of the rate of growth of the firm and of managerial utility were presented as enhancing longer term profits at the expense of short run profits. The behavioral theory of the firm postulates that firms are satisficers, being content to attain predetermined targets, or aspiration levels, in several variables. If these targets are revised periodically, one can argue that this strategy allows the firm to converge on the long-term-profit-maximizing price and output levels. Markup pricing under conditions of uncertainty was examined and seen to be consistent with marginalist pricing, when the percentage markup holds the correct relationship with price elasticity of demand. It is a rational, profitmaximizing response to an uncertain environment, if the firm’s prior expectation is that the search costs will exceed the extra revenues obtained from the better information derived by the information search procedure. We saw also that markup pricing under inflationary conditions helps preserve the purchasing power of the firm’s profits, facilitates the coordination of price adjustments, and can be adjusted to reflect the pursuit of longer term objectives. Nonprice competition was examined and we concluded that oligopolists can be caught in a situation in which they cannot independently reduce these expenditures without suffering a leftward shift of their demand curves. Coordination of advertising and promotional efforts would probably increase the profits of all firms. Firms may prefer to expend large sums on nonprice competition, however, since this reduces their vulnerability to rivals’ promotional efforts, contributes to future sales revenue, and operates to raise barriers to the entry of

new firms.

DISCUSSION 1.

314

QUESTIONS

Explain why you would not expect short run profit maximization to be an appropriate objective function for the firms in an oligopoly market.

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

2.

Why is the maximization of the firm’s net present worth effectively a longterm-profit-maximizing strategy?

3.

Why is sales maximization

(subject to a minimum-profit requirement) a

proxy for long-term-profit maximization? Why is a minimum-profit level desirable? 4.

Using Fig. 13-4 as a starting point, suppose there are four firms in the market, each one taking an equal share. Draw in the mutatis mutandis and ceteris paribus demand curves of the price leader and the price followers. Then draw in the SAC curve that each firm should operate on.

5.

Explain why each of the managerial and behavioral models of the firm can be said to involve a tradeoff between short run profits and profits to be received in the future.

6.

When are crude rules-of-thumb the optimal pricing policy? How far off can the selected price be without it being better to use the marginalist pricing rule?

7.

Explain the circumstances under which the markup price will be exactly equal to the profit-maximizing price.

8.

Explain how markup pricing policies facilitate coordination of price adjustments in oligopolistic markets.

9.

Discuss the prisoner’s dilemma as it applies to the advertising and promotional activity of oligopolists. Suppose the firms do agree to reduce expenditures to some lower level. What incentive exists to cheat on this agreement?

10.

Explain how advertising and promotional expenditures can be regarded as an investment and how this ties in with the notion that these expenditures operate to maintain barriers to entry.

SELECTED

REFERENCES

ALCHIAN, A.A., and H. DeMseTz, ‘‘Production, Information Costs and Economic Organization,’’ American Economic Review, 62 (Dec. 1972), 777-95.

BAUMOL, W.J., Business Behavior, Value and Growth (2nd ed.), esp. chap. 6. New York: Harcourt Brace Jovanovich, Inc., 1967.

CoMANOR, W.S., and T.A. WILSON,

“Advertising, Market Structure, and Performance,”

Review of Economics and Statistics, 49 (Nov. 1971), 423-40.

CyerT, R.M., and J.E. Marcu, Prentice-Hall, 1963.

Hawkins, C.J.,

A Behavioral Theory of the Firm, Englewood Cliffs, N.J.:

Theory of the Firm, esp. chaps. 4, 5. London: Macmillan, 1973.

KouTSOYIANNIS, A., millan, 1979.

Modern Microeconomics

(2nd ed.), chaps. 13-18. London: Mac-

“The Corporation, Competition, Marris, R., and D.C. MUELLER, Hand,” Journal of Economic Literature, 18 (March 1980), 32-63.

and the Invisible

Further Topics in Oligopoly Markets

315

NEEDHAM, D., ‘Entry Barriers and Non-Price Aspects of Firms’ Behaviour,” Journal of Industrial Economics, 25 (Sept. 1976), 29-43. SCHERER, F.M., Industrial Market Structure and Economic Performance, esp. chaps. 5-14. Chicago, Ill.: Rand McNally, 1970. SILBERSTON, A.,

WILLIAMSON, J.H.,

‘‘Price Behavior of Firms,” Economic Journal, vol. 80, Sept. 1970.

‘Profit, Growth, and Sales Maximization,’’ Economica, 33, no. 129

(1966), 1-16.

WILLIAMSON, O.E., “Managerial Discretion and Business Behavior,’ American Economic Review, vol. 53, 1963.

316

THE THEORY OF THE FIRM: PRICE AND OUTPUT DETERMINATION IN THE PRODUCT MARKETS

PARTV > Factor Markets: The Interaction

of Producers and Resource Owners

CRES

ERS 1A MeowES

< ©oe ‘a

4

om ARE OAL

aa

Factor Price Determination: The Cost of Resources Used in Production

1. INTRODUCTION We now begin to examine the third main area of microeconomics, which is that known as distribution: To recap our progress so far, recall that we studied first the area of consumption, in which we investigated why consumers demand the goods and services that they do, and how they would be expected to react to changes in economic variables influencing their consumption behavior, such as changes in prices, incomes, availability of substitute and complementary products, and other factors. We then turned to production, where we examined the requirements for technical and economic efficiency in the supply of the goods and services to the product markets. Production theory led to cost theory, since all inputs in production have a cost involved, and cost theory guided us through an analysis of how the components of total and average costs varied with output levels both in the short and the long run production situation. Under the theory of the firm, consumption and production were brought together in the various types of product markets, in order to determine the prices of the goods and services that are demanded by consumers and supplied by producers.

DEFINITION: Distribution theory is concerned with the distribution, or allocation, of the total revenues from sales of the goods and services in the product markets, among the various factors of production or resources used to produce those goods and services. In other words, in the distribution area of microeconomics, 319

we are concerned with the payments to each input or, alternatively, with the cost of each input in the production process. Up until this point in the text we simply took factor prices as given; now we look into the question of the wage level, the rate of interest, and the rate of profits, to find out why each factor has the rate of payment that it does, and why not more or less. Fortunately, the road is pretty much downhill from here. Coming this far in the text, you already know most of the terminology, concepts, and methodology of microeconomics. From now on it is a relatively simple matter of applying the marginalist concepts and methods of earlier chapters to the specific situations encountered in the markets for resources. The resource markets are similar to the product markets in many respects: There is a supply of resources and a demand for these resources, and the price of the services of each resource is determined by the interaction.of this supply and demand. As in the product markets, the process of interaction and the eventual outcome depends in large measure on the structure of the resource markets. Given your exposure to the methods of microeconomic inquiry and the “tool box’’ of concepts you have gathered along the way, you should anticipate little problem in understanding the principles of distribution. There are, of course, a multitude of different resource inputs, each with its

own supply and demand, and each often competing with other resources to be employed in particular production processes. Within the overall resource market, the labor market alone is characterized by literally thousands of labor skills and levels of each skill. We proceed in this chapter to examine the basic principles of distribution theory, which are applicable to all markets for all inputs. Our model abstracts from the specific nature of the input and looks instead at the underlying factors that determine the level or rate of compensation forthcoming to each input in return for its services in production. In the three following chapters we examine specific resource markets and discuss the particular issues and problems pertinent to those markets. Chapter 15 is concerned with the labor markets and addresses the real world issues of wage, salary, and profit determination in an environment of inflation. Chapters 16 and 17 are concerned with the savings and investment decision and the determination of the various rates of interest in capital markets. In the present chapter we develop a simple model of factor price determination first in the context of purely competitive factor and product markets and then in the context of imperfect competition in these markets. The purpose of the simple, purely competitive model is pedagogical: By abstracting from the complexities of imperfect competition, we are best able to introduce the basic structure and interrelationships of the factor markets. Having obtained the necessary foundation, we are then prepared to relax the restrictive assumptions of the purely competitive model and are able to understand the influence of each new complexity as it is admitted to the model. Thus in the following pages we examine the determination of factor prices in purely competitive markets, then in imperfectly competitive markets, and finally address some issues and topics in factor market analysis.

320

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

ll. FACTOR PRICES IN PERFECTLY COMPETITIVE MARKETS For simplicity we initially assume the existence of pure competition in all markets. That is, the markets for all goods and services are purely competitive, as are the markets for all factors of production. Every market is therefore characterized by many buyers and many sellers, each unable to influence market price directly. Thus in the market for a particular labor skill, for example, there are many persons offering to supply this skill, and there are many firms wishing to purchase this skill in order to produce a product that will be demanded by many consumers in their product market. Each microeconomic agent, whether consumer, producer, or supplier of resources, must therefore take the market price of each product or resource as given and simply determine how much of each product or resource it will purchase, produce, or offer, as the case may be. In Chap. 5 we determined the principles of economically efficient production. The producer should demand each resource up to the point where the ratio of its marginal product to its price is equal to that ratio for all other inputs. That is, for least cost production of a given output level, the producer will set

MP,

MP,

MP, _

ee eee

_ MPa

eas

ee

where the subscripts a, b, c,...,n represent the identity of each separate resource or factor of production. To refresh your memory, recall that the marginal product of any factor is the increment to total product (output) resulting from the addition of another unit of that factor to the production process, with ceteris paribus. The things that must remain equal include the inputs of those resources that are fixed in the short run, as well as other inputs that can be varied in the

short run. From the formula above you appreciate that if resource A costs twice as muchas resource B, that is, P, = 2P,, then MP, must be twice the value of MP,, in order for the least cost condition MP, /P, = MP,/P, to hold. That is, the marginal unit of resource A, costing twice as much as resource B, must add twice as

much to output compared with the marginal unit of resource B. In Chap. 9 we discovered that a producer wishing to maximize its profits should produce and sell up to the point where its marginal cost of production equals the marginal revenue from sales of the product. This profit-maximizing rule is expressed as MC = MR (14-2) Recall that marginal cost is the increment to total cost for a one-unit change in the output level. Note that in a production situation, output will change if we employ one more unit of a variable factor; this in turn will cause the change in total costs. Suppose that we employ an extra unit of labor for $10 per hour, and that this additional unit of the labor input causes 20 more units of output to be produced. The ratio of marginal product to factor price is therefore

MP,

20

Pisenatl.O.4,

Factor Price Determination: The Cost of Resources Used in Production

321

Since the increment to total cost is equal to P;, and the increment to output is equal to MP,, we can find the marginal cost of one unit of output to be

MC

ATC may: = —~— = —— = 0.50 g AQ. MP,

Thus we can state that MC is equal to the ratio of the price of the input to the marginal product of that input.

Mc =—

™

(14-3)

Suppose we now attempt to sell the 20 units produced by the addition of the marginal unit of labor. In a purely competitive product market, we can sell these at the market price, which is constant regardless of our activity. Marginal revenue, the increment to total revenue due to the sale of an additional unit, is

thus equal to the market price of the product. Since the profit-maximizing rule is to produce until MC = MR, it is implied by Eq. (14-3) that we should produce until

MR RULE:

~ MP,

(14-4)

If we should produce to the point where MR = P;/MP;, we should employ units of labor up to the same point, since changes in output level are only possible given changes in the employment of the variable factor. Equation (14—4) thus contains the decision rule for employing variable inputs: The firm should employ each variable factor up to the point where its ratio of price to marginal product equals the marginal revenue obtainable in the product market. Rearranging terms in Eq. (14—4), we have

DEFINITION: The expression on the left-hand side, MR: MP;, is known as the marginal revenue product of labor (MRP,), and can be seen to be equal to the value of the marginal product of labor.1 At this point we should also rename the element on the right-hand side of Eq. (14-5). P;, the price per unit of labor, can be called the marginal factor expenditure on labor (MFE;,); it is the cost of employing one more unit of labor. In pure competition, it is equal to the market price of labor, since successive units of labor can be purchased by the firm at the same price level. In imperfectly competitive factor markets, we shall see that the MFE is equal to the change in total factor expenditure, due to the employment of an incremental unit of that factor. In such markets, increasing demand for a factor by any one firm may raise the price per unit over the whole market, and so the MFE exceeds the price of the incremental unit. ‘Since price equals marginal revenue in purely competitive product markets, the MRP, for such cases can be expressed as P- MP, and as such is often called the value of marginal product. The MRP specification is more general, applying to both purely competitive product markets and imperfectly competitive product markets, in which marginal revenue is less than price.

322

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

Substituting MRP, for MR: MP, and MFE, for P; in Eq. (14-5), we find

MRP, = MFE,

(14-6)

Thus the firm’s decision rule is to hire labor up to the point where the marginal revenue product of the last unit equals the marginal factor expenditure on that unit. This decision rule is, of course, an extension of the marginalist principle and should be intuitively clear to you. If the firm wants to maximize its profits, it should demand each input up until the point where the incremental value of that input, that is, its MRP, is just equal to the incremental cost of that input, its MFE. To summarize and to generalize to the case of n inputs, the decision rule starts with the requirement that MP, ae

MP, _ MP, _ is Pp

ag re

.

a

_

thie

oa le

Since profit maximization requires MC = MR, and since P,

ue

MP,

Ms

MP,

ted

ES

=

MP,

as

aes

ps

MP,

Ga

~ MP,

then ie

as

P,

=

MP,

he

sist

—

MP. ~

Pa

~ MP,

Multiplying through by MP; (i = a, b, c, ... ,n), we find the decision rule for

each input

MR-MP,=P, MR-MP,=P, MR-MP,=P,

or MRP, = MFE, or MRP, =MFE, or MRP, =MFE,

MR-MP,=P,

or

MRP,

= MFE,

Thus the firm should demand each input up to the point where its marginal revenue product is equal to the marginal factor expenditure on that input. Let us pursue this further, first in the case of a single variable input, and later in the case of two or more variable inputs. The Firm’s Demand Curve for a Single Variable Input

In the purely competitive factor market situation, a firm demands a variable input as long as the marginal revenue product of that input is greater than, or equal to, the price of the input. The firm’s demand curve for the input reflects, thereFactor Price Determination: The Cost of Resources Used in Production

323

fore, the shape of the input’s marginal product curve multiplied by a constant, namely, the price of the output units. Recall from Chap. 5 that the law of variable

proportions might cause the MP, curve to rise at first, remain constant, and then

fall as diminishing returns set in and become progressively more severe. Without loss of generality, however, we can confine our attention to the falling, negatively sloped section of the marginal product curve.” Suppose that the production process is such that the inputs of labor give rise to output as shown in Table 14—1. Note that as total product increases due to the addition of variable factors of production, the marginal product increases initially and then declines after the second unit of labor, as diminishing returns become progressively more severe. We suppose that market price for the output is $0.20 per unit, and hence marginal revenue is constant at $0.20, regardless of output level. The final column showing MRP; is the product of the preceding two columns. Note that MRP, necessarily follows the shape of the MP, curve, rising initially and then falling. Table 14-1

Marginal Revenue Product of an Input

Factor Input

Total Product

; Marginal Product

1 2 3 4 5 6 i, 8

80 180 270 350 420 480 530 570

80 100 90 80 70 60 50 40

(units)

(units)

(units)

-

Marginal Revenue

($)

pe 7

0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20

Marginal Revenue Product

($)

16.00 20.00 18.00 16.00 14.00 12.00 10.00 8.00

In Fig. 14-1 we show the MRP, curve plotted from the data in the last column of Table 14-1. Also shown is the cost of labor, P;, presumed to be con-

stant at $10.00 per unit, this being determined by the forces of market supply and demand in the (assumed) purely competitive labor market. Notice that P; = MFE, in the purely competitive situation. The profit-maximizing firm wants to employ labor up to the point where its MRP, just equals the price of that labor. Accordingly, the firm employs 7 units of labor, determined by the intersection of the MRP, and P, curves. Note that 714 units of labor being employed would be less than profit maximizing, since the last half unit of labor would have to be

paid more than it was worth. Similarly, employing only 642 units of labor is less

2Whether or not the firm’s production process has an initial phase over which increasing or constant returns to the variable factor prevail, the firm will prefer to produce somewhere in the input range where diminishing returns to the variable factor prevail. This occurs because, if MRP, initially ex-

ceeds P,, it will continue to do so as long as MP, continues to rise or stay constant, since MR is

constant: It is not until MP, begins to fall that the possibility exists that

324

P, exceeds MRP,.

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

FIGURE 14-1 The Firm's Demand Curve for a Single Variable Input

L (Hours)

than fully profitable, since extra fractions of labor units would contribute more to the firm’s revenues than they would cost, up until 7 full units of labor are employed. The marginal revenue product curve is in effect the firm’s demand curve for the resource input. The firm demands whatever level of the input indicated by the intersection of the MRP,

and the P,; curves. Since theP,

curve is horizontal

in this purely competitive case, we may simply read off the MRP, curve at the appropriate level of P; to find how many units of labor the firm will demand. The Firm’s Demand Curve for One of Several Variable Inputs

If the firm has several variable inputs, it cannot regard the MRP curve for each input as the demand curve for that input, since variations in the other variable inputs change the marginal product (and hence the MRP) for each input. This is because a particular input’s marginal productivity depends upon the combination of other factors it is working with.

EXAMPLE:

As a simple example, note that the productivity of a painter (measured in square feet painted) would be considerably greater with more brushes rather than fewer brushes to work with, since the painter would not have to spend as much time cleaning brushes before changing colors. Similarly, five painters with more brushes would be more productive than five painters with fewer brushes. In effect, the impact of having more brushes to work with is to shift the MRP, curve upward: Each incremental unit of labor enjoys a higher MP; when using more brushes, and hence the MRP; is higher for each labor unit. Let us take this example a little further. Suppose the price of brushes falls from P; to Ps as shown in Part (a) of Fig. 14—2. At first, this would cause the firm Factor Price Determination: The Cost of Resources Used in Production

325

to increase its demand for brushes along the MRP,

curve to brush input level B’.

This in turn would raise the MRP of labor as shown in Part (b) of Fig. 14—2. This in turn would have an impact on the marginal product of brushes: With more

labor to work with, each brush will spend less time lying idle, and hence its marginal productivity will be higher. The MRP curve for brushes shifts upward, causing more brushes to be purchased. The process of adjustment continues— more brushes, more labor, more brushes, more labor, and so forth. Fortunately, the adjustments become progressively smaller and,insignificant after a point. In Fig. 14-2 we show the comparative statics of the adjustment process. (Comparative statics are the “‘before-and-after’’ view, whereas dynamics includes all the intermediate adjustments.) The marginal revenue product of brushes has shifted from its initial location at MRP; to its final position at MRP3. Similarly, the marginal revenue product of labor has shifted from MRP, to MRP.

FIGURE 14-2 The Firm’s Demand Curve for One of Several Variable Inputs a. Brushes

b. Labor

What, then, is the firm’s demand curve for brushes? Observe that at price P; the firm demanded B units of brushes, whereas at price P, the firm finally settled on its quantity demanded of B” units. Thus M and N are points on the firm’s demand curve for brushes, and we could generate more points by repeating the procedure for different price levels. The firm’s demand curve for brushes, therefore, passes through points M andN, and is shown in the figure as the curve dy. Notice that it is comprised of a single point from each MRP, curve, rather than being coextensive with the MRP curve, as in the simple case of one variable product.

NOTE:

Thus we have seen that the demand curves for variable inputs to the production process tend to slope downward to the right: More is demanded when the input price is lowered, and less is demanded when the input price is raised. Just as in consumption theory where utility maximization caused consumers to demand

326

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

more of a product as its price fell and less as its price increased, in distribution theory it is profit maximization that causes producers to demand more of an input when its price falls and less when its price rises. The law of demand strikes again! Let us now move from individual firms’ demands for inputs to the aggregate or market demand for those inputs. Market Demand Curves for Factors of Production

In the product markets we were able to add horizontally the individual consumer demand curves, in order to arrive at the market demand curve for each particular product. In the factor markets, it is not quite so simple, however, since there is a secondary effect on the individual firm’s demand for a particular input—a result of other firms’ demands for that input. To see this, note that if all firms increase their quantity demanded of a particular input, due to a reduction in its price, then all firms subsequently increase their production, since output is a positive function of the inputs. Thus the supply curve in the product market shifts to the right, and, given the product market demand situation, it causes the market price of the firm’s output to be reduced. This in turn reduces the MRP of the input at each level, which causes the firm’s demand curve for the input to shift downward. In Fig. 14-3 we demonstrate the primary and secondary effects of a price change on the demand for an input by a representative firm. The consequent impact on the market demand for the input is also shown. First of all we show the reduction in the input price from P, to P;. This causes firms to react initially by increasing their quantity of labor demanded from L to L’, as shown in Part (a) of Fig. 14-3. This greater labor input by all firms means greater output from all firms, which depresses the price in the product market (not shown). Since the firm’s demand curve for the input depends upon the product’s price and its FIGURE 14-3 Market Demand for a Variable Input a. A Representative Firm

b. The Factor Market

Factor Price Determination: The Cost of Resources Used in Production

327

marginal revenue, that demand

curve must shift downward

as a result. Each

firm, experiencing a shift of its demand curve for the input from d, to d; as shown in Fig. 14-3, reduces its employment of the factor from L’ back to L”. This readjustment from L’ to L" is the secondary effect of the change in the price of the input, and is in response to the change in the product’s price, which resulted from the initial change in the input price. The market demand curve for the input is shown in Part (b) of Fig. 14—3. Note the difference in the horizontal scales between Parts (a) and (b) of the figure. The market demand for the input is many times as large as that of the representative firm at each input price level. Again, the market demand curve simply shows the comparative statics of the situation. At price P;, aggregate demand is SL, being the L units demanded by each firm, multiplied by the number of firms. At price P;, and after the necessary adjustments made by each firm, aggregate demand is now 3L", being the L” units demanded by each firm, multiplied by the number of firms. Recall from our discussion in Chap. 9 that we can use the concept of the representative firm in purely competitive markets, since the competitive forces in such markets ensure that all firms gravitate to the same (most efficient) plant size and output level. It follows, therefore, that these firms require the same input levels of each resource when in long run equilibrium. Derived Demand for Inputs

It is important to note that the firm’s demand for inputs is dependent upon the product market’s demand for the firm’s output. By demanding the product, consumers indirectly demand the inputs that produce that product. If prices are higher in the product market, the firm’s MRP curves are higher for each product and hence the firm’s demand curve for each product is higher. Given the price of each input, the firm employs more units of each input when product prices are higher, compared with when they are lower. To describe this dependence of the firm’s demand for inputs upon the consumers’ demand for outputs, we say that there is aderived demand for the inputs of production. EXAMPLE:

An example of some proximity to both you and me is the demand for professors. You are demanding an education from your university or college. Your

college or university has established a production process, which includes fixed factors such as buildings, classrooms, administrators, tenured faculty members, and other instructors holding shorter term contracts. Variable inputs include tutorial and laboratory assistants, chalk, slide transparencies, paper, typing services, copying services, and so forth. Your university demands these inputs because you demand education. If student demand continues to decline, due to the people who were born during the baby boom between 1946 and 1962 passing through their twenties and thirties, the universities and colleges of the United States, Canada, Britain, Australia, and New Zealand, for example, will hire fewer professors, will not replace others when they leave, retire, or die, and will shift more professors into administrative functions. So please stay in school! Take a masters degree! We depend on you! | 328

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

Market Supply Curves for Factors of Production

The supply curve for a particular factor of production represents an offer of varying amounts of the services of that factor at different price levels. Use of these services sometimes results in the destruction of the factor of production, as in

the case of oil used for heating. In other cases the factor of production survives to serve another day, simply by offering its time and efforts, labor and machinery, for example, or its location, land, for example. For the most part, we should expect the supply curve of an input to be a positive function of the price being offered for that input. That is, as the price is raised, more of an input is supplied. At higher prices, it is more profitable to offer more services of an input or, alternatively, at higher prices it now becomes profitable to offer the services of the marginal unit, which may have a relatively high marginal cost of production. EXAMPLE:

For example, the high gold prices of 1979 called forth an increase in the supply of gold, partly due to governments and other hoarders finding it profitable to liquidate their inventories, and partly because mining activity was undertaken in places where the yield of gold (per ton of rock) was previously too low to be profitable. At higher gold prices, low-yield gold mining is now profitable and is undertaken. The theory of production and supply from Chap. 5 allows us to determine exactly how much each supplier of inputs offers to the market at each price. Most inputs to the production process are themselves outputs of a production process. As implied above, gold is an input to the jewelry, dentistry, aeronautics, and electronics industries, but is an output of the gold mining industry. We assume each gold mining firm in our hypothetical world of pure competition wants to maximize profits, and will produce and supply gold up to the point where its marginal cost of production equals the marginal revenue from its sale (equals price in a purely competitive gold market). We saw in Chap. 9 that the marginal cost curve of the purely competitive firm can be viewed as that firm’s supply curve of its output. Given the phenomenon of diminishing returns to the variable factors of production, we expect this supply curve to be upward-sloping to the right. The horizontal summation of the marginal cost curves of all producers therefore gives rise to a positively-sloping aggregate supply curve.

The Backward-Bending Supply Curve of Labor

All inputs of production are owned by someone or, like air and water, they are jointly owned by society and nobody minds you using a bit as long as you keep it clean. These “free goods” are thus available to the producer for the asking. All other inputs get put to work by their owners when the price is right. Thus the owners of raw materials, manufactured components, energy resources, land and buildings, and so forth, are expected to supply more of the services of their resources when price is higher, as compared with when price is lower, with all other things being equal. Factor Price Determination: The Cost of Resources Used in Production

329

Labor may be a little different, however. Labor is owned by itself; it makes up its own mind when it works and when it does not, unlike other inputs, which are simply put to work by their dispassionate owners. There is considerable reason to believe that, as the price of labor rises, labor supplied for work will after some point begin to decline rather than further increase. This phenomenon is known as the backward-bending supply curve of labor and is illustrated in Fig. 14-4. Notice that as the price of labor is increased from P,; to P;, the quantity nents of labor supplied is reduced from L toL’. aN FIGURE 14-4 The Backward-Bending Supply Curve of Labor

NOTE:

The backward-bending supply of labor can be explained by the theory of consumer behavior. Suppliers of labor are also consumers and as such are postulated to be committed to the pursuit of utility maximization. A consumer derives utility from income, of course, since it allows the consumer to purchase goods and services that are expected to generate utility during the consumption process. But the process of earning income takes time, and time has an opportunity cost to the consumer, who could otherwise spend that time in leisure. The consumer can be expected to derive utility from leisure, both for its own sake and because it gives the consumer time to consume the goods and services bought with the income earned. Clearly a sailboat, a stereo, and similar goods and services will not give much utility if you never have time to use them. Thus there is a tradeoff between work and leisure, as we noted in Chap. 2. After a point additional income is not worth the leisure given up, and the individual may maximize utility by working fewer hours at the higher rate. Note that in the case depicted by Fig. 14—4, the individual earns more money by working fewer hours, since the wage rate (P,) has risen proportionately more than the individual’s labor supply has fallen. Total income is measured before the price change by the rectangle OP, AL (the wage rate times hours worked), as compared with the rectangle OP’, BL’ at the new price of labor.

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FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

The backward-bending supply curve for labor might be observed for individuals, but will be less noticeable in aggregate and in the real world. In aggregate, the market supply curve includes individuals with different taste and preference patterns between income and leisure. Those wishing to work more at higher wage rates may outweigh those reducing their input, and so the net or aggregate effect may be that more labor is supplied at higher wage rates. In the real world, where recent inflation rates continue to undermine the real value of income, most wage increases serve only to restore or slightly improve the real value of income, and so the substitution of leisure for income might be expected to be slight. Over the past several decades, however, we have seen the average work week decline progressively from 60 to 70 hours per week to the current 35 to 40 hours per week. This decline has surely been assisted by the pressure of unions and has been accompanied by a major increase in the real incomes of wage earners. The persistence of inflation into the 1980s may slow down this trend, however, as real income gains have been reduced or eliminated for many

people as a result of the ongoing inflation. Price Determination in Factor Markets

We are now ready to bring together the market demand and supply curves for particular factors of production and determine the equilibrium level of price for each input. In Fig. 14-5 we show the market situation for a particular resource. Just as in Chap. 9, price determination in a purely competitive market is a result of the interaction of the forces of aggregate supply and demand. Excess demand causes the price to be raised by the bidding of unsatisfied buyers. Oppositely, excess supply causes the price to be lowered by the price cutting of unsatisfied suppliers. When there is neither excess demand nor supply there are no forces operating to raise or lower price, and hence the market price is at the equilibrium level. This price level is shown as P* in Fig. 14-5, at which L* units of the input are both supplied and demanded. FIGURE 14-5 Price Determination in Purely Competitive Factor Markets $/L

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331

To summarize the model of factor price determination in purely competitive markets, the firm’s demand for each factor depends upon the marginal productivity of that factor and the price of the firm’s output in the product market. Market demand for each factor is comprised of the demands of all firms, after adjustment by each firm for the effect that changing demand for the factor has upon output and the subsequent change in the market price of that output. Individual suppliers of factors of production offer the services of their inputs up to the point where the marginal cost of producing that input just equals the price (marginal revenue) received for that input. Suppliers of labor, also being consumers, are likely to make their supply decision based on utility maximization, and accordingly may reduce their supply at higher price levels for their services, being content with a larger total income and more leisure time. In aggregate therefore we expect the market supply curve for each input to be positively sloping, with the possible exception of the supply curve for labor, which may bend back at higher levels of compensation for labor services. Finally, the interaction of supply and demand forces determine the market price for each input. Given the market price of the input, each firm knows its marginal factor expenditure and employs each factor until its marginal revenue product falls to that price level, in order to maximize its profits. Each supplier of inputs, knowing the market price, offers to supply up to the point where its marginal cost of supplying the input is just equal to that price. You can see that the determination of the equilibrium market price requires the simultaneous determination of all demand side and supply side decisions. The equilibrium market price ensures that the aggregate supply of each factor just equals the aggregate demand for each factor, despite the independent decision processes of the many suppliers and demanders of each resource.

Ill. FACTOR PRICE DETERMINATION IN IMPERFECTLY COMPETITIVE MARKETS We now relax the restrictive assumptions of pure competition in the product

and factor markets. In the real world, of course, most product and factor markets do not fulfill the conditions required for pure competition. Those assumptions of the purely competitive model which are most difficult to find in practice are the existence of many buyers and many sellers in the same market, and the homogeneity of all units of the product or service offered in that market. Recall, however, that we use the purely competitive model mainly as a pedagogical device: It allows us to understand the operation of a market in its simplest terms, free from the added complexities of fewness of buyers or sellers and the existence of product differentiation. As a corollary, the purely competitive model serves as a “‘benchmark” from which we can measure the effects of fewness and of product differentiation when these are added to our models of firm’s behavior. In the following pages you will appreciate the value of having examined the issue of factor pricing in the simplistic context of pure competition. Since the basic model is already known it is relatively easy to follow the factor price determination models for monopolistic competition, oligopoly, and monopoly 332

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markets, since all we have to do is modify the structural assumptions and see how these change the price determination problem. We shall do this in stages. First, we consider imperfect product markets and ascertain the impact these have on the firm’s marginal revenue product curve and subsequent demand curve for each factor. Second, we consider imperfect factor markets and ascertain their effect on the marginal factor expenditure curve faced by the firm. We then look at the implications of monopsony demand for a factor, monopoly supply of a factor, and finally bring these two together in the situation called bilateral monopoly. The Effect of Imperfect Product Markets on the Firm’s Demand for a Factor

In imperfect product markets, the firm faces a downward-sloping demand curve for its product, whether that market is monopolistically competitive, oligopolistic, or a monopoly. In each case, the firm cannot sell all it wants to at the market price, since its product is either differentiated from other available products or the firm is relatively large compared to the market. To sell more units of its output, the firm must reduce its price, offering this lower price to all potential buyers. Given a downward-sloping demand curve, marginal revenue is less than price and declines as quantity demanded increases. A declining marginal revenue causes marginal revenue product (MRP) to decline faster, since MRP is now the product of a declining marginal product of the factor and a declining marginal revenue in the product market. To demonstrate this, let us modify Table 14—1 above to reflect the impact of declining marginal revenue. In Table 14—2 we show the same total product and marginal product schedules, but multiply the latter by a decreasing value for marginal revenue. Recall that MR was constant at $0.20 in Table 14-1, this

being the equilibrium market price. In imperfect competition, MR is high at first and then falls below the purely competitive market price level. For Table 14—2 we have presumed that the firm faces a specific demand curve in its product TABLE 14-2 Marginal Revenue Product of an Input Given Declining Marginal Revenue EEE EIEy SE SN

Factor Input

(units)

Total Product

(units)

Marginal Product

(units)

Marginal Revenue

($)

ee es 0.54 80 80 1 0.40 100 180 2 0.27 90 270 3 0.16 80 350 4 0.06 70 420 5 -—0.02 60 480 6 -—0.09 50 530 7 -0.15 40 570 8

rs

Marginal Revenue

Product

($) 43.20 40.00 24.30 12.80 4.20 —1.20 —4.50 —6.00

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333

market. The marginal revenue figures shown in the table relate to that presumed demand curve.? Notice that as marginal revenue declines and becomes negative in the product market, it causes the MRP of the factor to decline more quickly and become negative as well. Thus the MRP curve, as shown in Fig. 14-6, is considerably more steep under conditions of imperfect competition compared with the pure competition situation depicted earlier in Fig. 14-1.

FIGURE 14-6

me

\

The Marginal Revenue Product Curve, Given Imperfect Product Markets

Factor units

To find the firm’s demand curve for each factor of production, we proceed as we did in the pure competition case. If the firm uses only one variable factor, the MRP curve is the firm’s demand curve. If the firm employs two or more variable factors, its demand curve for each input is derived from the MRP curves, taking into account the shifts in each MRP curve that are due to changes in the employment of the other variable factors. In all cases we expect the firm’s demand curves for the factors of production to be steeper than they would be if the product market was purely competitive. The Effect of Imperfect Factor Markets on the Firm’s Marginal Factor Expenditure

When factor markets are imperfect, we should not expect the firm to be able to purchase any amount of the factor at the same price. In pure competition where the firm was very small relative to the market and where units of the factor input >We presume that the firm’s product demand curve intercepts the price axis at $0.65 and slopes downward $0.07 for every 100 units demanded. Algebraically, the firm’s demand curve is P = 0.65 — 0.0007Q. The firm’s marginal revenue curve, having the same vertical intercept and twice the slope, is therefore MR = 0.65 — 0.0014Q. By substituting the total product figures from Table 14-2 for Q, we find MR at each level of Q.

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from different suppliers of the factor were homogeneous, we could say that the firm faces a perfectly elastic supply of all inputs and hence could demand as much or as little as it pleased at the market price for that factor. If the suppliers of factors are relatively few in number, they can influence the market price by their actions, and are likely to ask higher prices for their services when demand is greater. Similarly, where there are many suppliers of a factor, but the services of these factors are differentiated on the basis of skill, talent, productivity, or other differences, each factor is likely to want higher prices for its services when it is being asked to supply greater quantities. Because of its differentiated service, the supplier of the factor is like a monopolistic competitor with a limited amount of control over the price it asks for its product. Thus we expect the supply curve for factors to be upward sloping to the right in imperfectly competitive factor markets. This supply curve indicates the price per unit the firm must pay for various quantities supplied of a particular input to the production process. Note that this supply curve is also the curve of average factor expenditure (AFE), as shown in Fig. 14—7. Since average factor expenditure—at each level of inputs purchased—is equal to the price per unit at that input level, the supply curve also reflects the firm’s average cost per unit of the factor purchased. As the price per unit rises for larger quantities supplied, so too does the firm’s average factor expenditure. FIGURE 14-7 Average and Marginal Factor Expenditure Curves in Imperfect Factor Markets S/F MFE

AFE=S

0

Factor units

In the preceding chapters, we have learned that every average curve hasa corresponding marginal curve, and that if we know the location of one of these curves, we can infer the location of the other. If the average curve is falling, we know the marginal curve lies below and is steeper than the average curve—for example, the average revenue (demand) curve and marginal revenue curves. If the average curve is rising, we know that the associated marginal curve lies above and is steeper than the average curve—for example, marginal cost of proFactor Price Determination: The Cost of Resources Used in Prod uction

335

duction pulls up the average variable cost of production. The average factor expenditure (AFE) curve is no exception. There is a curve that shows the marginal factor expenditure (MFE) and that lies above and is steeper than the AFE curve. This curve is shown in Fig. 14—7 as MFE. It is a locus of the values for the change in total factor expenditure divided by the change in total factor inputs. It lies above the AFE curve, because to purchase each additional unit of the factor requires that a higher price be offered to that unit and all preceding units. Thus total factor expenditure increases to the extent of the cost of the last unit purchased plus the additional amount that must be paid to all preceding units. If all ° preceding units are not paid the higher rate, they would simply withdraw their services and wait to be the last unit employed, resulting in chaos. Determining the Factor Price and Quantity Demanded

We can now bring the two sides together and find the equilibrium price of the factor and the amount of that factor that the firm demands at the equilibrium price. Using the case of labor, we show in Fig. 14-8 the superimposition of the demand for labor curve (D,) upon the average and marginal factor expenditure curves for labor. Recall that the profit-maximizing firm employs labor up to the point where the MFE, just equals the marginal revenue product of labor (MRP;). The MRP; is involved in the construction of the D, curve, of course, and every point on the D, curve represents a point on a MRP, curve. Thus the firm should employ L* units of labor, since it is at this input level that the MRP; = MFE,—at point A in Fig. 14-8. Notice that the firm is willing to pay onlyP} per unit of labor, since any higher price would cause the MFE, to exceed its marginal revenue product. At price Pj per unit, the suppliers of labor offer L* units, and so the factor market is in equilibrium, with supply equal to demand at that price. FIGURE 14-8 Factor Price Determination in Imperfect Product and Factor Markets

$/L

Labor (L)

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DEFINITION: Note that the firm in the above scenario is acting like amonopsonist. That is, it is the only buyer for the particular resource in question, and there are many suppliers of that resource. EXAMPLE:

An example of a monopsony is a town that exists because of a lumber mill and in which all workers, including those employed in the company store, are employees of the company owning the mill. More generally, people who do not have the mobility to move elsewhere in search of jobs, due to family considerations, for example, may find themselves with only a single nearby demander for their services. Alternatively, people with highly specialized skills, such as ballet dancing and circus acts, may have only one possible employer in some countries. Examples of such employers might be the National Ballet of Canada or the Moscow State Circus.

Monopoly Supply of a Factor of Production

Suppose now that the entire supply ofa particular input is controlled by a single entity, such as the monopoly producer of a rare metal or the union representing a particular group of workers. INCO was for many years a monopoly supplier of nickel. Such a supplier has the market power to dictate price, and the firms desiring that input have no option but to pay the price asked (other than to forego the use of the factor altogether). How will the monopoly supplier determine its price level? Being a monopoly supplier, it sees the market demand curve for the factor as its own demand curve, with an associated marginal revenue curve. If it is a profit maximizer, it will set price such that its marginal revenue from the sale of the factor is just equal to its marginal cost of producing that factor. We show this in Fig. 14—9 for the case of a monopoly producer of a precious metal, such as kryptonite. The monopoly supplier of kryptonite sets price equal toP;, at which price (and associated demand and output levels), the monopolist’s marFIGURE 14-9 Factor Price Determination Given Monopoly Supply of the Factor

Kryptonite (units)

Factor Price Determination: The Cost of Resources Used in Production

337

ginal cost of producing the metal rises to equality with the marginal revenue from the sale of the metal. Bilateral Monopoly

DEFINITION: As the name implies, a bilateral monopoly exists when there is only one seller and only one buyer fora particular product or resource. From the foregoing it can be appreciated that such situations are more likely to be found in resource markets than in product markets. In particular the labor markets often display bilateral monopoly conditions. EXAMPLE:

If all the workers in a company town become unionized, for example, the result is a bilateral monopoly. Similarly with only one Wernher von Braun and only one NASA, one can suppose there was a bilateral monopoly situation involved in establishing Dr. von Braun’s salary in the early days of the space program. More generally, any person with special skills or abilities may find themselves in a one-on-one situation with a potential employer when it comes to establishing the rate of remuneration. The individual doesn’t have any other job offers and therefore the employer could force the salary level down. On the other hand, the employer does not have any other candidates with these special skills and abilities. Therefore the candidate could force the salary level up. In all these cases, what is the final solution? The bilateral monopoly model of factor price determination is constructed by bringing together the cases of a monopsony buyer (Fig. 14-8) and a monopoly seller (Fig. 14-9). Superimposing one upon the other, we obtain Fig. 14—10. Considering the monopsony buyer first, this firm or entity prefers to set price at P,, such that the marginal factor expenditure just equals the marginal revenue FIGURE 14-10 Bilateral Monopoly

MC = AFE

Units of the Factor (F)

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FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

product from that factor (shown by the demand curve D,). The seller, on the other hand, would prefer to set price Ps, so that the seller’s marginal cost of producing the factor just equals the marginal revenue that may be obtained from the sale of the marginal unit. Thus we have a conflict: The buyer wants to buy F, units at price Ps, and the seller wants to sell F, units at price Ps. How is this conflict resolved? Unfortunately the microeconomic principles have taken us as far as they can. We cannot solve for an equilibrium resource price, because the problem is not simply an economic one. The final price is settled upon by means of negotiation and depends on the resolve and bargaining power of the two parties involved. All the microeconomic principles can do is establish the upper and lower bounds: Neither party wants a price above Ps or below P;. The seller tries to raise the buyer’s offer above Pz, and the buyer tries to reduce the seller’s offer below Ps. Ultimately the price is set somewhere in between. We return to this issue in the context of wage and salary negotiation in the next chapter.

IV. TOPICS IN FACTOR MARKETS We now turn to several issues that are suggested by the foregoing analysis. Economists often speak of rents and quasi rents, to the great mystification of others. Rents and quasi rents sound like something to do with renting an apartment, but in economic terms the meaning is quite different. A brief examination of the concept of economic rent is quite instructive. Following that we investigate the issue of factor price differentials for qualitative differences in input units. Why does Guy Lafleur earn more than Bobby Clark, when both play hockey in the same league and spend about the same time on the ice? Let us read on and find out. Economic Rent and Quasi Rents

DEFINITION: Economic rent is defined as that part of the payment to a factor of production that is over and above the payment necessary to secure the services of that factor. Recall that in order to secure the services of an input, the firm must pay the input at least as much as it could earn in its next best alternative employment. Thus economic rent is equal to the total payment to the resource less the opportunity cost of that resource. EXAMPLE:

Consider the case of a professional wrestler who has little education and no other skills. As a wrestler he earns, let us say, $30,000 per annum. Suppose his next best alternative employment is as a “bouncer” in a nightclub, where he would earn $20,000 per annum. This person therefore receives an economic rent of $10,000. Note that it is nowhere implied that he is not worth $30,000 in his

employment as a wrestler: His marginal revenue product presumably equals or exceeds that figure or else the employer would refuse to hire him as a wrestler. In other situations persons receiving economic rents may not be “worth” Factor Price Determination: The Cost of Resources Used in Production

339

their salary, but they remain on the payroll for legal or humanitarian reasons. For example, a tenured professor receiving $60,000 per annum may be doing minimal teaching and no research. Without tenure, he or she could be replaced by a younger professor who would do at least as much work for $30,000 per annum. Similarly, members of strong unions may retain their jobs, despite being paid more than their MRP and more than it would cost to replace them, by virtue of the threat of a labor strike if union members are fired. Also, persons near retirement age may be kept on the payroll on the basis of noneconomic considerations, such as it being ‘‘unfair’’ to fire them atthis stage in their career.

In the short run the inputs of some factors are fixed, and thus their opportunity cost is zero, since they cannot obtain employment elsewhere until a long run situation is achieved. Thus the entire payment to fixed inputs in the short run is an economic rent, since the entire payment is the amount over and above

that necessary to secure the services of these inputs. Economic rents received by factors that are fixed in the short run are called quasi rents, since the situation is transitory. In the long run situation, these inputs have alternative uses and therefore an opportunity cost that must be paid to secure the services of these inputs for the subsequent short run period. If total revenue exceeds total costs in the short run, the firm is receiving economic rent. That part of total revenue which equals the firm’s total fixed costs is a quasi rent, whereas the excess of total revenue over total costs is arent accru-

ing to the owners of the firm. That is, economic profits earned by the owners of the firm are economic rents. The owners keep their resources in the firm, even in the long run, as long as normal profits are obtained. Any profits above the normal profit level therefore constitute an economic rent. Thus total rents received in the short run are equal to the quasi rents plus economic profit and are therefore equal to the excess of total revenue (TR) over total variable costs (TVC). To appreciate this, note that the firm continues to produce as long as TR exceeds TVC under short run conditions, and hence any revenue over and above TVC constitutes an economic rent, since it is not necessary to secure the services of the

inputs and hence ensure that production takes place in the short run. Notice that a fixed factor has a vertical supply curve: It supplies a given amount of services regardless of the price offered. In Fig. 14-11 we show the supply and demand curves for land, and demonstrate that given the amount supplied, the price of the factor is determined by the demand side alone. If demand is represented by the curve D, the price per hectare of land is P. Alternatively, if demand increases to D’, price is P’. To go further, N units of land are supplied whatever price is offered, since being fixed it cannot go elsewhere and has zero opportunity cost in the short run. In the long run, of course, the owners of the land are able to lease their land to a different firm, and therefore they require at least the value of that lease to remain in the present line of business. Economic rents have been considered to be an appropriate base on which to levy taxes. It is argued that since rent is the payment over and above that necessary to secure the services of the input, placing taxes on rents would not alter the allocation of resources in the economy. In the example of land above, suppose now that Fig. 14-11 represents a different scenario. The initial demand 340

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

FIGURE 14-11 Economic Rent as a Component of Factor Price $/N

Land (Hectares)

situation is now represented by the curve D’, and the government decides to place a tax ofP’ — P on every hectare of land. Demanders still demand the same amount of land as they did before, and it is immaterial to them who receives the money they spend to rent it. Instead of the full price P’ per hectare going to the landowner, now only P goes to the landowner and the tax P’ — P goes to the government. In total, the tax is represented by the rectangle PP’BA, and the new payment to the landowner, comprised entirely of rent, is represented by OPAN. Notice that the tax does not change the price nor the quantity supplied or demanded: it simply skims off some of the economic rent accruing to the landowner.

Corporate profit taxes, to the extent that corporate profits approximate

economic profits, can also be viewed as a tax on economic rents accruing to the owners of firms. Since profits are the residual after all price and output decisions are made, tax on these profits should not change the allocation of resources into the production process. Rather, it reduces the residual accruing to the owners of the resources.* Finally, let us introduce the notion of producer surplus as an economic rent. Producer surplus is the excess payment a factor receives over and above the payment necessary to induce that factor to supply its services. In Fig. 14-12 we show the supply and demand curves for a particular factor market, under conditions of pure competition. The equilibrium price is P*, and it is paid to all units of factor X up to factor input level X*. Notice that the very first unit is supplied even if the price is down near pointA. Similarly all subsequent units are supplied at the price indicated by the supply curve for each level of factor X 4The term rent is derived from the rental payments by tenant farmers to land owners in the nineteenth century. Such classical economists as David Ricardo and Henry George were concerned that these payments were exploitative, since they appeared to be in excess of what was required to call forth the services of the land. Hence George’s proposal to tax away some part of this surplus for the benefit of society as a whole. The concept of economic rent is a broadening of the term “rent,” and it encompasses all situations in which revenues exceed the total variable cost of producing output. Factor Price Determination: The Cost of Resources Used in Production

341

supplied. The producer surplus, which is clearly an economic rent accruing to the owners of this resource, is thus the vertical distance between the supply curve and the line P*C, at each input level. In total, the producer surplus or economic rent is equal to the triangle AP*C and represents the total excess payment beyond that necessary to induce the factor services to be supplied.® FIGURE 14-12 Producer Surplus as an Economic Rent

Factor X (units)

Factor Price Differentials

For simplicity of exposition in the foregoing we have made the implicit assumption (for the most part) that units of a particular factor are homogeneous. That is, they have identical abilities, skills, and productivities in the case of labor or, in the case of raw materials, they have exactly the same physical composition and quality. In the real world we know that abilities differ among people, that some iron ore is richer than other iron ore, and that components from some suppliers last longer than those from other suppliers. We also observe that price differentials exist to reflect the qualitative differences in input units. Does the heterogeneity of inputs invalidate the marginal productivity model? Fortunately not, and the incorporation of heterogeneous inputs into the model is quite simple. Recall that we established the general decision rule for employing a factor of production: The producer should employ each factor up to the input level where that factor’s marginal revenue product (MRP) is equal to the marginal factor expenditure (MFE). The rule remains the same for heterogeneous inputs: The firm should hire each one to the point where its MRP = MFE. Each factor has its price determined either by the market or by a monopsonistic buyer, or it chooses its own price if it is a monopoly supplier of certain skills, abilities, or qualities. ‘Notice that the triangle P*BC in Fig. 14-12 represents consumer surplus or the amount that consumers are willing to pay for each of the units of the factor, but are not asked to, since the market price settled at P*.

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EXAMPLE:

Why does Guy Lafleur earn more than Bobby Clark and most other forwards in the National Hockey League? By now you should know the answer, or at least be able to make some close guesses. Mr. Lafleur’s marginal physical productivity is relatively high—he adds more to total product (goals scored) than most players. Further, the presence of Mr. Lafleur tends to sell hockey games to the public, due to his exhilarating rushes and playmaking abilities. Thus Mr. Lafleur’s marginal revenue product is very high. Finally, he doubtless has some rather strong bargaining power based on his exceptional abilities and the monopoly supply he has over the input called “‘Guy Lafleur.” Similarly, raw materials and other inputs of different qualities have different marginal productivities in the production process, and the input quality influences the market price for the output with consequent impact on the MRP of the factors. Thus higher quality inputs tend to be paid more than lower quality inputs. This is not to say that irregularities don’t occur from time to time, such as someone who is paid more than someone else, but who does less work. These are usually temporary aberrations and will be removed as time passes if the firm is a profit maximizer. It takes time to discover and verify such aberrations, and it may take even longer to achieve a satisfactory solution to the problem within the legal and moral constraints imposed upon the firm. If the firm is not a profit maximizer, but a satisficer, for example, such inequities may not be dealt with until they endanger the achievement of the firm’s satisfactory targets for profits, market share, labor productivity, or other variables.

V. SUMMARY In this chapter we have examined the marginal productivity theory of distribution, which explains the determination of prices in the factor markets. Under conditions of pure competition, in which factor prices are market determined, the individual firm employs each factor up to the point where the market value of that factor’s marginal product just equals the market price of that factor. This is the profit-maximizing condition and applies to the inputs of all factors of production. Where the firm employs two or more variable factors, its demand for each factor is no longer simply the marginal revenue product curve of each factor, but a locus of points on the various MRP curves for different levels of the supporting variable inputs. As any given variable input has more of the other variable inputs to work with, its MRP curve tends to shift to the right. This in turn causes more of that factor to be demanded, raising its market price. The firm’s demand curve for each factor is the locus of equilibrium market prices and the point on the MRP curve that is finally settled on for each equilibrium market price. Individual demands and supplies of factors are aggregated to find the market demand and supply curves and the equilibrium market price. It was noted that the supply curve of labor may bend back at higher wage and salary levels as a utility-maximizing response to the choice between income and leisure. Factor price determination under imperfect market conditions has two Factor Price Determination: The Cost of Resources Used in Production

343

main impacts on the basic model. First, the MRP curve becomes steeper as a result of marginal revenue being less than price in the product markets. Second, the supply curve of each input required by the firm is likely to slope upward to the right, meaning that the marginal factor expenditure curve lies above and is steeper than the supply curve. A monopsonistic employer of a factor may exploit that factor market by employing only to the point where the factor’s MRP equals its MFE, with a relatively low factor price as a result. Oppositely, a monopolistic supplier of a resource sets price at a relatively high level, maximizing its own profits. A bilateral monopoly situation is indeterrhinate, with the actual price being negotiable between the upper and lower limits set by microeconomic principles. Finally, we examined the concept of economic rent and quasi rents, which are payments to factors that exceed the factor’s opportunity cost. Such rents may be taxed without altering the allocation of resources, in the short run at least. Factor price differentials to reflect qualitative differences in the factor units are a logical extension of the marginal productivity theory.

DISCUSSION

344

QUESTIONS

1.

Explain the inverse relationship between the marginal productivity of the variable factor(s) and the marginal cost of output. Link the argument from this chapter with the relationship between the TVC and TP curves discussed in Chap. 6.

2.

What is the decision rule for the employment of a particular input to the production process? How does this depend on the supply and demand conditions in the product markets as well as these conditions in the factor markets?

3.

Why is the marginal revenue product curve effectively the firm’s demand curve for the variable input in the case of a single variable input to the production process?

4,

How is the firm’s demand curve for a particular variable input constructed in the case of several variable inputs to the production process?

5.

Explain how the market demand curve for a particular input is constructed? Why is it not simply the horizontal addition of the firms’ demand curves for that input?

6.

Why might we expect the supply curve for labor to bend back at higher wage levels, whereas other inputs are expected to exhibit supply curves that are positively sloping throughout?

7.

Imperfect product markets cause a change in the demand side of the factor markets, and imperfect factor markets cause a change in the supply side of the factor markets. Explain.

8.

Using graphical analysis, show the maximum and minimum price levels that would be possible under conditions of bilateral monopoly. What determines the actual price?

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWN ERS

9.

Explain the concept of economic rent. Give several examples of an input to a production process that receives rent. What is the relationship between rent and barriers to the entry of new firms?

10.

How does the marginal productivity theory of factor price determination explain why a quarterback’s salary is typically higher than that of a linebacker? Why are some quarterbacks paid more than others?

SUGGESTED

REFERENCES

BRONFENBRENNER, M., “Neoclassical Distribution Theories,” in The Distribution of National Income, ed. J. Marchal and B. Ducros. London: Macmillan, 1968.

FERGUSON, C.E., The Neoclassical Theory of Production and Distribution. New York: Cambridge University Press, 1969. Hicks, J.R.,

The Theory of Wages. New York: Macmillan, 1932.

HIRSHLEIFER, J., Price Theory and Applications (2nd ed.), chaps. 14, 15. Englewood Cliffs, N.J.: Prentice-Hall, 1980. JOHNSTON, J., “A Model of Wage Determination under Bilateral Monopoly,” Economic Journal, vol. 82, 1972. Kautpor, N.,

“Alternative Theories of Distribution,’ Review of Economic Studies, vol.

23, 1955-1956.

KOUTSOYIANNIS, A.,

Modern Microeconomics (2nd ed.), chap. 21. London: Macmillan,

1979.

ROTTENBERG, S.,

‘The Baseball Players’ Labor Market,” Journal of Political Economy,

64 (June 1956), 242-58.

RUSSELL, R.R., ‘Onthe Demand Curve for a Factor of Production,’ Review, 54 (Sept. 1964), 726—33.

American Economic

WorcEsTER, D.A., ‘A Reconsideration of the Theory of Rent,” American Economic Review, 36 (June 1946), 258-77.

Factor Price Determination: The Cost of Resources Used in Production

345

| =

Profits, and Inflation

I. INTRODUCTION In the preceding chapter we examined the theory of factor price determination. Although you may think that little of this theory relates to the real world, the theory of factor price determination does explain and predict actions, events, and trends observable in factor markets to a remarkable degree, but only after you cut through the fog created by real world complexities. These complexities include inflation as the number one obscurer of simple economic analysis, followed by the false claims and poorly reasoned statements of vested interest groups in society, which in turn are often prompted by the effects of inflation. Such claims may include a labor union asserting that it deserves a larger share of the firm’s revenues, and management asserting that any further increases in the wage rate will cause the firm to go bankrupt. A careful microeconomic analysis of such statements might show that they are simply part of the rhetoric of negotiation, rather than a reflection of sound economic reasoning. In this chapter we examine the real world complexities associated with wages, profits, and inflation. Inflation emerged during the 1970s and continued on into the 1980s as a pernicious economic problem, creating hardships for individuals and society in general. Who is to blame for this seemingly endemic problem? Popular culprits are the large and powerful labor unions and the large and powerful corporations, each asking for a larger share of the economic pie. But the only way that everyone can have more pie than before is for the pie to get 346

larger. This it does in nominal dollar terms by the process of inflation. To make more profit, the firm raises prices. This causes wage earners to suffer reduced real incomes and to make demands for higher wages. These demands, once met, reduce the firm’s profits, so it again raises prices, and on and on it goes. If the real value of production does not change or changes less than the money value, both parties may become worse off, not better off, as time passes. For both labor and management in the modern business firm operating under inflationary conditions, it is a continual process of slipping back, catching up, slipping back again, and so on, as inflation persistently erodes the purchasing power of labor’s wage dollar and management’s profit dollar. At this stage there is no point in trying to attach blame: It doesn’t matter who started it, it is more important to understand the phenomenon of inflation and to search for solutions to the problem. In the following we examine the wage determination process when it involves labor unions as collective bargaining units in the negotiation process. Briefly noted is the historical development of unions, their extent today, their objectives, and the bargaining strategies that they might employ. We turn then to the issue of profits. Are profits justifiable? How should we measure profits, and what might happen if profits are insufficient, both in the short and the long run? We then turn to the issue of prices and inflation. Who is responsible for inflation? Why does the process continue? Can we control inflation, and if so, by what means?

Il. WAGE DETERMINATION INVOLVING COLLECTIVE BARGAINING DEFINITION: As the name implies, collective bargaining is the process whereby an entity acts as the spokesperson and negotiating agent for a group of people. In the wage determination process, this entity is typically the labor union representing the workers involved. Rather than have all individual workers negotiate with their employer for wage rates and other conditions of employment, the workers designate a person or group of persons through the union to bargain collectively for higher wages and better working conditions. Collectively the workers have the strength of a monopolist (the single seller of a service), whereas individually they are vulnerable to the competitive pressures of each other. Labor Unions

At the start of the 1980s only about 22% of all American workers belonged to unions, this proportion having fallen from around 25% in the early 1950s.' There is markedly less unionization in the United States than in some other Western countries such as Canada, Britain, and Australia. These latter countries have shown a greater tendency toward collective endeavors in other areas as well; socialized medical care is the most notable. Japan has a long history of paternalThe Ruins Gave Rise to Big Labor,” Business Week, September 3, 1979, pp. 26-8. Wages, Profits, and Inflation

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istic employers who treat their workers like family members, although in recent years increased job mobility and affluence are causing this image to change. The figures above relate to all workers. Many workers, however, are not union members—the self-employed, those involved in managepotential even or large enterprises, or those who are unlikely to want medium, small, of ment some other reason. Farm workers are typically not for union a to belong to are the employees of firms hiring relatively few usually, Neither, unionized. the relationship between employer and enterprises, scale small such In workers. and the employee either gets what direct, and close rather usually is employee he or she wants or finds a job elsewhere. The employer can usually replace one or a few dissatisfied workers without much trouble. The greatest potential for unionization occurs in larger industrial enterprises where ownership of the firm is separated from management of the firm and management is typically insulated from the workers to a substantial degree. The first American union is said to have been the shoemakers of Philadelphia, who formed an association of craftsmen in 1792.7 Other craft unions were formed soon afterwards in other northeastern cities. These unions were formed mainly as a defensive strategy by skilled workers to protect their incomes in a time of increasing competition among merchant capitalists. As markets for their products grew, skilled workers were faced with competition from less-skilled labor (the segmentation of tasks into more simple subtasks) and the invention of labor-saving machines. Thus unionization gradually became more common. Unions tended to flourish in good times and disappear almost entirely in depressions. In 1886, the American Federation of Labor (AFL) was formed as the collective association of these individual craft unions. The dominant figure in the new labor movement that dates from this time was Samuel Gompers, whose antipathy toward socialism probably accounts for the procapitalist orientation of American unions to this day. American unions, rather than involving themselves in political issues, as British and Australian unions often do, almost totally confine their actions to economic matters benefitting their members. A major event in the development of the labor movement was the Great Depression from 1929 to 1933. This cataclysmic collapse of the economy forced 11 million Americans into unemployment after they had enjoyed the bouyant good times of the Roaring Twenties. The hardships endured in the early thirties helped change the attitudes of workers toward unionization. The resultant conflict between labor and management brought the government into the picture to protect the unions. The National Labor Relations Act of 1935 (The Wagner Act) was passed to prevent some of the practices of management against unions, such as firing workers who joined unions, employing “‘bullies,” and having company spies report on the activities of the workers. The Wagner Act gave workers the right to unionize, gave the union the right to bargain for its members, and prohibited some other employer practices.3 The depression gave substantial impetus to another trend in the labor movement—it accelerated the growth of industry-wide unions, rather than the Lloyd G. Reynolds, Labor Economics and Labor Relations, 7th ed. (Englewood Cliffs, N.J.: Prentice-

Hall, Inc., 1978), p. 334.

3“Ruins,” Business Week, pp. 26-8.

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fragmented craft-unions favored by the AFL. John L. Lewis, the President of the United Mine Workers, was a major force in the formation of the Committee (later Congress) for Industrial Organization (CIO) in late 1935, after trying unsuccessfully to induce the AFL to broaden its appeal and its power in the economy. In its first two years, the CIO made substantial inroads into the American labor market, achieving unionization of General Motors and U.S. Steel, as well as major companies in the rubber and electrical industries. The decade from 1935 to 1945 was the heyday of American unionism, with membership jumping from 3.4 million workers (11.6% of the nonfarm work force) in 1930, to 14.3 million workers (about 34%) in 1945. After the interruption of World War II, employers fought back on the legislative front. The TaftHartley Act of 1947 outlawed certain union practices and led to a significant reduction in union power. Union memberships, although increasing in numbers until 1970, began a gradual decline as a proportion of the American workforce to its present level of about 22%—approximately 19 million workers. In 1955, after nearly two decades of negotiations, the AFL and the CIO finally merged, and there was then a single umbrella organization representing most of America’s unionized workers. Several major unions, however, notably the Teamsters, remained outside the AFL-CIO.

NOTE:

In more recent years the labor movement has allowed issues to move from the bargaining table to general legislation. Minimum wages, working hours per week, pensions, and health and safety issues are now legislated for the benefit of all workers. Union memberships may continue to decline as workers look to the government for protection in the work place. But the attitude of American unions is also changing, and this may increase their appeal. In January 1980, the Longshoremen’s Union refused to unload Soviet ships in response to the Soviet invasion of Afghanistan. This type of political and social action represents a new front for American labor.

Objectives of Labor Unions

The economic objectives of labor unions are rarely stated unambiguously. Samuel Gompers is reported to have said ‘“‘We want more, more, more, now!’’* More of what is the crucial issue. More money for those already employed? More employment for the entire labor force? Maximum earnings for labor as a whole? More time off work, more job security, more freedom of movement and choice while on the job? More equity in the labor market? More justice for oppressed peoples? More environmental quality? In fact all these factors have been objectives of one union or another at one time or another. These objectives tend to conflict with each other, however, when they are sought simultaneously.

Maximization of the Wage Rate. If workers are already receiving the equilibrium wage, so that supply of labor equals demand for that labor, a union-forced increase in the wage rate causes a reduced demand for labor and leads to unemployment of some workers previously employed, as firms begin to substitute 4Reynolds, Labor Economics, p. 345. Wages, Profits, and Inflation

349

equipment and prefinished materials in place of labor. In Fig. 15—1 we show a hypothetical labor market situation. Suppose the prevailing wage is initially Wo per hour, so that the market is in equilibrium with labor supply (S) equal to labor demand (D) at Ly hours per week. Now suppose that the labor union succeeds in raising wages to W, per hour. Demand for labor then falls to L, hours per week in aggregate, as firms discover that this new wage exceeds the marginal revenue product of their marginal workers. These firms then take steps to reduce the input of labor into their production process, including layoffs, less overtime work and nonreplacement of workers who resign (known as labor attrition). The higher wage rate, W,, induces more hours of work to be offered, so that there exists L’ — L, hours of unemployed labor per week. FIGURE 15-1 Maximization of the Wage Rate $/L (Wage rate)

L (Hours/week)

NOTE:

Which workers are expected to join the ranks of the unemployed? Most likely it is the least skilled, those with least seniority, and in some cases of bigotry, those belonging to a minority group. These people will probably not have a very loud voice in the union, if in fact they are even members, and we might expect union leaders and most members to justify this unemployment as being in the interests of the union membership as a whole. This stragegy amounts to increasing the income of the “core” members of the union, at the expense of nonmembers, new members, and “‘unimportant’’ members.

Maximization of Total Wage Income. Alternatively, let us suppose the union’s objective is to maximize the wage bill—the total wage income of its members. Since the total wage bill is the total revenue associated with the demand curve for labor, the union in this case would want to press wages to the point where the marginal revenue from the last unit of labor demanded is zero. In Fig. 15-2 we demonstrate that the wage rate should be W in order for the total wage bill to 350

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

be maximized. Whether the resultant quantity of labor supplied, L*, is equal to the supply of labor at that wage rate is another matter. There might be either excess supply of, or excess demand for, labor at that wage, with resulting impacts on unemployment or additional nonmonetary and covert monetary compensation, respectively. FIGURE 15-2 Maximization of Total Wage Receipts S/L

L (Hours/week)

Maximization of Employment of Labor. A third objective might be to maximize the level of employment in the labor market. Since no employer can be induced to hire more labor than it wants at the going wage rate, and since no union wants to settle on a wage lower than it currently receives, this objective is likely to be feasible only when labor receives less than the equilibrium wage rate. We saw in the preceding chapter (see Fig. 14-8) that an employer with monopsony power wants to employ labor only to the point where the marginal factor expenditure (MFE) equals the marginal revenue product (MRP) of that factor. In Fig. 15-3 we show the monopsonist’s average factor expenditure (AFE) and the MFE curves superimposed on that firm’s demand for labor curve (derived from the MRP of labor). Without countervailing pressure from the union, the firm would set wages at Wo, and employ Ly units of labor, where MFE = MRP. The union would endeavor to raise the wage rate to W*, where supply equals demand for labor. At this rate, L* units of labor are demanded. This is the maximum employment level that can be achieved. Any higher wage reduces demand, and any lower wage reduces the supply of labor. This solution requires that the union is sufficiently stronger than the monopsonist buyer of labor, so that the union is able to dictate the wage rate. If the union and the monopsonist are almost equal in terms of their bargaining power, we would have a bilateral monopoly with indeterminate outcome, as discussed in Chap. 14. (See Fig.

14-10.) Wages, Profits, and Inflation

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FIGURE 15-3 Maximization of the Employment Level

L (Hours/week)

Nonwage Objectives. Other union objectives, such as shorter work weeks, better work conditions, better pension plans, longer vacations, and so forth, all boil down to the same thing for the employer: They raise the cost of labor and reduce the firm’s profits. These other objectives, from the firm’s point of view, could be expressed graphically as an upward shift in the supply curve of labor. Each level of labor supplied costs more in terms of the actual wage rate plus the monetary equivalent of the other features of the employment contract. Employers must take into account these additional costs of labor, which are typically not at all insignificant. For example, there may be an additional cost of as much as 10% for contributions toward vacation pay, pension or retirement plans, and company medical schemes. Bargaining Procedures and Tactics As a current contract nears its end, union representatives typically present man-

agement with a list of their demands—in both wage and nonwage matters—for the next contract. Management representatives typically study these demands and make a counter offer, and so negotiations proceed. In the final stages both sides meet together and come to an agreement, each making small compromises in order to finalize the terms of the new contract. Since the process inevitably ends with these compromises, both sides are encouraged to include ‘“‘unreason-

able” demands in the initial stages of the bargaining process. Labor asks for more than it reasonably expects to receive, knowing that it will eventually be able to trade off some of its increased wage demand for an improved pension plan, or longer layoff notices, or other benefits. Management offers less than it reasonably expects to have to pay, knowing it will eventually give a little more in hourly wages in order to avoid some more odious concession elsewhere. Bargaining for one’s own income and for the income of one’s constituents against another group that is also interested in its own income and its constitu352

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ents’ (shareholders’) income, is a situation of inherent conflict. In many cases this conflict is not settled amicably at the bargaining table, and the proponents feel obliged to resort to forceful alternatives. Physical violence and sabotage are both illegal and not generally socially acceptable, of course. Instead unions usually have a legal right to strike after the passage of a certain amount of time, and employers may lock out employees and cease wage payments until the issue is settled or, at least, until bargaining resumes. Both parties attempt to inflict economic loss on the other, in the hope that the other party will realize that the preferred course of action is to give in to the demands of the other. In some cases of exceptional intractability of one party or very poor perception of the other, these strikes or lockouts are prolonged to the point where the firm actually goes bankrupt, or where the majority of workers find employment elsewhere and are unavailable when work finally resumes. The cost of strike and lockout activity is not confined to the strikers and the struck firm alone. In most cases these events cause disruption of the smooth functioning of related industries and a disturbance of the normal lives of people living in that geographical area.The social costs of strikes and lockouts often far exceed the private costs borne by the parties directly involved. We return to this issue in Chap. 20. The Impact of Unions

While there is general agreement that labor unions have had a positive impact on wage levels, there is considerable controversy as to the extent of this impact. Lewis concludes that unionized industrial workers have earned on the average about 10% to 15% more than nonunion workers.* A more recent survey by Parsley indicates that the union-nonunion wage rate differential varies widely across industries, and that sex and race differentials also vary widely within industries and sectors. Parsley notes the considerable measurement problems that make it very difficult to state unambiguously the exact degree to which unionization has helped enhance the wages of workers in both the U.K. and the U.S. economies.® Unions have also had an impact on working conditions, job security, pension and health plans, and other nonwage aspects of employment. Many of these items are now subject to legislation, and the role of the union in the current economic environment is less clear. Nonunion labor tends to follow union labor in the acquisition of wage gains and improvements in working conditions, by virtue of the competition for labor services in the labor market. Firms have to pay the going rate in order to hire workers, whether union or not. It is possible that in some instances union labor receives the same wage settlement that nonunion labor would receive anyway. When unions have raised wages above the market rate in the short run, the subsequent tendency of firms to substitute laborsaving equipment and materials for labor tends to counteract the overall gains to labor in the long run. 5H.G. Lewis, Unionism and Relative Wages in the United States (Chicago, Unversity of Chicago Press, 1963).

6C.J. Parsley, ‘Labor Union Effects on Wage Gains: A Survey of Recent Literature,” Journal of Eco-

nomic Literature, 18 (March 1980), 1-31.

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A case in point is that of the Teamsters, whose members drive large trucks for transportation firms. Only some of these trucking firms are unionized, however, and this sector of the industry has been forced to pay significantly higher rates to its drivers. (The force applied has allegedly included physical violence and sabotage, resulting in deaths and substantial loss of property.) Due to the higher wages, the unionized sector of the industry was forced to raise its prices, and it has suffered a substantial decline in its share of the trucking business, because of the competition of nonunionized and independent truckers. As more and more unionized trucking firms go out of business, teamsters are beginning to realize that they must modify their wage demands for fear of eliminating their own jobs.’ ——_ Undoubtedly unions have substantially increased the income levels and working standards in the labor markets in particular instances. One should not impute all such improvements to unions, however, since many of these would have taken place in any case due to the pressure of competition for labor services and evolving notions of social equity. Unions remain as the watchdog for labor, ensuring that labor obtains a fair wage and safe working conditions,that individuals are not victimized or treated arbitrarily, and that the standard of living of the wage earner grows at a sufficient rate within the constraints imposed by the overall growth rate of the economy.

EXAMPLE:

Ill. PROFITS: THEIR ROLE AND MEASUREMENT Let us now take a closer look at profits, the other most widely assumed culprit in the search for a place to lay the blame for inflation. In this context, profits are seen as the spoils, which are left over after all the deserving have been paid for their services. They are thus an undeserved bonus for grasping capitalists. Greedy firms, it is said, continue to raise prices in order to maintain or improve

their profit margins; thus they contribute mightily to the continuing process of inflation. Is this a fair statement of the problem? Does the faintest glimmer of economic reasoning intrude into this sort of emotional condemnation of profits and profit-makers? Let us, in the calm dispassionate manner of economists, look further into the issue. Accounting Profits

We saw in Chap. 6 that profits are regarded differently by economists, as compared with accountants and the general public who read about the record profits of large corporations on the same page as they see news of price increases for the same and similar corporations.

DEFINITION: Accountants measure profits as the residual accruing to the owners of the firm, after all operating costs have been paid and after allowance has been made for depreciation of assets purchased in previous accounting periods. The owners of the firm, who have their money invested in the firms’ assets, then take these ™The Teamsters Aim at the Guidelines,” Business Week, April 2, 1979, pp. 56-65.

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profits as a percentage of their investment to find out what rate of return they are receiving from that investment. If the firm’s shares are traded on the stock exchange, the dividends paid out to shareholders are calculated as a percentage of the price the shareholder paid for his or her shares to calculate the shareholder’s yield on that investment. In all cases, if the investor’s rate of return or yield ona particular investment is too low, the investor may wish to sell his or her holdings

in that firm or, at least, to refuse to provide any new funds for the firm’s investment proposals. Economic Profits

DEFINITION: The economic profits of the firm are defined as total revenues less the opportunity cost of all resources utilized in the production process. Thus the rate of return that investors could receive elsewhere (in the next best alternative investment project of similar riskiness) would be included as a cost of employing the capital in this particular production process. Any economic profit left over is then pure profit or profit in excess of that required to keep the capital employed in this particular enterprise. Economic, or pure, profits may be regarded as the reward for monopoly market power or the reward for innovation of new products and new production technologies, or simply as windfall gains. We expect such excess profits to be eroded over time by the entry of new competition, the development of new technology, and the changing tastes and preferences of consumers. In some circumstances

economic

profits may persist due to the presence

of insurmountable

barriers to entry; herein lies some justification for government or legislative action to promote competition in such markets. To the extent that a firm continues to earn economic profit as a result of its continued innovation of new technology, its anticipation of changes in tastes and preferences, and its satisfaction of these preferences with new products, we should rest content in the knowledge that this firm is a driving force in society’s quest for economic growth and improved social welfare. The Necessity of Profits Without accounting profits of sufficient magnitude to induce investors to leave their funds invested in a particular production process, the latter would suffer from the withdrawal of capital, and would eventually be unable to continue in production. As assets wear out, the lack of sufficient funds to replace these assets means that the firm will eventually be unable to keep the production line rolling, and that output will cease. In the economist’s jargon, if profits fall below the level of normal profits, those resources would be better off in a different production process. In this situation the rational owners of the resources are expected to shift their resources to more profitable production opportunities as soon as possible, that is, as soon as long run conditions are attained and the firm can

liquidate its fixed factors of production. If profits are below normal levels in only a few industries, we should have little concern. This is probably the normal ebb and flow of the competitive capWages, Profits, and Inflation

355

italist system. Firms in dying industries, such as those in the 1920s producing saddles and horse-drawn vehicles and those in the 1980s producing mechanical

wristwatches, must expect to move on to new industries as technology and con-

sumer taste patterns shift to new frontiers. At the same time, other industries, such as the automobile industry in the 1920s and electronic watch manufacturing in the 1980s enjoy above normal or pure profits. Rational investors are expected to shift their capital out of dying industries and into growth industries in search of the best return on their investment. When profits are below normal levels almost everywhere, we have great cause for concern. This means that investors will not be willing to leave their funds in major industries that are vital to society’s economic and social welfare. Moreover, calls for additional capital to replace worn-out equipment would go unheeded, as investors would transfer their capital to other types of investment and to other countries where better returns on investment could be realized. If railroads, construction, automobiles, steel, chemicals, and other major indus-

tries do not earn at least normal profits, investors transfer their funds to other less-productive but more remunerative investments. Gold bars, objets d’art, and land for recreational use might attract a large amount of capital, which previously supported more productive industries that in turn employed thousands of workers. Alternatively, if domestic investments become less profitable, investors might be expected to transfer a larger portion of their portfolios to foreign countries where rates of return are expected to be greater for one reason or another. Less competition in a foreign market may allow monopoly profits, or the absence of government regulation may avoid costs to a sufficient extent to allow normal or pure profits to exist. Similarly, a lower rate of inflation in another country may allow more profitable investment opportunities. Let us find out why. The Impact of Inflation on Profits

Inflation reduces the purchasing power of the dollar, by depreciating the dollar in terms of the goods and services it might purchase. Thus profits amounting to one million dollars today are worth substantially less in terms of the goods and services, including plant and equipment, one can purchase at today’s prices, compared with a million dollars worth of goods and services purchased at the general price level existing five years ago. Thus for profits to be constant in real terms, they have to increase in nominal or money terms each year at a rate equal to the rate of inflation.* Given recent inflation rates in excess of 10% per annum, it is clear that a substantial part of any claimed increase in corporate profits is a monetary illusion. But the problem is more than that. Even when discounted for the rate of inflation, most corporate profit figures overstate the actual accounting profits of 8One might argue that the general rate of inflation, or the rise in the consumer’s cost of living, is less appropriate here than the increase in some index of “relevant” goods and services. That is, a particular firm’s real profits are affected only by the rate of inflation of the goods and services that firm actually purchases.

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the enterprise, due to two other major problems. One is the method of inventory valuation used by many firms, and the other is the legal requirement to limit depreciation allowances to the historical cost of the asset being depreciated. Let us examine these issues in turn.

Understatement of Cost of Goods Sold. When the firm subtracts the cost of goods sold from its sales revenue, it is required by the Internal Revenue Service (IRS) to value those goods sold on either of two bases. It may use either the firstin—first-out (FIFO) system of inventory valuation or the last-in—first-out (LIFO) system. Under inflation there will be a difference among the actual costs of the goods held in inventory, depending largely upon how long ago they were purchased. The FIFO system seriously understates the cost of replenishing the firm’s inventory, as we shall see.

EXAMPLE:

Suppose the firm sells in September a unit that was purchased in March. Let us suppose the sale in September, at $10.00 per unit, has charged against it the March invoice cost of $6.00 per unit. The firm appears to make a $4.00 contribution toward overhead and profits as a result of this sale. But if it costs $8.00

per unit in September to replenish the inventory of that product, it can be seen that $2.00 of the contribution is immediately consumed by the additional current cost of repurchasing the product for inventory. Moreover, the FIFO system values the firm’s inventory for balance sheet purposes as the historical cost of purchasing all the items currently held in inventory. Given inflation, the market value of the inventory is significantly higher. Thus the FIFO system tends to undervalue the firm’s assets and consequently leads to an overstatement of the firm’s rate of return on its investment. The LIFO system of inventory valuation charges the cost of the most recently acquired units of the product that was sold against current revenues. Suppose the most recently acquired units in inventory cost $7.50 apiece, the understatement of replenishment cost is, therefore, considerably less severe. Similarly the valuation of inventories for balance sheet purposes as the most recent cost per unit multiplied by the number of units in inventory, more nearly reflects the current market value of the firm’s inventory. As long as there is a discrepancy between the cost of the unit most recently purchased and the current market value (current cost of purchasing another unit to replenish inventory), the LIFO system will also undervalue the opportunity cost of goods sold and the total worth of inventory. It will consequently overstate accounting profits and the firm’s return on investment. Nevertheless, LIFO is a substantially more acceptable measure of inventory value and cost of goods sold than is FIFO in an economy in which inflation has become a continuous process. Firms are required by the tax collecting arm of the government (the IRS in the United States) to use one method or the other without switching back and forth from time to time, since switching could allow the firm to avoid taxes, as well as to confuse the investing public. Firms may switch from FIFO to LIFO, however. This would have the immediate impact of substantially reducing reported profits and the reported rate of return on investment. On the bright side, it means that the firm pays less tax and is able to keep Wages, Profits, and Inflation

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more cash in hand, both substantial advantages in times of high inflation and interest rates.? Understatement of Opportunity Cost of Assets. Depreciation of plant and equipment on the basis of historical cost (actual cost in dollars when purchased) is the other major factor leading to the distortion of accounting profit figures in inflationary times. The firm, using traditional depreciation procedures, charges against revenues each year a share of the initial cost of the asset over the life of life the total historical cost will the asset, so that at the end of the asset’s useful have been charged against revenues and thereby sheltered from tax. In theory the firm has set aside a sum of money equivalent to the historical cost of the asset, and this sum should then be available to pay for the replacement of the asset. At current prices, however, the replacement cost is likely to exceed substantially the accumulated provision for depreciation charged against revenues during the asset’s life. Thus the firm must dig into its other cash reserves or borrow money at current interest rates, in order to replace the piece of plant or equipment and to continue producing. The lack of a sufficiently large provision for replacement investment can cause the firm to incur substantial interest costs, cash flow problems, and a reduced market value of its shares, due to the change in its debtequity (leverage) ratio.

NOTE:

In economic terms, the depreciation of the asset’s historical cost over its useful life has resulted in an understatement of the opportunity cost of that asset. As inflation continues the replacement cost of the asset exceeds its historical cost;

likewise, the market value of the asset (on the second-hand market) exceeds its remaining book value. The opportunity cost of continuing to employ the asset in this particular production process is the value of that asset in its next best alternative use, which exceeds the depreciation allowance actually charged against revenues. Thus costs were understated in economic terms and profits were consequently overstated. To be properly stated in economic terms, the depreciation expense needs to be calculated as the amount of money the asset could have made in an alternate production process during that particular year, or the amount of interest income on the market value of the asset, whichever is greater.

The Extent of the Overstatement of Accounting Profits. How large a problem is this? To what extent are accounting profits overstated by the use of FIFO inventory valuation methods and historical cost depreciation? In 1978 the illusory profits of American industry amounted to more than $42 billion.!° As a result, corporations paid $17 billion more in taxes than they should have (based on profits adjusted for the effects of inflation). These same corporations paid out a record $49 billion dollars in dividends in 1978, which seemed to them to be an acceptable 42% of after-tax earnings. As a proportion of ‘‘adjusted” profits, however, it was an unacceptably high 65%. Consequently, these corporations not *The Profit Illusion,” Business Week, March 19, 1979, pp. 108-12. 10“The Profit Illusion,” Business Week, pp. 108-12.

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only paid tax on illusory profits, they also distributed too much to shareholders, with the result that many firms then found themselves cash poor and were forced into the financial markets to raise cash for necessary replacement investment expenditures. Many firms are unable to afford replacement investment—or are able to do so only after shareholders have subscribed to more equity in the corporation—and are practicing capital consumption, or the reduction in the value of their net assets. This can only have deleterious effects on their longer-term survival and the associated growth of the economy. Why do managers of such corporations continue to overstate the real value of accounting profits? They have to a large degree, perhaps, a vested interest in doing so. First, their own reward systems are often tied directly to the accounting profit performance of the firm. Smaller, more realistic profit figures would possibly mean smaller incentive bonuses, less chance of promotion, or in some cases termination of employment for the manager.!! Second, management is afraid that the sudden revaluation of the firm’s assets and cost of goods sold resulting from a switch to LIFO from FIFO would cause excessive selling pressure on the stock market, driving down the firm’s market value and, consequently, reducing its ability to raise new equity and to borrow money at competitive rates. Such setbacks could cause the demise of the firm or at least exacerbate the problem of insufficient real profits. As this problem continues, one would expect more firms to switch to LIFO

inventory valuation; and that mounting pressure on the IRS will lead to a change in the depreciation schedules permitted for tax purposes. Until such a reform in the corporate tax legislation is achieved, it is likely that firms will continue to report record profits that are nonetheless illusory, whereas at the same time they will continue to experience severe cash flow problems and declining stock market valuation. As a result, firms might be expected to continue as they have before, periodically raising prices of their outputs in order to make even greater accounting profits, in a vain attempt to improve their cash flow position and stock market valuation. In summary, firms are motivated to continue raising prices whenever pos-

sible in order to solve their own short-term cash flow and market valuation problems. These problems arise not only from the increasing cost of labor and materials, but also from the overstatement of accounting profits due to outmoded and inappropriate conventions for inventory valuation and allowance for depreciation.

IV. PRICES AND INFLATION So who is to blame for inflation and the continuing erosion of the purchasing power of the dollar? Though some groups are more responsible than others, it seems that a host of people and groups contribute to the inflationary process. In the following we see that consumers, wage earners, and other sellers of services 11“New Targeting for Executive Pay,” Fortune, May 4, 1981, pp. 176-84.

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contribute to inflation; price setters and profit earners contribute to inflation; and inappropriate legislative requirements and the monetary and fiscal policies of governments contribute to inflation. Let us start with the governments. Expansion of the Money Supply

DEFINITION: The money supply is defined as the total stock of coin and paper currency in circulation plus the demand deposits held by commercial banks. The rate of inflation depends to a large degree on the rate of expansion of the money supply. National governments, through their Central Bank—the Federal Reserve System in the U.S.—can expand the money supply by the use of reserve ratio requirements, interest rate adjustments (known as discount policy), and open-market purchases or sales of government bonds and other securities. For example, the money supply may be increased by reducing the reserves that commercial banks are required to hold, bylowering interest rates, or by the Central Bank buying government bonds and other securities, thus putting into the system cash that was previously kept out of circulation in their vaults.1? Broadly speaking, if the rate of growth of the money supply exceeds the rate of growth of the economy’s output, inflationary forces are generated. This is the result of ‘too much money chasing too few goods.” That is, increases in the money supply cause a situation to develop of excess (monetary) demand for some or all products, resulting in upward pressure on the prices of those products. In terms of the demand function, increased money supply operates to shift the demand curve to the right as consumers find themselves with increased monetary income to spend. The resultant excess demand situation causes consumers to put upward pressure on prices, and suppliers see that they can raise

prices and still sell all they want to, and so prices rise. Throughout the sixties and the seventies, most Western economies experienced growth of the money supply at a rate in excess of the rate of increase in the economy’s output. National governments, often in response to political pressures, became involved in a variety of programs that have cost a lot of money. Defense, the space program, health and welfare programs, highways, housing projects, and the regulation of various industries are examples. These projects required large budgets for personnel and materials. To finance these expenditures and to avoid other problems that would arise, governments tended to “print money,” that is, to expand the money supply to support these additional expenditures. The Monetarist School, originating largely with Milton Friedman and others at the University of Chicago, has focused attention on the fact that the rate of

expansion of the money supply is a critical element in the control of inflation Monetary policy is a subject that is treated in a macroeconomics course and that requires a basic knowledge of the macroeconomic system to be understood. Accordingly, the treatment here is brief and does not attempt to explain how expansion or contraction of the money supply actually works. See F. Zahn, Macroeconomic Theory and Policy (Englewood Cliffs, N.J.: Prentice-Hall, Inc. 1975), or P. E. Kennedy, Macroeconomics, (Rockleigh, N.J.: Allyn and Bacon, 1979).

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and in macroeconomic policy more generally.!3 The monetarists contend that a controlled expansion of the money supply at arate equal to the expected growth of real gross national product would reduce inflation to desirable levels. Governments, however, find it difficult to restrain monetary growth to this extent. EXAMPLE:

Let us look at an example of the magnitudes of the rate of growth of the money supply (MS) and of real gross national product (RGNP) in the U.S. over the period from the second quarter 1976 to the second quarter 1980. MS grew at the compound annual rate of 7.1%, while RGNP grew at only 2.7%. Over the same period, consumer prices grew at a compound annual rate of 9.7%. Over the twoyear period from the second quarter 1978 to the second quarter 1980, MS grew at the compound annual rate of 6.1%, RGNP at only 0.6%, and consumer prices at Pret

ee

It can be argued that the rate of growth of MS should be a couple of percentage points greater than the rate of growth of RGNP, in order for it to act as a lubricant for the structural shifts and other adjustments of a dynamic economy. In the same vein, a few percentage points of inflation are considered to be beneficial, for the benefits noted above and as a boost to business and investor confidence. But growth of the money supply at a rate substantially above the growth of the economy’s real GNP has the inevitable consequence of contributing to the problem of inflation. Let us now consider the role of consumers in the inflationary process. Demand-pull Inflation

Consumers, firms, and governments can contribute to inflation by increasing their demand for a particular product, so that there exists excess demand for that

product. In the face of excess demand, suppliers can and do raise the price of the product, with a resultant increase in the general price level. Prices that go up tend to stay up, especially in an inflationary environment. The inflexibility of prices in the downward direction is due in some part to the greater difficulty and market-share risk associated with raising prices, as compared with lowering them. Once raised the prices tend to stay raised, since consumers’ and rival producers’ reactions are uncertain, and the firm may not wish to risk loss of market share in the future by lowering prices now and having to raise them again at a later date. Thus, even as demand patterns shift across the goods and services

available, there may be an inflationary effect that is due to the upward mobility of prices for products subject to excess demand and that is not offset by price reductions for products now in excess supply. Expectations of consumers play a major role in their purchasing behavior. If consumers expect a particular product to cost significantly more next period, 13M, Friedman, Studies in the Quantity Theory of Money (Chicago, University of Chicago Press, 1956); and “The Role of Monetary Policy,” American Economic Review, 58 (March 1968), 1-17. For an extensive bibliography, see A.R. Nobay and H.G. Johnson, “Monetarism: A Historic-Theoretic Perspective,” Journal of Economic Literature, 15 (June 1977), 470-85. 14Pqcific Basin Economic Indicators, 5 (Sept. 1980) 75—80 (San Francisco: Federal Reserve Bank of San Francisco).

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they are likely to demand more of it in this period, causing the demand curve for that product to shift to the right. This in turn causes excess demand, with ceteris paribus, and the market price of the product is likely to increase. The expectations of higher prices for the product become a self-fulfilling prophecy, independently of any shift in the supply curve or other reason to shift the demand curve. EXAMPLE:

Such self-fulfilling prophecies are often evident,and lead to windfall gains to the supplier. Examples include the energy shortages of 1974 and 1979 following crises in the Middle East. The available supply in each case was sufficient for current consumption. The shortage arose because individual consumers were demanding future consumption needs along with current consumption needs. If all autos on average have their gas tanks half full, and an energy shortage scare causes drivers to fill their tanks more often, so that gas tanks are on average 75% full, this causes an immediate 50% increase in consumer demand. This is not to

mention the other methods of increasing personal inventories for future consumption, such as carrying gas cans in the trunk and installing large sunken storage tanks in one’s back yard. Thus the aggregate action of consumers anticipating a shortage or higher prices in the future for whatever reason, can have an inflationary impact in the economy, whether or not the initial’reason for their concern ever comes to pass. Given the downward inflexibility of prices, the resultant price increases tend to remain, even after consumers reduce their current demands. Governments have traditionally been the largest contributors to the creation of excess demand. Their expenditures on defense, foreign aid, the space

program, health and social welfare, public works, highways, and myriad other areas of involvement in the economy, constitute a large fraction of aggregate demand. Often governments find it politically desirable or otherwise necessary to expand their expenditures beyond their current budgets. If expenditures exceed revenues from tax collection and other income, we say the government is operating at a deficit. It finances this deficit by the accumulation of long-term debt. Government deficits, often amounting to billions of dollars annually, con-

tribute to excess demand since they introduce new funds into the economy without a concurrent increase in productivity capacity. If the economy is near the full employment level of its industrial capacity, or is subject to supply bottlenecks in at least some areas, deficit spending places upward pressure on prices and therefore contributes to the inflationary process. Such inflationary pressure is called demand-pull inflation, because the excess demand created by consumers tends to pull up the price level. Let us now examine a couple of factors that tend to push up the price level. Wage-push Inflation

Wage earners and, more generally, the suppliers of all services feel the pinch on their own purchasing power as the general price level rises. At the present price of their labor, or other, services, their real incomes are reduced by the rise in the 362

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general price level. To the extent that they are able, these suppliers of services attempt to maintain or increase their real income by raising the price of their services. This means that the prices faced by purchasers of these services—firms and consumers—are increased. The firms and consumers affected might be expected to take steps to maintain their own profits and real income levels, with the result that the general price level is pushed up by the initial demands of wage earners and other suppliers or services. To what extent will the suppliers of services be able to exert upward pressures on prices? This depends upon the extent of market power possessed by these suppliers. If a person is a monopoly supplier of a special talent, that person is clearly able to exert pressure for an increased rate of compensation. Similarly, groups of suppliers acting in unison may be able to force up the prices for their services. Labor unions and the more loosely controlled associations of such professionals as doctors, lawyers, and dentists have shown the ability to raise their wages or fees in response to increased costs of living or other stimuli. Individuals without appreciable market power and without membership in an organized group for the purposes of wage or salary bargaining, are unable to force up the rate of compensation they receive. Notice that the forces of competition in a particular factor market ensure that those factors are paid their marginal revenue product or, in the real world, some approximation thereof. If a firm is able to raise the price of its product in inflationary times, the MRP of the factors producing the product also increases in nominal dollars. In order to retain the services of its factors of production in a competitive factor market, the firm must raise its rate of compensation in nominal dollars. If it does not, its factors go to other firms who do pay compensation equal to the factor’s MRP. If the price of the industry’s product rises at the same rate as the general price level, the real income of the factors is maintained, regardless of their having no market power individually or as a group. We ought to distinguish between the part of a wage or compensation increase that is due to the competitive demands of firms for workers (or other inputs) and the part that is due to the market power of the factor of production. Unions often receive credit for all wage increases, when some part or all of these increases would have been offered by employers in any case, in order for them to retain the services of workers in a competitive labor market. As long as factors are paid the real value of their MRP, there is no inflationary effect. It is only when wage (or other factor price) increases exceed the increase in the real value of MRP that inflation is generated. It is generated because relatively too much money begins to chase relatively too few goods and services, and the prices of these goods and services are subsequently raised. Profit-push Inflation

Firms similarly attempt to maintain their incomes, which in this case are measured as profits. Profits earned are distributed in part to the owners or shareholdWages, Profits, and Inflation

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ers of the firm, and the balance is retained for future investment purposes. If profits fall in real or monetary terms, the owners receive smaller dividend payments and the firm’s ability to replace worn-out assets or expand production facilities now and in the future is threatened. Thus we should expect firms to attempt to maintain or increase the real value of their profits in an inflationary environment. As the firm experiences increases in the cost of its factors of production, it sees its profits declining, ceteris paribus. If the firm has market power, it is motivated to raise the price of its products in order to restore its profit situation. Notice that when a firm raises its prices at the same rate as the increase in the general price level, it is simply restoring the real value of its profits, and hence it is not contributing to any new degree of inflation. If, on the other hand, it raises prices at a rate faster than the general rate of inflation, it causes profit-push inflation, and the rate of inflation increases. If it is a monopolist, or an oligopolist led by a price leader or similar joint pricing practice, or a monopolistic competitor, the firm has the market power to increase its prices at the same rate or faster than the general price level. The pricing practices of firms also contribute to the propagation of inflation. To avoid search costs for more information about their cost and revenue functions, most firms adopt simple pricing conventions, such as markup pricing. Rather than daily examine the cost and demand situations, firms routinely add a percentage markup to the per-unit direct or variable cost. As this cost changes, due to pressures in other markets, the firm simply applies the same percentage markup to the new direct cost. Thus the cost increase is routinely

and without much delay passed on to the consumer. Moreover, the same percentage markup on a high cost base means that the firm is able to maintain the real value of the contribution to overheads and profits made by the sale of the product. As we saw in Chap. 13, if the direct cost increases 10% from $6.00 to $6.60 and if the markup is 40%, the price changes from $8.40 to $9.24—a 10%

increase but an absolute increase of $0.84, compared with the $0.60 increase in direct costs. Notice the general ‘‘pass it along” mentality of the inflationary process. Given some initial stimulus to increase prices, such as an excess demand situation created by a jump in consumer expectations, wage earners try to pass along

the hardship to the firm by demanding increased wages. The firm might acquiesce willingly or only after a struggle, but it then makes every effort to pass along the hardship to consumers by raising the prices of its products. But these same consumers are also suppliers of labor and other services, and they in turn pass it along to the firms again. And on and on it goes. As long as all parties maintain their real incomes and profit levels, the rate of inflation remains stable.

When some parties ask for and receive a larger share of the real value of output, the rate of inflation must increase, ceteris paribus. But some parties in society are not part of this continuing merry-go-round. People without sufficient control over their incomes become the victims of others that do have control; they are the true casualties of the inflationary process. Let us look into this question more closely. 364

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Who Wins and Who Loses by Inflation?

It might be a surprise to hear that some parties do benefit by inflation. Anyone who owes money (a debtor) benefits by the depreciation of the monetary unit, since debtors must pay back the nominal amount that was borrowed plus interest; they are, however, likely to pay back a smaller real amount. Oppositely, creditors lose as a result of inflation, since they lend full-value dollars and are paid back in less-valuable dollars. Of course, creditors adjust the rate of interest to compensate for the expected rate of inflation. In such situations debtors gain and creditors lose only if the actual rate of inflation exceeds the anticipated rate. During the sixties and seventies, however, the actual rate of inflation edged persistently higher and higher, so that creditors typically underestimated the rate of inflation. Hence debtors did gain and creditors did lose during that period. Governments are very large debtors, having financed previous war efforts and budget deficits by long-term borrowing. These debts must be paid back over time, but the real cost of this borrowing is reduced if the inflation rate increases over this time. One might argue that governments have a vested interest in inflation, since the retirement of long-term debt is facilitated by inflation, and since doing so allows the government to look better when election time comes around again. Governments also benefit by inflation to the extent that their tax collections are based on a progressive tax structure. If the rate of tax increases with the amount taxable, as in the case of personal income tax, tax revenues automatically go up as incomes rise, but by a larger proportion. Thus governments collecting taxes on a progressive structure are able to expand their services and increase their involvement in various sectors without having to take the politically undesirable step of raising the tax structure. Business firms are also usually net debtors, having borrowed from the public to finance past investment and expansion projects. Inflation helps them retire this debt more quickly and at a lower real cost. Business firms also appear to link their investment activity to the expectation of rising prices in the product markets. Business ‘‘confidence” in the future is said to be enhanced by a moderate rate of inflation, since the firm can expect to recoup, at least in nominal terms,

the initial investment cost in a shorter period of time. Given the sometimes strong support of political parties by business, one wonders if governments do not have both a direct and indirect incentive to allow inflation to continue. The big losers in inflationary times are the people on fixed incomes, pensions, and wages that are adjusted only infrequently. Inflation has dramatically eroded the purchasing power of the life savings of many people now in retirement. Trying to live off the interest of past savings becomes progressively more difficult. Similarly, the fixed incomes and pensions of the old, the widowed, and the disabled command progressively smaller purchasing power year by year. The virtual eradication of many people’s retirement savings places a substantial burden on society to support these people in their old age, not to mention the enormous personal burden placed on these people. Finally, society as a whole suffers a significant loss as a result of the inflationary process. Inflation tends to cause the misallocation of resources away Wages, Profits, and Inflation

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from productive investments, for example, in manufacturing activity, and toward speculative investments in less productive or even nonproductive areas.

Inflation during the sixties and seventies, for example, fueled investment in real

estate for residential and recreational purposes, siphoning off funds that might have otherwise been channeled into more productive areas. Similarly, investment in “hedges” against inflation, such as objets d’art, gold bars, and old coins funneled investment resources into purchases essentially designed to hoard and protect wealth from the ravages of inflation, rather than to increase wealth significantly. The social cost of this misallocation of'resources is compounded as time passes and as the lack of investment in more productive ventures allows the rate of growth of the economy to fall below what it might have been.

Solutions to the Problem

If the control of inflation were a simple matter, it would not still be a problem. Literally millions of hours of work by economists and government researchers and officials attest to the fact that there is no easy way out. Thus the solutions we discuss here are at best only partial solutions. Although we obviously have great difficulty fully eradicating inflation, we can control it to some degree, provided the right measures are taken at the right time. Let us take a brief look at several measures, which each serve to reduce inflationary pressures and which, if applied jointly or in combinations, might be expected to reduce the inflation rate significantly. This is necessarily a superficial look at only some of the possible solutions, since the problem is very complex and is usually treated in courses on macroeconomics. However, many of the elements of the solutions have microeconomic foundations, as we shall see.15

Monetary Policy. The price level depends to a large extent upon the quantity of money available in the economy. In simplest terms, more money bidding for the same amount of output has an inflationary impact on the prices of that output. Governments must attempt to restrict the growth of the money supply in line with the anticipated growth in real national product. Control is difficult, however, and many of the control mechanisms are imprecise. Moreover, an expanding money supply lubricates growth of output and serves to remove bottlenecks in the economy. There is thus a trade-off between inflation and real economic growth, which governments and monetary authorities must consciously consider. Political considerations may enter as well. Governments, mindful of the next election, may be reluctant to reduce expenditures in many areas, due to expected adverse public reaction. International factors also influence governments to maintain or increase expenditures on particular items, such as defense

and foreign aid. Unless these public sector expenditures can substitute for private sector expenditures, they must be additional to what the rest of the economy SRecent studies have emphasized the microeconomic elements of the inflation process. See James W. Dean, “The Inflation Process: Where Conventional Theory Falters,” American Economic Review, 71 (May 1981), 362-7, and Harvey Leibenstein, ‘‘The Inflation Process: A Micro-Behavioral Analy-

sis,’’ American Economic Review, 71 (May 1981), 368-73.

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is spending, and hence they must be financed by an expansion of the money supply in one way or another. In order to curb the problem of inflation, governments must curb their expenditures to a level that is supportable by the economic system. The monetary policy of a federal government, through its central bank and the banking system, must also be applied with more precision and better results. And finally, it appears that we don’t yet know enough about how the monetary system works. Thus further study is necessary by economists and financial theorists to derive a better understanding of the important variables and the causal relationships, including the leads and lags involved, in the monetary system. Fiscal Policy. Fiscal policy is concerned with the budgetary surplus, balance, or deficit of governments. If governments balance their budgets, they spend exactly the amount they collect through taxes. If governments spend more than they collect, they incur a deficit that is financed by long-term borrowing, often from outside the country. This has the effect of an increase in the money supply, and it contributes to an excess demand situation within the economy, with consequent inflationary impacts. If a government budgets and spends for a surplus, this has deflationary effects, since the government is taking more money out of the economy than it is putting back in. Budget deficits tend to be expansionary and are used to stimulate the economy after a period of recession or slow growth. Unfortunately such periods are now characterized by inflation, so that fiscal policy to stimulate the economy also tends to exacerbate inflation. Clearly a fine touch is necessary, as is a responsible attitude on the part of governments. It is also possible that a desire to be re-elected might cause some governments to emphasize projects and policies that ensure their re-election at the expense of a more effective treatment of the inflationary problem. Labor Productivity. Any measures that serve to raise the marginal physical product of labor also serve to increase the real value of total output and, consequently, to take some pressure off the price level. For example, suppose labor is the only factor of production and produces 100 units per week. These are sold at a market price of $10.00 per unit for total revenue of $1,000.00. Total costs are,

let us say, $20.00 per hour for forty hours, or $800.00 weekly, leaving $200.00 profit per week. Now suppose labor productivity goes up 5%, and the general price level goes up 10%. In order to maintain real income or profits, labor now wants $22.00 per hour, or $880.00 per week, and the firm now wants $220.00 in money profits. Thus the firm needs $1,100.00 in total revenue to maintain its real profits. Labor is now producing 105 units weekly, which must be sold at $10.48 per unit in order to attain total revenue of $1,100.00 per week. Thus the firm must raise price slightly less than 5% in order to maintain its real profits. As the share of labor cost in total costs becomes smaller, the price increase necessary to compensate for an increase in labor cost also declines. If the productivity of all labor in the economy increases and all firms subsequently raise prices only to the extent necessary to maintain their real profits, the next round of wage increases is at a lower rate. If labor’s productivity continues to improve, the next round of price increases is at an even smaller rate. Eventually this process con-

verges on zero wage increases and zero price increases.

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Unfortunately there are two main problems preventing this happy solution to the inflationary problem. First, neither labor nor the profit seekers are typically content simply to maintain their real income or profits. Increased marginal physical product means increased marginal revenue product, thus labor feels (justifiably so) that it has earned an increase in its real income. Profits seekers, on the other hand, feel that at least some part of labor’s increased productivity is due to the new equipment and technology introduced by the owners of the firm and that they, therefore, deserve an increase in their real profits. Second, the personal income tax structure is progressive. Accordingly, a 10% increase in money income before taxes might amount to only a 7% increase in money income after taxes. In order for after-tax (or disposable) income to increase by 10%, the employee may need to receive, say, 13% more before taxes. If labor productivity has not increased significantly, and if labor cost takes a large share of total revenues, it is conceivable that the firm may wish to raise prices by more than the original 10%, thus accelerating the inflationary process. In any case, the progressive structure of personal income taxes operates to inhibit the cooling down of inflation through gains in labor productivity. Legislation to Promote Price Competition. If firms do not expect all rivals to simultaneously raise prices to pass along cost increases, at least some firms will prefer to wait and see rather than take the risk of losing some part of their market share. A firm might decide to absorb the extra cost and take a chance on enlarging its market share if other firms raise their prices. This requires a ‘‘sense of competition” which is reinforced to a large degree by legislation that promotes price competition. Price fixing, or co!lusion as to price levels, is illegal in most Western economies, since it would typically operate to the detriment of the consumers. Simultaneous and equal price adjustments by firms in a particular market are not prima facie evidence of collusion, since the firms might be simply reacting independently to acommon stimulus. Nevertheless, better enforcement of existing legislation might reveal that some of the cases in which independent action was claimed were actually covertly collusive in nature. Another area of legislation that promotes price competition is that of encouraging small business development. Small- and medium-sized firms are usually particularly anxious to expand their market shares. Also they are not usually in close contact with the “‘old timers’ ” network, which may exist among the larger, older firms and which would facilitate the operation and maintenance of collusive practices. Voluntary Restraint.

If everyone behaved themselves, there would be no mis-

behavior, right? Governments and politicians often appeal to labor and management to practice moderation in their wage and profit demands, urging them to keep in mind that their actions, while self-serving in the short term, actually contribute to the perpetuation of the problem over the medium to long term. Such appeals are seen to fall on deaf ears, especially when one or a few groups begin to put self-interest ahead of community interest. The remaining parties see that their sacrifice becomes the private gain of another group, rather than having the effect of reducing inflationary pressures for the benefit of all. In such 368

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cases one can hardly expect people to do less than to jump in and grab for their share too. Voluntary restraint would work a lot better if the population at large better understood the nature of the inflationary process, and could see that an excessive wage or profit demand by any one group has external effects on other groups and society as a whole. These external effects, or externalities, are discussed in detail in Chap. 20. It suffices to say here that private actions to increase incomes and profit excessively have an antisocial effect. Full awareness of this effect and consequent peer group pressure on such greedy people, would increase the workability of voluntary restraint as a solution to the problem of inflation. Guidelines and Review Boards. The next logical step after calls for voluntary restraint is for the government to set up guidelines and a review board, first to establish the general level of restraint requested, and second to institutionalize an entity to act as keeper of the private conscience. Typically such review boards do not have much power, but they are able to publicize cases in which the guidelines are exceeded. This serves to bring bad publicity to the offending parties, which may embarrass or otherwise injure those parties currently or in the future. To the extent that the government deals with these parties, the government might threaten to do no further business with the firm concerned. Such action would have an impact directly upon the firm and indirectly upon the firm’s labor. A major problem with guidelines is that they must be general in principle, whereas the cases that come before the review board are particular, with complex histories and special circumstances. Exemptions from the guidelines and special cases almost inevitably mount up, with the result that the credibility of the whole process begins to suffer, until almost every group is pleading ‘‘special circumstances’”’ in order to qualify for exemption. In any case, if the review board has no power apart from the ability to confer bad publicity, some groups may be impervious to such publicity and thus have little incentive to respect the guidelines.

Control Boards and Compulsory Arbitration. An extension of the philosophy for voluntary restraint is to give binding decision power to a control board or arbitration council. All proposed price increases and wage contracts are presented to the price and wages control board for endorsement or veto. An arbitrating body might be established to decide on wage and salary levels in the event that employers and employees are unable to come to prior agreement. Each case would require substantial investigation on the part of the control body, resulting in significant inputs of time and money on the part of the firms and unions involved. It is obvious that such review or control boards tend to expand in size to match the enormity of their task. It is likewise obvious that company and union lawyers and accountants will be employed solely to circumvent or modify the impact of the guidelines or controls. There is a correspondingly substantial burden placed on society by this misdirection of money and talent into an essentially unproductive activity. Even if it did work, the cure might be worse

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had the undesirable effect of shifting economic decisions out of the market and

into a bureaucracy, with consequent impacts on longer term economic growth.

Tax-based Incomes Policies. As an extension of the philosophy of wage and price controls, policies have been proposed which encourage responsible behavior from both labor and management through the personal and corporate income tax structure.’° Briefly, if the target rate of wage increase is, for example, 8% per annum, firms giving more than this wguld be subject to higher rates of corporate tax, whereas firms giving less than 8% would benefit from a reduced corporate tax rate. At the same time, labor groups accepting less than the target rate of increase would receive income tax refunds which effectively increase the rate of increase beyond the target rate. Major advantages of the tax-based incomes policies are as follows: First, no great bureaucracy is necessary to arbitrate on each case—it requires relatively simple modifications to the existing income tax reporting and assessment process. Second, it simply modifies the market mechanism rather than supplants it. If a particular firm in a rapidly growing industry feels it must give more than the guideline rate of wage increase, it can do so knowing the increased tax burden of doing so. On the other hand if the firm does not face a labor shortage the prospect of increased rates of corporate tax serves to strengthen its resolve in the

negotiating process.

Underlying the tax-based incomes policy solution to inflation is the recognition that the problem of inflation has microeconomic foundations—that individuals seeking private gain impose an external cost on society as a whole. The standard microeconomic response to modify the behavior of individuals or firms imposing external costs is to place a tax on those costs, as we see in Chap. 20. Tax-based incomes policies do seem to have great potential in the control of inflation but at this point have not been tested in practice. Monetarists argue that their solution has not been given a fair test yet either, due primarily to the politically-undesirable consequences of limiting the growth of the money supply. Together the tax-based incomes policy and the controlled expansion of the money supply appear to be the major elements in a solution to the problem of inflation. In combination they provide the major part of a solution which is both politically feasible and which promises substantial results in the control of inflation. In summary, the solutions to the problem of inflation all seem to have their disadvantages and implicit trade-offs. What seems to be required is a truly joint effort by the various groups in society to reduce the rate of inflation to an acceptable level. Consumers, producers, employees, and governments all have a part to play: All parties must act responsibly and be cognizant of the wider social impact of their personal demands and actions. 1eThis proposal is largely due to Sidney Weintraub, Henry Wallich, Arthur Okun, and Lawrence

Seidman. See D.C. Colander, ed.; Solutions to Inflation, New York: Harcourt Brace Jovanovich, Inc.

1979, pp. 155-220, and A.M. Okun, Prices and Quantities—A Macroeconomic Analysis, Washington, D.C.: The Brookings Institution, 1981.

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V. SUMMARY In this chapter we have taken a grand tour through the real world of big labor, big business, and the problem of inflation. We have discovered that there is no single culprit to blame for inflation and that there is no easy cure for the problem. It seems that all groups in society can contribute to the inflationary process simply by putting their own short-term objectives ahead of the long-term objectives of society. Consumers who buy more of a product than they usually buy, because they fear that it will be unavailable or more expensive later on, create a self-

fulfilling prophecy. Such consumers avoid an imagined short-term hardship, but contribute to a continuing longer term problem, as prices increase and tend to stay up, due to the absence of effective price competition in most markets. Labor and other suppliers of services and resources are also sometimes motivated to protect self-interest first and social interest later. Efforts to maintain and increase real incomes of the suppliers of inputs to the production process can have substantial inflationary impacts. Progressive income tax structures

mean that labor must ask for more than the rate of inflation in order to maintain real income. This causes a transfer of wealth from the firm to labor and then to the tax collector. Thus governments, which benefit by inflation as large debtors, also experience an increase in their relative fiscal power within the economy as a result of inflation. Governments may also put their re-election considerations ahead of the more immediate control of the inflation problem. Business firms also do their share to increase inflation. Monopoly or oligopoly pricing power, conferred by the evolving structure of markets and the “‘don’t-rock-the-boat”’ attitudes of management in large impersonal corporations, has allowed business firms to routinely pass on cost increases to consumers and at times to benefit from the windfall gains of speculative consumer buying ahead of current consumption needs. To be sure, business has its problems and its constraints. Accounting practices and conventions not suitable for a régime of continuing inflation cause profits and rate of return to be overstated, while at the same time the firm is cash poor, is forced to borrow at increasingly higher interest rates, and is actually eating up its own capital. Public sympathy has not been great for business firms, due to the record nominal profits they announce each year. This has no doubt strengthened the resolve of union negotiators and consumer activists. Solutions to inflation start with the individual: first, as a consumer, then, as a supplier of inputs to production or as a shareholder in any production process, and last, as a constituent of government. Recognition of the fact that inflation is a social disease should induce individual action to eradicate the problem. Simply abstaining from adding to the inflationary process until it is treated would form the major part of the treatment. But beyond the immediate human

factor, it is clear that major modifications are necessary in the legal and financial structure of the economy. Tax structures, tax-deductibility of expenses and capital investments, calculation of profits in real or constant purchasing-power terms, and other issues must be rethought and constructively modified. These

Wages, Profits, and Inflation

371

factors, as well as the “me first” attitude of many individuals in society, need to change significantly before inflation can be kept to agreeable levels.

DISCUSSION

QUESTIONS

1.

Discuss the impact of the Great Depression of 1929 to 1933 on the American labor movement.

2.

How did legislation affect the labor movement after the depression?

3.

Outline some of the major objectives of labor unions, and explain how these objectives tend to conflict wih one another.

4.

Why is it inaccurate to impute all the wage gains and improvements in working conditions (in an industry that is at least partly unionized) to the efforts of the union?

5.

Reconcile the notions of accounting profits and economic profits. What is normal profit, expressed in accounting profit terms?

6.

Why does inflation in many cases operate to cause accounting profits—on net assets, for example—to be overstated?

7.

Explain how governments may contribute to the problem of inflation. Why do you suppose they sometimes act in a way that conflicts with society’s best economic interests?

8.

How do people—both as income earners and consumers—contribute to the problem of inflation?

9.

Which groups tend to gain and which groups tend to lose in the inflationary process? If a little bit of inflation is socially desirable, in what ways could the losers be compensated for their loss, so that everyone is either better off or at least no worse off because of inflation?

10.

Discuss the possible solutions, or components of a solution, to the problem of inflation.

SUGGESTED BoskINn, M.J.,

REFERENCES

“Unions and Relative Wages,” American

Economic

Review,

62 (June

1972), 466-72.

CoLANDER, D.C.,ed.,

Solutions to Inflation. New York: Harcourt Brace Jovanovich, Inc.,

1979.

DEAN, J.W.,

‘The Inflation Process: Where Conventional Theory Falters,’’ American

Economic Review, 71 (May 1981), 362—7.

FRIEDMAN, M.,

“The Role of Monetary Policy,’’ American Economic Review, 58 (March

1968), 1-17.

Hort, C.C, “Job Search, Phillips’ Wage Relation, and Union Influence: Theory and Evidence,” in Microeconomic Foundations of Employment and Inflation Theory, ed. E.S. Phelps, and others, pp. 53-123. New York: W.W. Norton & Co., Inc., 1970. 372

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

JOHNSON, H.G.,

Inflation and the Monetarist Controversy. Amsterdam: North-Holland,

1972.

LEIBENSTEIN, H., ‘‘The Inflation Process: nomic Review, 71 (May 1981), 368-73.

A Micro-Behavioral Analysis,” American Eco-

Lewis, H.G., Unionism and Relative Wages in the United States. Chicago: University of Chicago Press, 1963. Oxwun, A.M., Prices and Quantities—A Macroeconomic Analysis. Washington, D.C.: The Brookings Institution, 1981. PARSLEY, C.J., ‘‘Labor Union Effects on Wage Gains: A Survey of Recent Literature,” Journal of Economic Literature, 58 (March 1980), 1—31.

PATINKIN, D., “The Chicago Tradition, the Quantity Theory, and Friedman,” Journal of Money, Credit, and Banking, 1 (Feb. 1969), 46—70. REDER, M.W., ‘‘Unions and Wages: The Problems of Measurement,” Journal ofPolitical Economy, 73 (April 1965), 188-96.

REYNOLDS, L.G., Labor Economics and Labor Relations (7th ed.). Englewood Cliffs, N.J.: Prentice-Hall, 1978. TALLEY, R.,

“The True Condition of Profits as Reflected in Stock Prices and the Rate of

Capital Formation,” Business Economics, vol. 13, Sept. 1978. THOMPSON,

E.A.,

‘‘On Labor’s Right to Strike,’’ Economic

Enquiry,

18 (Oct. 1980),

640-653.

Wages, Profits, and Inflation

373

fe

Bee.

Savings, Interest, and Investment

|. INTRODUCTION In this chapter we concern ourselves with the saving and investment decision of individuals, firms, and other institutions. Why is it that individuals and institutions abstain from current consumption in order to set aside savings for future periods? Why do institutions in particular and also individuals as shareholders in these institutions invest in capital formation that has production capability in future periods? We shall see that the rate of interest induces people to save from their current incomes, and that it is the price other people must pay in order to borrow funds for capital formation. What factors determine the rate of interest for a particular loan? We shall see that the individual’s impatience for current consumption, as well as the rate of inflation and the degree of risk associated with the loan, each have a part to play. The issue of savings rather than consumption is a matter of intertemporal choice on the part of the consumer. Intertemporal choice is concerned with the consumer’s allocation of available income over time. By saving in this period, the consumer may consume more in a subsequent period, having the amount saved plus the accrued interest to spend at the later point in time. We can utilize indifference curve analysis to demonstrate that some consumers wish to save more, some less, depending upon the rate at which they are willing to substitute future consumption for current consumption. This rate is known as the rate of time preference. 374

5)

Oilman

tine

i)

Sie

bog

|

5A_t

In the real world ofinflation and uncertainty of future cost dnd demand )_” ) levels, lenders want to be compensated for the expected decline in the value of

their dollar due to inflation, as well as for the risk that the loan might not be repaid due to its use in a poor investment. Thus the interest rate includes a margin for the anticipated rate of inflation and a premium for risk, over and above the lender’s rate of time preference. Since loans are made for differing periods of time, there is also a term structure of interest rates: The interest rate will vary according to the length of the loan, ceteris paribus. _ a e\

«

ll. INTERTEMPORAL CHOICE: SAVINGS VS. CONSUMPTION

im

7

4

ae

ej Lotz

DEFINITION: Savings are defined as the excess of income over consumption expenditures in any time period. Savings are thus the residual funds remaining out of current income that may be spent (along with interest earned) in future time periods. We shall start with the simple two-period model of an individual who has an income during the present period and who does not expect any income during the subsequent (future) period. This person wants to save some part of current income in order to buy goods and services in the future. We then examine a more complex case, in which the individual expects to receive incomes in both

the first and second period, and who consequently might either save or borrow during the first period. In our simple model, if this person borrows in the first period, it is clear that repayments have to be made in the second period, in order to square up the accounts before the expiry of the two periods. It is not very difficult to see the implications of the two-period model for a multiperiod scenario. We take a brief look at these implications after discussion of the two-period models. A Simple Two-period Model

EXAMPLE:

Jock Exertius is a professional athlete who has a contract for the present year, but at this time has no knowledge of what income he will receive in the following year. Imagine further that given the high probability of injury during the present year, the individual expects to earn no income at all during the second year. Since Jock must eat and pay accommodation costs in the second year, however, he realizes that he must save some of this year’s income in order to pay for next year’s consumption expenditures. The savings of the first year can be deposited at a bank or trust company to earn interest during the first year, so that his consumption expenditures during the second year will be equal to the savings of the first year plus the interest income accrued on those savings. Suppose Jock receives $100,000 in the first year, out of which he might save all, some, or none at an interest rate of 10% per annum. In Fig. 16—1 we

show the consumption possibilities open to him. He could consume his entire

income in year 1: This choice is depicted at pointA, with $100,000 consumption

in year 1 and zero consumption in year 2. At the other extreme, he could put the entire $100,000 into a bank at 10% interest, and spend nothing on consumption in the first year. In this case he could spend $110,000 in the second year, this o \\ My =

Savings, Interest, and Investment

375

V

being the original $100,000 (the principal) plus the accrued interest. This choice possibility is depicted at pointB in the figure. In between these extremes, which would see him starve in either the first or second period, Jock could choose any

linear combination of the two. One such consumption possibility is point C,

which represents consumption of $70,000 in year 1 with the balance being saved. In year 2, these savings of $30,000 have grown to $33,000 at the 10%

interest rate; hence Jock can spend the latter amount on consumption in the second year. N \ DEFINITION: The line BCA is the consumer’s intertemporal budget constraint; it encompasses all attainable combinations of current and future consumption possibilities. The slope of this line is OB/OA or 110/100, and is determined by the rate of

interest available to savers. Clearly if the interest rate is only 5%, the slope would be flatter, whereas a 15% interest rate would cause it to be steeper. FIGURE

16-1

The Intertemporal Consumption Possibilities Set Consumption in Year 2 (units of

$1,000)

:

p,

.

110

{

ithe’

hy

t

\

, p

:

ie) AD

33

100

Consumption

Saving

Consumption in Year 1

(units of $1,000)

It is clear that the extreme points, A and B, are not likely to be the preferred choice of the athlete in the circumstances hypothesized. But neither is it obvious that point C will be chosen. Perhaps Jock will prefer to save $40,000 in the first year and spend $44,000 in year 2 or, alternatively, perhaps he will save most of the first year’s income, $80,000, for instance, leaving a substantial nest egg for the future? To answer this question, we need to consider Jock’s impatience for

current consumption rather than for future consumption, which is known as the consumer’s rate of time preference.

‘The slope of the line is, of course, equal to the vertical rise over the horizontal run. For any $1 reduction in current consumption expenditure, the consumer can obtain $1(1 + r) of consumption in the second period, where r is the rate of interest. Thus the slope is 1(1 + r)/—1 or —(1 +r) and can be seen to be positively related to the rate of interest.

376

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

The Rate of Time Preference

DEFINITION: An individual’s rate of time preference is defined as the amount of future consumption he or she is just willing to give up for an additional unit of current consumption. This rate is determined by the individual’s own preference structure between consumption now and consumption later. If the individual is relatively impatient, he or she prefers to consume most of current income now and save only a relatively small amount for the future. Oppositely, someone who looks forward patiently to the future is inclined to save more in the present, in order to have more funds to spend on future consumption. Since consumption in the present and consumption in the future are conceptually separate items, an individual has indifference curves reflecting his or her preferences and indifferences between various combinations of current consumption and future consumption.

EXAMPLE:

Imagine the case of Melody Moro, a female singer in a rock band, and refer to pointA in Fig. 16—2. At this point in intertemporal consumption space, Melody is offered $50,000 in the first year plus $80,000 in the second year. Suppose that her rate of time preference is such that she would be prepared to give up $20,000 of the second year’s income in order to obtain an extra $10,000 in year 1. In that case, an indifference curve, shown as Io, joins points A and B in the figure. Similarly, points C and D are postulated to lie on the same indifference curve. Note that for $70,000 in year 1—an extra $10,000—Melody is willing to give up only $15,000 of year 2 income. Further, for $80,000 in year 1—the next $10,000 increase—she is willing to sacrifice only $5,000 of year 2 income. FIGURE

16-2

Indifference Curves in Intertemporal Consumption Space

Consumption in Year 2 (Co)

Consumption in

59 60

70

80

Year 1 (C;) Savings, Interest, and Investment

377

Recall from Chap. 2 that the consumer’s rate of time preference between current and future consumption can be referred to as the consumer’s marginal rate of substitution (MRS) between current and future consumption. It is equal to the amount of future consumption that the consumer is just willing to give up for another dollar’s worth of current consumption, so that the consumer’s total utility remains the same. It is thus equal to the slope of the indifference curve at any point. We expect a diminishing MRS between future and current consump-

tion: The more current consumption the individual has, the less future consumption he or she is prepared to give up for additional current consumption, and vice versa. Accordingly, we have shown the indifference curve as convex to the origin. The other properties of indifference curves are also expected to hold: Higher curves are preferred to lower curves, indifference curves do not touch or

intersect, and indifference curves are negatively sloping throughout length, approaching each axis asymptotically. NOTE:

The individual’s rate of time preference, or MRS between current and future consumption, is determined independently of the interest rate. It depends only upon the individual’s preference between current and future consumption and the starting point from which the substitution is contemplated. Thus from point A to point B in Fig. 16—2, the MRS is (on average) equal to 2.0, whereas from point B to C it averages 1.5, and from C to D it averages 0.5. Over each of the discrete intervals shown in the figure, the MRS is defined marginally, for small ($1) changes in current consumption. It is easy to see, for example, that the MRS is higher at point A than at point B, since the slope of the indifference curve becomes progressively flatter as we move down it to the right. The value of 2.0 calculated over the range fromA to B is thus an average of the actual values of MRS of every point between pointsA and B. FIGURE

16-3

The Savings Decision

20

378

their

40

60

80

100

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

The Savings Decision

We are now ready to bring together the consumer’s preferences between current and future consumption and the consumption possibilities afforded by the consumer’s income in year 1 and the interest rate available. Going back to the case of the professional athlete, Fig. 16-3 shows his indifference curves superimposed over his consumption possibilities. The highest attainable indifference curve is shown as I,, which is just tangent to the consumer’s intertemporal budget line at pointA. The athlete’s expected utility is therefore maximized by consuming approximately $55,000 in the first year and saving the remainder. The remaining $45,000 grows to $49,500 at the 10% interest rate, allowing the

athlete to consume $49,500 worth of goods and services in the second year. Note that for other individuals the choice might have been quite different. In Fig. 16—4 we show two other consumers with different tastes and preferences between current and future consumption. In Part (a) of the figure we show an individual whose MRS is relatively high at the intertemporal combination represented by pointA. This individual would prefer to trade-off future consumption for more present consumption, and does so until the tangency point B is attained, which represents $80,000 consumption in year 1 and $22,000 in year 2. This person’s attitude might be characterized as “‘live for today and let tomorrow take care of itself.’’ In Part (b) of Fig. 16—4 we show another individual whose MRS is relatively low at the combination represented by pointA. This individual prefers to give up some current consumption for increased future consumption,

and does so until the tangency point C is attained, at which point $30,000 is consumed in year 1 and $70,000 is saved for eventual consumption of $77,000

in year 2. This person prefers to save a relatively large proportion of current income for future consumption. FIGURE

16-4

Different Rates of Time Preference Cause Different Savings Decisions a. Low Savers

b. High Savers

30

55 ee —~ ee

100

1

Ma ae

Savings, Interest, and Investment

379

Although the three consumers each had a different MRS at the combination represented by pointA, the MRS, or rate of time preference, of each person is equal at their equilibrium points, A, B, andC, respectively, since each person’s indifference curve is tangent to the intertemporal budget line, which is common to all three. Even if all three did not have the same income in year 1, their equilibrium rates of time preference will be the same, since the slopes of their intertemporal budget lines would be the same; that slope is determined by the rate of interest available to people willing to save some of their current incomes. In another section we examine the determination of the interest rate available to savers, but first let us consider a more complex two-period model in which the individual may either save or borrow. Borrowing against Future Consumption

DEFINITION: Borrowings are funds obtained from the capital market to finance the excess of current consumption expenditures over current income. In the real world we notice individuals borrowing in the current period, in order to buy consumer goods and services that they cannot afford out of their current income. Given the prospect of future income, individuals may consume beyond their income in the current period by borrowing, but must consume within the limit of their income in the future, while they pay back the amount borrowed plus the interest charged. EXAMPLE:

Let us consider the borrowing decision in the context of the simple two-period model. Imagine a student who wins a scholarship which pays $10,000 in year 1 and $10,000 again in year 2, and must decide how to allocate his income opti-

mally over the two years of the scholarship. Let us find the extreme situations, as we did in the simple two-period model, in order to construct the individual’s intertemporal budget constraint line. If the student consumes nothing in the first year, there is $10,000 plus the interest earned on that $10,000 to add to his sec-

ond year income of $10,000. Thus the maximum consumption expenditure available in year 2 (if year 1 consumption is zero) is $10,000 + $10,000 (1 + r) wherer is the rate of interest. Assuming that the interest rate is 10%, thenr = 0.1, and the consumer will have

a maximum of $10,000 + $10,000 (1.1), or $21,000,

for expenditure in the second year. At the other extreme, suppose the student spends all current income plus the maximum borrowings in the first year, and spends all his year 2 income paying back the loan. How much can he borrow against his second year’s income? Look at this from the reverse aspect: How much can he afford to pay back in the second year? He can afford only $10,000, his entire income in year 2. But

this repayment must include both the interest charged on the loan and the amount borrowed. The maximum that can be borrowed is $9,090.91, since this

sum plus 10% interest ($909.09) totals $10,000. Thus the maximum consump-

tion expenditure in the first year is $10,000 + $9,090.91, or $19,090.91 in total.2 2In Chaps. 13 and 17 we discuss the process of discounting future values to obtain present values, which is essentially what we have done here to find the value $9,090.91. Discounting is the converse of compounding and is achieved by dividing (rather than multiplying) by (1 + r) Symbolically, if Y, represents year 1 income, and Y, represents year 2 income, the extreme consumption points are set by Y. + Y,(1 +r) in year 2, and by Y, + Y,/(1 +r) in year 1.

[yo 380

OE:

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

| FN

In Fig. 16—5 we show the extreme points as calculated above, and we join them to find the student’s intertemporal budget constraint line, MN. Point A represents the point of zero saving and zero borrowing: The student would spend $10,000 on consumption in each year. The highest attainable indifference curve, I, is tangent to the budget constraint line at point B, however. This student evidently prefers to spend more on consumption in year 1 than is earned, financing the excess by borrowing. He earns $10,000, spends $14,000, and necessarily borrows $4,000. In the second year, part of his $10,000 income must be

used to repay the loan of $4,000 plus the accrued interest of $400. Accordingly,

only $5,600 is spent on consumption in year two, and the remaining $4,400 is used to repay the loan. FIGURE

16-5

Borrowing in the Two-period Model

Bh A

|

a

Cy

Peo?

(units of

+

$1,000)

a

ot

21

Year 2 Repayments

C, (units of $1,000)

The two-period model with known income in both periods also allows for saving behavior. In Fig. 16-6 we show a different student with the same scholarship, who chooses to save in the first year and spend a larger amount in the second year. This person’s preferred position is at point C, involving consumption of $5,000 and savings of $5,000 in the first year, and consumption expenditure of $15,500 in the second year. Year 2 consumption is financed by $10,000

income in the second year, plus the $5,000 saved and the $500 interest earned on those savings. Thus some people will borrow and some will save, depending on their individual rates of time preference.

NOTE:

The adage “neither a borrower nor a lender be”’ is clearly a Victorian admonition in line with other antihedonist strictures of the time, since most people increase their total utility by being either a borrower or a lender, unless by complete chance their highest attainable indifference curve is tangent at the point of zero savings and zero borrowings. Savings, Interest, and Investment

381

FIGURE

16-6

Saving in the Two-period Model

Generalization to More Than Two Periods

While the model becomes considerably more complex when it is extended to more than two periods, it is relatively easy to imagine the implications of the two-period model for multiperiod cases. In the present period, consumers may either save, borrow, or spend their entire income on consumption. If they choose to save, they may save for consumption in future periods more distant than the second period. Thus people save for their retirement and for major events, for which they might plan years in advance. Similarly, people save for several years in order to go back to school on a full-time basis. Conversely people borrow in the present period far beyond their ability to pay back in the subsequent period alone. Automobile loans are typically repaid over a two-year to a four-year period, for example, whereas loans to purchase a house are obtained on a mortgage loan of twenty, twenty-five, or thirty years. In each of these cases the individual’s time horizon (or planning period) extends beyond two years, and the individual is attempting to maximize utility over that time horizon. Thus young people borrow to finance a college education, a car, and other consumer durable goods, including a house. These people expect to receive a continuing stream of incomes over their lives and are prepared to pay back later in order to consume more today. Alternatively, older people tend to save from their incomes for future consumption, since they expect their incomes to fall substantially when they retire, yet they wish to maintain the lifestyle to which they have become accustomed.

III. INVESTMENT AND INTEREST RATE DETERMINATION We have seen that some people save and some people borrow during any particular time period, depending upon their rate of time preference for consumption. People also borrow for another reason—for investment purposes. 382

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

DEFINITION: By investment we mean the application of funds to a production process, whereby these funds are used to purchase assets, equipment, and raw materials to be used in a production process. Investment serves to both replenish and add to the firm’s capital stock. Replacement investment is that which replaces assets, equipment, and materials that have been worn out or used up in the production process and therefore restore the firm’s plant to its original size and capability. New investment serves to expand the firm’s capital stock, augmenting the plant’s size and productive capability.

NOTE:

Be careful not to confuse savings with investment. Savers supply funds to the market for capital, whereas investors demand funds from that market. In com-

mon usage investment is often meant synonomously with savings—for example, my uncle says he invested $1,000 in corporate bonds. Really what he did was to save $1,000 by lending it to a corporation on the promise that at the end of a prescribed period the sum of $1,000 plus interest would be repaid by the corporation. If the corporate bonds are traded on the stock exchange, the holder of the bonds may sell them prior to their expiry date, if this seems financially advantageous. In either case the individual has lent money to the corporation and expects to receive a payment in excess of that loan after the passage of time. The person buying the bonds on the stock exchange has simply purchased the initial loan to the corporation and has the same expectation that after a period of time he or she will be able to either resell the loan or be repaid by the borrower for a monetary gain. These people are savers, not investors, since they are simply

postponing consumption to a future period by lending their money. The borrowers who use the funds for capital replacement or augmentation in a productive process are the investors. Thus savers supply funds for current consumption and for investment purposes, while borrowers demand funds for either or both of these purposes. There is consequently a market for these funds, which we call the capital market, and an equilibrium price of the funds is established and rises or falls as demand or supply conditions change. The price of these funds is the rate of interest payable to lenders by borrowers for the use of the funds. Let us now establish what the demand curve and the supply curve look like, and then bring the two together to find the equilibrium rate of interest. Investment Demand for Funds

Investors borrow funds in the expectation that they will receive revenues from the investment of sufficient magnitude to repay the loan plus interest and leave some funds left over as a profit on their investment. Investors will perceive investment opportunities and will undertake those investments when they expect the rate of return on the investment to exceed the rate of interest payable to the lender who provides the necessary funds.

DEFINITION: The rate of return can be defined as the percentage by which total revenues from the investment exceed total costs (excluding the interest cost of borrowing) associated with the investment. Savings, Interest, and Investment e

383

EXAMPLE:

Suppose that your professor perceives an investment opportunity that involves the printing of special T-shirts for next year’s orientation week at the start of the fall semester. For simplicity we assume that the printing machine will last only one year and that the professor will hire student labor and continue his or her own teaching, research, and administrative responsibilities. Being a professor, he or she will have no spare cash to invest but will have to borrow the funds required at an interest rate of 10% per annum. It will cost $10,000 to purchase the machine, a supply of blank T-shirts, printer’s ink, and the services of student labor. Your professor expects to make $12,000'in revenue from the sale of the

printed T-shirts next September. Thus the expected return on investment is $2,000 over the $10,000 initial cost, for a rate of return of 20%. Since this exceeds

the cost of borrowing (the rate of interest), the professor should go ahead and make the investment. After paying $1,000 interest on the loan, the investor will have a residual profit of $1,000, which can be regarded as a reward for his or her

enterprise in perceiving the investment opportunity and acting accordingly. It is clear that some investment opportunities are more lucrative than others. Some appear to promise relatively high rates of return, others moderate rates of return, and still others offer relatively low rates of return. Keeping in mind that we are dealing with certainty rather than uncertainty, the investor prefers investment opportunities with higher rates of return over those with lower rates of return. Suppose that an investor perceives a set of investment opportunities as shown in Fig. 16—7. She has ranked the investment opportunities in order of their expected rates of return, and has identified them as projects A, B,C, D, E, F, and G. Notice that project A requires $10,000 and has an expected rate of return of 26%, whereas projects B and C each require an investment of $15,000 and promise a 22% and 18% rate of return, respectively. Similarly the width of each of the other blocks represents the initial cost of the project, and the height represents the rate of return. Thus project D requires only $5,000 and promises to return 15% on this investment, and so on.

Suppose, for the sake of this example, that our investor can borrow as much as she wants at 12% per annum. She should therefore invest in projects A, B, C, D, and E, since each one of these has a rate of return higher than 12% and therefore leaves her with a residual profit for her enterprise. Accordingly she will borrow $55,000 at the 12% interest rate. Suppose alternatively that she could borrow at 9%; this would cause project F to be marginally profitable—it returns 10%—and she should borrow $75,000 at that interest rate. If on the other hand,

the interest rate had been 20%, you will readily see that she would only borrow $25,000, since only projects A and B are profitable at that interest rate. NOTE:

Thus the investment demand for funds is inversely related to the rate of interest. At higher interest rates investors demand fewer funds, and at lower interest rates

the demand for funds for investment purposes is greater. (The law of demand strikes again!) The individual’s demand curve for investment funds can be shown in this case as the stepped line D’, which incorporates the top of each block representing an investment opportunity. When the demands of all investors are aggregated (each with their different perceptions of the available invest384

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

FIGURE

16-7

Expected Rates of Return on Investment and the Demand for Investment Funds Expected rate of return (%)

10

20

30

40

50

60

70

80

90

100

Quantity of funds invested

(units of $1,000)

ment opportunities), we expect the demand curve for investment funds to be relatively smooth, like D, in Fig. 16—7. In either case we have established that

the demand curve for investment funds has a negative slope. Let us now look at the other part of borrowings—the demand for consumption funds for expenditure on goods and services in the current period. The Demand for Funds for Consumption

Borrowers’ demands for funds for current consumption are also inversely related to the rate of interest. Earlier in this chapter we depicted a student who borrowed in the current period, in order to increase consumption expenditure (see Fig. 16—5). We reproduce that situation here in Fig. 16—8 to show how the borrower

reacts to a change in the interest rate. Recall that the individual expected to receive $10,000 in each of the first and second periods, and could either borrow

or lend in the first period (and repay or be repaid in the second period), in order to exercise intertemporal choice in his consumption expenditure. Point A in both Figs. 16—5 and 16-8 depicts the consumer’s initial endowment of income. Point B represents the student’s preferred point in intertemporal consumption space, where the highest attainable indifference curve is tangent to his initial intertemporal budget constraint. Recall that the intertemporal budget constraint passing through point B is predicated on an interest rate of 10% per annum. Thus its intercept on the vertical axis is equal to year 2 income ($10,000) plus year 1 income ($10,000) plus the interest earned on year 1 income ($1,000). This is the absolute maximum available for consumption in year 2, given the 10% Savings, Interest, and Investment

385

interest rate. Similarly, the maximum available for expenditure in year 1 is year 1 income ($10,000) plus the amount that could be borrowed against year 2 income ($9,090.91), which with interest ($909.09) is equal to year 2 income. FIGURE

16-8

The Demand for Funds for Current Consumption, Given Different Rates of Interest

Cy (units of

$1,000)

C, (units of $1,000)

Now imagine that the interest rate is 20% per annum rather than 10%. The student’s initial endowment (point A) remains unchanged, but the intertemporal budget constraint rotates through pointA, because of changes in the consumption possibilities for year 1 and year 2, due to the higher interest rate. Let us find the points where the new budget constraint line cuts the two axes. If the student completely foregoes consumption in the first year, in year 2 he would have year 2 income ($10,000) plus year 1 income ($10,000) plus the interest on year 1 income ($2,000 at the 20% interest rate). Thus maximum year 2 consumption is $22,000, if year 1 consumption is zero. Oppositely if the student wants to consume everything in year 1 and nothing in year 2, he could spend the sum of year 1 income ($10,000) plus the maximum borrowings against year 2 income ($8,333.33), which with interest at 20% ($1,666.67) is equal to year 2 income.

Thus the new intertemporal budget constraint intersects $22,000 on the vertical axis and $18,333.33 on the horizontal axis, necessarily passing through point A, since at that point funds are neither borrowed nor loaned. The new budget constraint causes the student’s previously preferred point B to become unattainable. The indifference curve Io, which was tangent to the old budget constraint at B, now lies completely above the new set of attainable intertemporal consumption choices. The highest attainable indifference curve is now I’, which is tangent at point C. Thus the student reacts to the rise in the 386

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

interest rate by borrowing less (approximately $2,000 rather than $4,000 if the interest rate was 10%). The higher interest rate causes the student to change his intertemporal

consumption

pattern: he now

chooses

to postpone

some

con-

sumption into the future period, as compared with the earlier situation. Notice also that the higher interest rate necessarily makes a borrower worse off, in that he must retreat to a lower indifference curve. We could repeat the analysis for other rates of interest to show that at even higher rates the borrower would wish to borrow even less, and that at lower rates the borrower would wish to borrow more, in each case adjusting his or her borrowings, in order to maximize intertemporal utility given the prevailing interest rate. The point is made, however, that the demand for funds for present consumption purposes borrowed against future income is inversely related to the rate of interest payable on those borrowings. Thus both components of the demand for funds behave according to the law of demand, and we shall have no reservations when depicting the demand curve for funds as downward-sloping to the right. Let us now examine the form of the supply curve of these funds. The Supply Curve for Loanable Funds

Using a similar analysis for savers, we can show that higher interest rates cause utility-maximizing consumers to save more in the present period than they would if lower rates prevailed. In Fig. 16—9 we reproduce the earlier example of the other scholarship winner who preferred to save in year 1, which was exhibited in Fig. 16—6. When the interest rate is 10%, that student faces the intertemporal budget constraint shown as YAX in Fig. 16-9, and is able to maximize her

utility on indifference curve I), which is tangent at point C. Now suppose the interest rate increases to 20%. As we have seen, this causes the budget constraint line to rotate through point A to its new position Y'AX’, changing the set of attainable combinations of year 1 and year 2 consumption possibilities available to the student. The individual depicted in Fig. 16-9 can increase her utility, given the higher interest rate, by moving from point C to pointD. This allows her to reach the highest attainable indifference curve I,. This means that she prefers to consume even less in the first period. That is to say, the higher rate of interest causes this person to save more in the current time period. We could repeat this exercise for interest rates of 5%, 15%, and 25%, for example, but the point is made: The supply of loanable funds in the current time period is directly related to the rate of interest. Thus we should expect the savings of individuals and of the society in aggregate to be represented by a positively sloping supply curve with respect to the interest rate.? 3It is possible that savings could exhibit a Giffen good response to changes in the interest rate. If an individual regards savings as a Giffen good at very high interest rates, his or her supply curve for savings would bend backward above some point. While this could occur in the simple two-period model, it is less likely in the multiperiod model, where the consumer’s time horizon is longer and where the consumer expects interest rates to fluctuate over time. Even if individuals do regard savings as a Giffen good, this is likely to be outweighed in the aggregate by others who wish to save more at higher rates of interest, and thus the aggregate supply curve of loanable funds is confidently expected to be positively sloping. Savings, Interest, and Investment

387

FIGURE

16-9

The Supply of Loanable Funds, Given Different Rates of Interest

10

xX’ X

4

The Equilibrium Interest Rate in the Market for Funds We have seen that the demand curve for (borrowable) funds is negatively sloping, and that the supply curve for (loanable) funds is positively sloping. Superimposing one upon the other, as in Fig. 16-10, we are able to find the equilibrium quantity of funds both supplied and demanded and the equilibrium interest rate. The two curves intersect at the interest rate depicted as i* and at total funds supplied and demanded Q*. These levels are equilibrium levels, because any higher interest rate would cause an excess supply of funds and any lower rate would cause an excess demand for funds. Under the competitive conditions of the capital market, we expect excess supply to lead to a reduction in the interest rate, whereas we expect excess demand to cause an increase in the interest rate.

The absence of either excess demand or supply means that there is no pressure on the interest rate to either rise or fall, and hence that the interest rate is at the equilibrium level, where it will stay until there is a shift of either the supply or the demand curve. Different Interest Rates in Different Markets

In the simple model of interest rate determination, we are able to find the interest rate under a specific set of assumptions. These assumptions included certainty as to the outcome of investment projects, no default by borrowers, and a single (one-year) duration over which all loans are made. In the real world, of course, there is uncertainty, default, and a multiplicity of loan durations. When these factors enter the question of interest rate determination we must modify the 388

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

FIGURE

16-10

The Market for Funds and the Equilibrium Interest Rate

Quantity of loanable funds

model accordingly. In effect we are dealing with a different market for loanable funds in each case. Different degrees of risk associated with the possible default by the borrower (or the failure of an investment project, causing the borrower to default on the loan) cause the lender to ask for higher interest rates on more risky loans. Different durations of the loan period also cause different interest rates to be offered by borrowers, since the lender must forego the use of his or her funds for a greater or lesser period. Let us examine these issues in some more detail. Risk Premiums above the Prime Rate. Lenders form an opinion about the likelihood of default by a particular borrower based on his or her income and employment history, the planned use of the funds, and other objective and subjective factors. In the real world of uncertainty, such judgments are based on generalizations made from previous examples of similar loans to similar people for similar purposes. Lenders demand arisk premium for loans that have a risk of default involved. The size of this risk premium is positively related to the amount of default risk perceived. The lender’s most trusted and financially solid clients are offered the prime rate, whereas other potential borrowers are offered an interest rate equal to the prime rate plus a premium for risk. This premium might be an extra 1% for a professor who wants to buy an automobile or an extra 212% for a student who wants to do the same. Similarly, the professor may be charged a risk premium of 3% for-a loan to start a small business venture, whereas a corporation diversifying into the same business venture might obtain the loan at 42 or 1% above the prime rate. The prime rate is determined, in theory, by the market for loans to clients who are “most trusted and financially solid”. Competitive pricing of their loans to these borrowers by lenders leads to an equilibrium level of the prime rate. In practice banks and other lending institutions tend to adjust their prime rate when the Federal Reserve in the U.S., or the Central Bank in other countries,

adjusts the rate at which it lends to the banks. In most banking systems, the Savings, Interest, and Investment

389

government bank acts as a lender of last resort to the commercial banks, lending the bank money at the “bank rate’ when a bank needs it to avoid a liquidity crisis. Given the other regulations affecting their lending, banks almost never have to borrow from the government bank, but they use the bank rate as the basis

upon which to base their own interest rates. Thus the prime rate might be one percentage point above the bank rate, and the risk premiums for different classes of borrowers are selected with an eye to the competitive rate of interest being charged by other banks and financial institutions to borrowers in each particular category.‘ The Term Structure of Interest Rates. Different interest rates for loans of different duration give rise to what is known as the term structure of interest rates. The normal situation is for loans of longer duration, ceteris paribus, to command a higher interest rate, in compensation for the longer period over which the lender must wait for reimbursement, and for the resulting greater uncertainty with respect to future outcomes of investment and other plans by the borrower. The longer the duration of the loan, the greater the probability, ceteris paribus, that the borrower will default. Also, as we look further into the future, the probability increases that there will be significant changes in the monetary unit due to inflation. The term structure of interest rates is established by competition among borrowers for the savings of individuals and firms, with the interest rates for each duration being fairly consistent across the market for loans of that particular duration, given that other factors are constant. Thus, for a particular risk

class of borrower, such as the major banks, savers might be able to get 10% for one-year term deposits, 1142% for two- to five-year term deposits, and 1212% for five- to ten-year term deposits. Corporate bonds, carrying a higher risk of default than bank deposits, might exhibit a term structure of interest rates uniformly higher than that of the banks, perhaps 12% higher for financially solid corporations and 212% higher across the board for a firm engaged in high risk investment projects, or whose financial situation is less solid. NOTE:

In recent years we have seen an abnormal or reverse term structure of interest

rates, due to abnormally high rates of inflation. During 1980 when the prime rate for borrowers soared to 20% in the United States and nearly as high in other Western countries, the interest rate for loans was inversely related to the duration of those loans. This was due to the widespread expectation, held by lenders and borrowers alike, that such high interest rates were temporary and would fall as soon as inflation was brought under a greater degree of control. Thus borrowers and lenders collectively expected the high current rates to be temporary and did not adjust longer duration rates upward to the same degree. Since borrowers expected inflation rates and interest rates to be lower in two to five years, and since lenders appeared to agree, they were able to attract sufficient funds for their needs at lower interest rates on long-term loans, as compared with their short-term deposit rates. ‘The Central Bank or Federal Reserve adjusts the bank rate as and when deemed necessary to adjust the total money supply, to control inflation, and to influence the level of other macroeconomic variables, such as the unemployment rate and gross national product (GNP). See F. Zahn, Macroeconomic Theory and Policy (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1975).

390

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

The Impact of Inflation on Interest Rates

Inflation, as we saw in the preceding chapter, serves to depreciate the purchasing power of the monetary unit. The intertemporal choice decisions of consumers, savers, and borrowers as discussed in this chapter have been implicitly based on an assumption of constant purchasing power of the monetary unit. Alternatively, given an expected rate of inflation, the consumer’s rate of time preference between current and future consumption could be understood to take into account the expected rate of inflation and hence the expected depreciation of the dollar. In a world of zero inflation, a particular consumer’s rate of time preference might be only 4% per annum. The expectation that the purchasing power of the dollar will fall by 10% in the coming year would raise his or her rate of time preference to 14% in nominal dollars, although it would stay the same in constant (adjusted for inflation) dollars.

NOTE:

Thus, three elements enter the determination of nominal interest rates for a particular class of borrower. First, there is the rate of time preference of buyers and sellers in constant dollars; second, there is the rate of inflation expected by savers and borrowers; and third, there is the risk premium to compensate for perceived risk of default on the part of the borrower. The first two elements influence the location of the demand curve for funds, and all three elements influence the supply curve for funds. Given the placement of the supply and demand curves in the market for loans of a particular duration and for a particular risk class of borrower, an equilibrium interest rate can be determined. Expected inflation shifts the demand and supply curves upward to the extent of the rate of inflation expected, and perceived risk shifts the supply curve upward to the extent of the risk premium demanded for that category of borrower. As implied in the earlier mention of reverse term structures of interest rates, changing expectations of future rates of inflation cause changes in the interest rates. If the current rate of inflation is 8%, and lenders expect it to average 10% over the duration of the loan due to an increase in the rate of inflation, they factor 10% into their supply curve for loanable funds. Conversely, if the current rate of inflation is 12%, and lenders expect it to average 9% over the next five

years because they expect the rate of inflation to decline, they add in only the 9% figure for loans over a five-year duration. It is this expectation of a declining rate of inflation over the medium to longer term that can cause the reverse term structure of interest rates to prevail, if the expected reduction in the rate of inflation more than offsets the premium one would normally expect for tying one’s money up for a longer rather than a shorter period of time.

IV. SUMMARY In this chapter we extended our analysis of consumer and producer behavior to encompass multiperiod situations. As soon as we go beyond the present time period, we find that consumers want to save and producers want to invest. ConSavings, Interest, and Investment

391

sumers save up to the point at which their personal rate of time preference equals the rate of interest available to them. Investors invest up to the point at which the rate of return on investment equals the rate of interest at which they can borrow funds. Other consumers borrow up to the point at which their personal rate of time preference equals the rate of interest. As long as borrowers and investors demand funds, and savers supply funds, there will be a market for funds and an equilibrium interest rate will exist in each market or submarket for funds. Submarkets for funds exist because loans,arefor different periods and for different purposes. This gives rise to the term structure of interest rates and risk premiums in submarkets for investors and borrowers of differing default risk. The interest rate for funds in each market or submarket can be viewed as the aggregate of the average rate of time preference, the premium for risk, and the expected rate of inflation. In the next chapter we address the issue of investment in capital equipment and other projects, under conditions of uncertainty as to the outcome of each investment opportunity. In the real world, of course, we have our expectations of how events will turn out, but there is ‘‘many a slip twixt the cup and the lip,” and the ex post outcome may be quite different from the ex ante, or expected, outcome.

DISCUSSION

392

QUESTIONS

1.

Explain the notion of a consumer’s intertemporal choice in terms of the concept of the marginal rate of substitution. If the consumer is neither a borrower nor a lender, what is his or her MRS?

2.

How does the consumer’s time horizon and expectation of income in future periods influence his or her consumption-saving decision in the current period?

3.

Why would you advise professional athletes and winners of lotteries to save money in the current period? Explain this in terms of the utility they may expect to derive from their income over their lifetimes.

4.

If some people prefer to save in the current period and others prefer to borrow, what guarantees that the amount saved will exactly equal the amount borrowed?

5.

When people save but don’t lend the money they have saved, we call this hoarding. Why is hoarding not a rational practice? Under what circumstances is it utility maximizing to hoard?

6.

Is it rational to both lend and borrow at the same time? For example, many home owners save money at the same time they are paying off the mortgage on their home. Under what circumstances is it utility maximizing?

7.

Justify the negative slope of the demand curve for loanable funds. (Remember that there are two elements to the demand for loanable funds.)

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

8.

Explain the positive slope of the supply of loanable funds curve. If saver’s expectations of the future became pessimistic enough, could this curve bend back at higher interest rates? Explain.

9.

Explain the existence of a multitude of different interest rates existing simultaneously in the economy. Are these at all related to each other? In what way?

10.

Why would you normally expect the term structure of interest rates to be positively related to the duration of the loan. When is it the opposite?

SUGGESTED

REFERENCES

BRIGHAM, E.F., Financial Management Theory and Practice, pp. 17-22. Hinsdale, III: Dryden, 1979. FISHER, I.,

The Theory of Interest. New York: Macmillan, 1930.

HIRSHLEIFER, J., Investment, Interest, and Capital. Englewood Cliffs, N.J.: Prentice-Hall, 1970.

, Price Theory and Applications (2nd ed.), chap. 16. Englewood Cliffs, N.J.: Prentice-Hall, 1980. MANSFIELD, E., Inc., 1979. MILLER, R.L.,

Microeconomics

(3rd ed.), chap. 18. New York: W. W. Norton & Co.,

Intermediate Microeconomics, chap. 6. New York: McGraw-Hill, 1978.

QurrK, J.P., Intermediate Microeconomics, chap. 11. Chicago: Science Research Associates, 1976.

Savings, Interest, and Investment

393

Capital Investment

Under Risk and Uncertainty |. INTRODUCTION In this chapter we consider the investor’s problem of choice among alternative investment opportunities under conditions of risk and uncertainty, as distinct from certainty.

DEFINITION: Risk and uncertainty are situations in which the decision-maker does not have full prior information concerning the outcome of each decision. Instead the investor faces a probability distribution of possible outcomes and must somehow evaluate that probability distribution in terms of its value and its risk. We shall consider the expected value of a probability distribution as a measure of its value and standard deviation of the probability distribution as a measure of its risk. Calculating these two statistics for each investment project allows us to compare and choose among alternate projects. We utilize indifference curve analysis to demonstrate the utility-maximizing choice procedure for the investor, whether risk averter, risk preferer, or risk neutral. When an investment project involves costs and revenues that occur in sub-

sequent time periods as well as in the current period, we must adjust these future profit flows to compare profits (or losses) from each period, in order to obtain a single measure of the investment’s value. We do this by discounting future cash flows back to present-value dollars, so that all cash flows can be compared on the same basis. Since future cash flows are uncertain, we calculate the expected 394

value of the probability distribution of cash flows in each period, and then discount this back to present-value terms to find the expected present value of the future cash flow. Choice among investment projects that have multiperiod profit streams in an uncertain environment can then proceed on the basis of the sum of the expected present value of the profit stream of each investment project. When the projects have differing degrees of risk, the discount factor is adjusted commensurately to allow the investor to compare the expected present values in riskadjusted terms. This analysis allows us to express the firm’s plant-size adjustment decision in terms of its financial advisability. Plant size is adjusted only when the expected present value of the proposed plant exceeds the expected present value of the existing plant.

Il. INVESTMENT

UNDER

RISK AND

UNCERTAINTY

The lack of certainty as to the precise outcome of a future event is due to the lack of complete information about the factors that determine the outcome of that event. For example, if we knew in advance the complete physical and mental condition of every horse in a race, which horses would get off to a good start, what their positions would be after two, four, and six furlongs, and so on, we might be able to predict the outcome of the race with complete accuracy before the event. People spend a lot of money trying to do so, to be sure, but it is the lack of complete information that causes them to be correct in their predictions only some of the time. Where there is less than full information, we say that the individual or the firm is operating under conditions of risk and uncertainty. Certainty, Risk, and Uncertainty DEFINITION: Certainty exists if the outcome of a decision, or a contest of any sort, is known in advance without a shadow of doubt. One speaks of acts or decisions that lead to events, or outcomes. Under conditions of certainty, an act leads to a single

possible event, which is foreseen. For example, if you are standing on the freeway and get hit by a Mack truck, it is certain that you will be killed, given the completely uneven contest between human frailty and mechanical might. Risk and uncertainty are situations in which an act leads to one of several alternative possible outcomes, but the exact outcome is not known in advance. Some people prefer to make a distinction between risk and uncertainty on the following basis: Under risk the probabilities of each of the possible outcomes can be assigned objectively, whereas under uncertainty these probabilities must be assigned on a subjective basis.1 Let us look into this further. EXAMPLE:

Risk is involved when one flips a coin, throws dice, or plays a hand of poker. The probability of flipping a coin and having it land “‘heads” is 1/2, since there are only two possible outcomes (ruling out the coin landing on its edge), and each is equally likely to occur, given an unbiased coin. Similarly, when one 1Frank H. Knight, Risk, Uncertainty and Profit (Boston: Houghton-Mifflin, 1921).

Capital Investment Under Risk and Uncertainty

395

throws two dice, the probability that they will turn up ‘“‘snake eyes,” or any other pair of numbers, is 1/6 x 1/6 = 1/36. The probability of drawing a “royal flush” in poker, or any other combination of cards can likewise be calculated. In each of the illustrations above the probability of each outcome is known a priori. That is, on the basis of known mathematical and physical principles, we can deduce—prior to the act—the proportion of the total number of outcomes that should be attained by each particular outcome. We can confirm this calculation by undertaking a number of trials. Although “heads” might appear three or even four times out of the first four tosses of’a coin, given a sufficiently large number of trials, the proportions will converge upon 1/2 for each of the two possible outcomes. A second class of risk situations is that in which probabilities are assigned a posteriori, or on the basis of past experience under similar circumstances. The business of insurance is based upon this type of risk situation. The possible outcomes are known: The life insured will or will not expire; alternatively, the building insured will or will not be destroyed by fire. Insurance companies keep extensive data on previous policies and claims and other pertinent data; from these they compile actuarial tables, which show the relative incidence of the various outcomes in past situations or trials. On the presumption that a particu-

lar life or a building is similar in all important respects to those of the data base, they are able to form an expectation (or assign a probability) of the chances of that particular life expiring or that building burning.

DEFINITION: A situation of uncertainty, as distinct from risk, is defined as one in which one of two or more events will follow an act, but the precise nature of these events may not be known and the probabilities of their occurring cannot be objectively assigned. That is, not all outcomes may be accurately foreseen, and the probabilities cannot be deduced or based on previous empirical data. Instead, the decision-maker must use intuition, judgment, experience, and whatever information is available to assign the probabilities to the outcomes considered possible in such a situation. Thus the assignment of probabilities in situations of uncertainty proceeds on a subjective basis, rather than the objective basis of risk situations. NOTE:

It is clear that perhaps the great majority of investment decisions are taken in an environment of uncertainty, as distinct from risk. The investor is usually required to estimate, rather than simply calculate, the probabilities of each event occurring. Having made the traditional distinction between risk and uncertainty, we shall for the most part in the following use the terms interchangeably: The fine distinction concerning the objective or subjective assignment of the probabilities should be kept in mind, but in common usage the terms refer simply to situations in which more than one possible outcome follows an act.

The Expected Value of an Investment Opportunity

Under conditions of risk and uncertainty the potential investor looks at an investment opportunity and foresees a probability distribution of outcomes. That is, several different levels of profit (or loss) on the investment are perceived as 396

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

being possible, and each of these is assigned a probability of occurring. How does the investor summarize all this data so that it can be compared with other investment opportunities? Expected value is a concept that allows the probability distribution of possible outcomes to be characterized by a single number, which can then be compared with the expected values of other possible investment projects.

DEFINITION: The expected value of an event is the value of that event multiplied by the probability of that event occurring. Since several events are possible under risk and uncertainty, the expected value of the investment opportunity is the sum of the expected values of all the possible events that may follow the decision to invest in that opportunity. In Table 17-1 we show a hypothetical probability distribution of profit levels that is expected to be possible outcomes of a decision to invest in a particular investment project. The first column shows the possible profit levels, ranging from a loss of $50,000 to a profit of $250,000. Consider these figures as

economic profits or losses, after the payment of all factors of production. The second column shows the probability of each profit (or loss) level, as assigned by the investor contemplating the investment. Thus there is considered to be a 5% chance of losing $50,000, a 10% chance of earning only normal profits, a 15% chance of making $50,000 profits, and so on. Note that the probabilities must total one, since all possible outcomes are included and these outcomes are mu: tually exclusive. TABLE

17-1

The Expected Value of an Investment Opportunity Possible Profit Levels

Probability of Each Occurring

Expected Value of Each Profit Level

($)

(P)

($)

—50,000 ) 50,000 100,000 150,000 200,000 250,000 Totals

.05 10 Kile) .20 25 AMS) .10 1.00

—2,500 ) 7,500 20,000 37,500 30,000 25,000 117,500

The third column in the table is the product of columns one and two. The expected value of each possible outcome is equal to the possible profit (or loss) associated with each outcome, multiplied by the probability of that outcome 2Formally, we define the expected value of a decision as

EV= > R;P; ee where © connotes “‘the sum of”; R; is the return of the i outcome; i = 1, 2, 3,

identifies each

probability of separate possible outcome; n is the total number of possible outcomes; and P; is the the it? outcome occurring. Capital Investment Under Risk and Uncertainty

397

occurring. The sum of the expected values of all the possible outcomes is $117,500. This is the expected value of the decision to invest in this particular investment opportunity. Note that the actual outcome will not be known until after the investment is made and all returns are in. The expected value is ana priori measure of the investment opportunity that allows the probability distribution of outcomes to be summarized as a single number. This expected value is actually a weighted average of the possible profit levels, with each possible outcome weighted by the probability that it will occur. Note that the possible profit levels are a finite Set of points on a continuum. The actual outcome might be, for example, $67,964.45, which does not appear as a possible outcome in Table 17-1. Obviously we must restrict the a priori outcomes to a limited number, in order that the calculation of the expected value is made relatively simple. Otherwise the table would be infinitely long with infinitesimally small prior probabilities for each outcome. For example, the probability of the outcome being exactly $67,964.45 might be somewhere in the vicinity of 0.0000001. Clearly it is more simple, and with insignificant loss of accuracy, to select points on the continuum of possible outcomes, and regard these as the midpoint of a range of possible outcomes, each of which is equally likely to occur. Thus the possible outcome of $50,000 shown in Table 17—1 represents all outcomes

from $25,000.01 to $75,000.00, the average of which is

$50,000. Similarly, the $100,000 possible profit is the midpoint of the range of outcomes from $75,000.01 to $125,000.00, and so on. The extreme points of —$50,000 and $250,000 obviously imply an arbitrary cutoff point for the largest possible loss of —$75,000 and the largest possible profit of $275,000. Since the probabilities at these extremes are relatively low in any case, this does not impose a significant problem. Measuring the Riskiness of an Investment Opportunity

How do we measure the degree of risk and uncertainty involved in an investment opportunity or in any other decision to be taken under conditions involving an a priori probability distribution of outcomes? How can we say whether one investment project is more or less risky than another? Again, a summary measure of risk and uncertainty is very useful for comparing the riskiness of alternate investment projects, just as the expected value measure of the profit outcome is useful as a single-number characterization of the value of the investment opportunity.

DEFINITION: +The degree of risk and uncertainty is measured by the dispersion of possible outcomes around the expected value. If the possible outcomes were clustered tightly around the expected value (or weighted mean) of the outcomes, we >To be completely accurate, and for situations in which the selected point is not the midpoint of the range in which it sits, each selected profit outcome may be regarded as the weighted average of all possible profit outcomes over the range it represents, where each possible profit outcome (for example, $67,964.45) is weighted by the probability of its occurring. Thus the possible loss of $50,000.00 might accurately represent the weighted average of losses ranging from minus infinity dollars to —-$25,000.00, when the probabilities of each loss figure in that range vary from zero for an infinite loss to some positive but very small value at —$25,000.00. These probabilities total 0.05 for all the possible loss outcomes within the range, of course.

398

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

would say that the investment opportunity involved relatively low risk. Alternatively, if the possible outcomes were spread over a wide range on either side ofae expected value, we would say that the investment involved relatively high risk. EXAMPLE:

In Fig. 17—1 we show two alternative investment projects plotted as probability distributions of the possible outcomes. Project A is the same one we examined in Table 17-1, with seven possible outcomes spanning a range of $300,000 (from —$50,000 to $250,000). Project B is another hypothetical investment Opportunity, which is expected to have only four outcomes spread over the range of $50,000 to $200,000. Visual inspection of these probability distributions suggests that project A is more risky than project B, because the possible outcomes of project A are more widely dispersed around the expected value as compared with those of project B.4

FIGURE

17-1

Probability Distributions of Two Alternative Investment Projects Project A

Probability

Project B

Probability

.30 .25

.20 He, 10 05

, 0

NOTE:

50)

9100)

150200.)

250

Profit ($1,000s)

0

50

100

HE

3

150

200

250

Profit

($1,000s)

Statisticians have long had a measure of the dispersion about the mean known as the standard deviation. The standard deviation of a set of numbers represents the average deviation (whether positive or negative) of all those numbers from the mean of those numbers. To obtain this average deviation in absolute terms, 4It is important to note that we are concerned here with what is known in the finance discipline as

business risk—that is, the inherent variability of the firm’s profits due to its uncertain environment.

Finance theorists also speak of financial risk, which is the risk of using debt rather than equity to finance a firm’s operations—insufficient profits could lead to bankruptcy and the ownership of the firm shifting to the debtors. Business risk and financial risk add to corporate risk. Investors’ risk, or

beta risk, is the risk faced by the owner or shareholder of the firm and is concerned with how the price of the firm’s stocks rise and fall in relation to the stock market generally. See, for example, Eugene F. Brigham, Financial Management Theory and Practice, 2nd ed. (Hinsdale, Ill.: The Dryden Press, 1979), chaps. 5, 12, 15.

Capital Investment Under Risk and Uncertainty

399

the deviations from the mean are squared—to eliminate the minus signs of negative deviations and prevent these from offsetting the positive deviations—then summed, and then divided by the number of observations. The resulting value is called the variance of the set of numbers. Taking the square root of the variance—to reverse the initial step of squaring the deviations—gives us the standard deviation of the set of numbers, which can be interpreted as the average absolute deviation of the numbers from the mean of those numbers. We can calculate the standard deviation of a probability distribution with two simple modifications to the procedure outlined above. Note that this procedure implicitly weights all observations equally, whereas this is not likely to be the case with a probability distribution. Accordingly, instead of dividing the sum of squared deviations by the number of observations, we multiply each deviation by its probability of occurring, before these are summed to find the variance. This is an equivalent procedure when all outcomes are equally likely, but when all outcomes have differing probabilities, this procedure correctly weights each outcome. The second change to the procedure is to regard the mean of the observations as the expected value of the possible outcomes.‘ Let us calculate the standard deviations of the probability distributions associated with projects A and B mentioned above. In Table 17—2 we proceed through the steps as indicated. To simplify calculations we express the possible outcomes in thousands of dollars and convert back to dollars later. For project A you can see that the deviation of each outcome from the expected value of the outcomes is squared, weighted by its probability, and then summed to find the variance. The square root of the variance is the standard deviation. The same process is followed for project B. Notice that the standard deviation is substantially greater for project A, at $81,048, as compared with $51,235 for project B, confirming what we observed in Fig. 17-1. Thus we can say that project A is more risky than project B.® 5If there are n outcomes that are equally probable, the probability of each outcome will be 1/n. Thus dividing by n is equivalent to multiplying by the probability of each outcome. Thus the formula for the standard deviation of a simple set of numbers is

> %) x) c=

n

Where o is the conventional notation for standard deviation; £ means summation of the series from i=1,2,3,...,n where n is the number of observations,X; is the i” observation, andX is the simple arithmetic mean of these observations. The modified formula for the standard deviation of a probability distribution is

o=\> Ki -EVyP, Where EV is the expected value (or weighted mean of the possible outcomes), andP, is the probability of each outcome occurring. 6A common conception of risk is the chance of making losses. Many people would immediately classify project A as more risky than project B, simply because with project A we might lose $50,000. This attitude is really loss aversion and not any measure of risk, since it takes no account of the variability of the possible outcomes and the probabilities of their occurring.

400

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

TABLE

17-2

Calculation of the Standard Deviation for Two Investment Projects a

Possible Outcome

EV

Deviation

PROJECT A Squared eviation

} ee

($1,000s)

($1,000s)

($1,000s)

($1,000s)

Probability

Deviation

—50 0 50 100 150 200 250

Pagz5 LA7e5 L175 117.5 117.5 117.5 L7e5

—167.5 —-117.5 —67.5 -17.5 8225 82.5 13225

28,056.25 13,806.25 4,556.25 306,25 1,056.25 6,806.25 17,556.25

.05 10 15 720 25 al'5 10

1,402.81 1,380.63 683.44 61.25 264.06 1,020.94 155.03

Standard deviation =\/Variance

Possible Outcome ($1,000s)

(1, 000s)

50 100 150 200

125 25 125 125

= 81.048 or $81,048

PROJECT B Squared Deviation Deviation ($1,000s) ($1,000s) -—75 —25 25 75

5,625 625 625 5,625

Variance

Probability

Weighted Squared Deviation

.20 .30 0) .20

25 ISAs) 187.5 iel25

Variance Standard deviation = \/ Variance

6,568.75

2,625

= 51.235 or $51,235

Risk Aversion, Risk Preference, and Risk Neutrality

DEFINITION: Risk aversion is defined as the derivation of disutility due to uncertainty. That is, the dispersion of possible outcomes of an act cause the risk averter to experience psychic dissatisfaction, or disutility. In general we expect investors to be risk averse: That is, investors do not like risk per se and are only prepared to undertake risky situations if adequately compensated for bearing the risk involved. Risk averters regard risk as a ‘“‘bad’”’—an item which gives them disutility—as compared with a ‘“‘good’’—one which gives them utility. Risk averters only accept risk if they at the same time expect to gain sufficient utility from the return (or profits) from the proposed investment project. The greater the risk perceived, the greater the return the investor requires to offset that risk. Conversely, investors are willing to trade-off return for reduced risk. They may accept lower expected returns if these are associated with lower degrees of riskiness. This risk-return trade-off is the characteristic of a risk averter: He or she is prepared to take risks, but only if there is sufficient compensation expected. We can depict a risk averter’s preference structure between risk and return in terms of indifference curve analysis. Since a risk averter gains utility from Capital Investment Under Risk and Uncertainty

401

returns (or profits) and disutility from risk, the indifference curves are not the conventional, negatively sloping, convex-to-the-origin curves we have dealt with earlier. Rather they are positively sloping to reflect the fact that risk is a “bad” and that it generates disutility rather than utility. In Fig. 17-2 we show risk—measured by the standard deviation of possible profit levels—on the horizontal axis and returns—measured by the expected value of the possible profit levels—on the vertical axis. Three arbitrarily chosen indifference curves are shown as], tol. The direction of preference is upward and to the left—that is, I, is preferred to I,, and is preferred to I;. Noticé‘that the indifference curves are concave from above, just as in the regular case, reflecting diminishing marginal utility of expected profits and increasing marginal disutility of risk. FIGURE

17-2

Indifference Curves for a Risk Averter in Risk-Return Space

Expected value of profits

($)

Risk (o)

Several points are shown in Fig. 17—2. Point A represents an investment project with risk o, and return E,. The investor is indifferent between this project and the zero risk, zero return situation represented by the origin. You can see that this investor requires E, dollars of expected return to compensate for bearing o» dollars of standard deviation or risk. Note that project A is preferred to project B, which has the same expected value but higher risk, o3. Similarly, project C is preferred to both A and B, since it has the same expected value but lower risk, o;. Finally, project D is regarded as being equally desirable to project B, but is inferior both to A and C. Project D has the same risk as A, but has less expected profits and has both more risk and less return as compared with project C.

The slope of the indifference curves between risk and return indicate the individual’s degree of risk aversion. We know that the slope of an indifference curve represents the individual’s marginal rate of substitution (MRS) between the two goods under examination. In the present case, one is a “good” and the other is a

402

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

“bad,” but the slope of the indifference curve still shows the rate at which the individual is just willing (without losing or gaining utility) to substitute one variable for the other. In Fig. 17—2 the individual regards investment projects D and B as equally desirable, and his MRS of return for risk over the intervening range is equal to the ratio AD/AB. Given point D as a starting place, the investor is indifferent toward project B, which has both extra risk (03; — o,) and extra profit (E, — E,). To be more precise, the investor’s MRS is the amount of expected return he or she requires before accepting an extra unit of risk. You can see that the individual’s MRS between risk and return is positive and increases as the level of risk and return increase, due to the diminishing marginal utility of expected profits and the increasing marginal disutility of risk. Different investors have different degrees of risk aversion. Graphically this is reflected in steeper or flatter indifference curves in risk-return space. In Fig. 17-3 we show an investor with a relatively high degree of risk aversion, contrasted with an investor whose preferences indicate a relatively low degree of risk aversion. Points A and D are the same on both graphs. Project D is inferior to project A, because for the same expected return, Eo, it has the larger risk, o,. In both cases the investor would only accept the risk level co, if this is accompanied by an expected profit larger than that of project A. How much additional expected profit would it take to make each investor indifferent between project A and a project containing co, units of risk? The more risk-averse investor in the left-hand graph requires DB dollars in order to remain at the same level of utility, and thus has a relatively high MRS of return for risk, measured by the ratio BD/AD. The less risk-averse investor on the right-hand side requires only the considerably smaller amount of extra expected profit, DC dollars, for the extra risk o, — Go, and thus exhibits a relatively low MRS of return for risk measured by the ratio CD/AD. FIGURE

17-3

Different Degrees of Risk Aversion

Relatively high degree (high MRS)

EV of profit

Relatively low degree (low MRS)

($)

Risk (o)

O

Risk (c)

Capital Investment Under Risk and Uncertainty

403

ve Risk Preference and Risk Neutrality. Risk preference and risk neutrality are not common among investors. Consumers, on the other hand, may show risk preference or neutrality in such situations as gambling, sporting, and recreational activities. Risk preference means that risk is viewed as a utility-producing good, and so the individual’s indifference curves are negatively sloping as

in the left-hand graph of Fig. 17-4. Such an individual is prepared to give up expected profits for a larger amount of risk. For example, a gambler might prefer a game in which the risk is greater (odds are poorer) and the expected value of gains is lower, over a safer bet on another game in which the expected value is somewhat higher.

FIGURE

17-4

Risk Preference and Risk Neutrality

Return

Risk Preference

Risk Neutrality

Return

Risk

(0)

Risk

Risk neutrality means that the individual is completely indifferent to risk, receiving neither utility nor disutility from risk regardless of the amount of risk involved. Such an individual’s indifference curves would be horizontal, as in the right-hand graph of Fig. 17-4. The arrow shows the direction of preference— more expected profit is preferred to less, regardless of the risk. Consider an athlete who desperately wants to win the season final. This individual will do whatever is necessary to help his team score or prevent the opposition from scoring. Thus hockey players block shots on goal with their faces and bodies, football players make suicidal plays that could easily result in broken bones, and racing drivers attempt that final pass on the last turn before the checkered flag. Choice among Alternative Investment Opportunities

We may now put several of the components mentioned above together and make some statements and predictions about investor’s preferences between and

among alternative investment projects. In Fig. 17-5 we resurrect investment projects A and B from Table 17—2 and add a hypothetical project C. Project A has 404

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

expected value $117,500 with standard deviation $81,048. Project B has ex-

pected value $125,000 with standard deviation $51,235. Project C is assumed to have expected value $150,000 with standard deviation $70,000. The indifference curves I, I,;, and I, represent a particular investor’s preferences between

risk and return. This risk averter prefers C to B to A. Project A is clearly inferior to B, since it has both more risk and less expected profit than B. Project C is preferred to B, despite C’s greater risk, because the investor’s trade-off rate (MRS) of return for risk is sufficiently low, so that he or she is prepared to take on more risk than the extra risk involved in project C ($70,000 — $51,235 = $18,765) for the additional expected profit of project C ($150,000 — $125,000 = $25,000). FIGURE

17-5

Investors’ Preferences among Alternative Investment Opportunities

Expected value of profits

($1,000)

100

Risk (c) ($,1000)

Notice an investor with a higher MRS of return for risk would prefer to play it a little safer and select project B. The indifference curves I’ and I” represent a more risk-averse investor who is not prepared to take on the extra $18,765 in standard deviation for the extra $25,000 in expected profits. Thus the risk averter’s choice among alternative investment opportunities depends on his or her degree of risk aversion. The higher the degree of risk aversion, the lower the amount of risk the investor will bear for an additional dollar of expected profits, and the more likely he or she is to prefer less risky investment alternatives. Conversely the less risk-averse investor is more likely to prefer the higher return investment projects.” 7 The coefficient of variation, which is the ratio of standard deviation to the mean (or expected value), has been suggested as a means of selecting among alternative investment projects. In effect it gives the amount of dispersion per dollar of expected profit, and it is said to be a means of adjusting for risk. As an investment criterion it is a crude tool, however, since it does not allow for differences in the degree of risk aversion. Capital Investment Under Risk and Uncertainty

405

We turn now to the concept of the present value of money, which must be considered whenever the proceeds of an investment project are expected to extend beyond the present period.

EXPECTED PRESENT VALUE ANALYSIS In the preceeding chapter we saw, in the context of intertemporal choice, that a dollar today is worth more than a dollar tomorrow, since today’s dollar can be deposited in a bank or used to buy an interest-bearing security and grow to become a dollar plus the interest earned on that dollar. It follows that an investor is not indifferent between a dollar received today and a dollar received later: The dollar has a present value greater than its future value. If the investor expects to receive profits in the present and in several future periods from a particular investment project, he or she should give different weights to those profits, depending upon when they are received. Not until they are received can they be deposited in a bank or reinvested to earn interest or a rate of return in another investment opportunity.

In this section we discuss the concepts of present and future values, compounding and discounting, and adjusting for differing degrees of risk. This allows us to broaden the preceding analysis of investor’s choice among alternative investment projects to include all irivestment opportunities, rather than just the simple case in which all profits are made in the present period. Present Value and Future Value

DEFINITION:

The future value in one year of $1 presently held is equal to $1 plus the

annual rate of interest times $1. That is,

FV = PV(1 +r)

where FV denotes future value, PV denotes present value, and r is the rate of interest available. For example, when the interest rate is 10%, r = 0.1, and the future value of $1 is

FV = $1(1 + 0.1) = $1.10 Now suppose we leave this money in the bank for a second year, also at 10% interest. The future value would be

FV = $1.10 (1 + 0.1) = $1.21 If the money remained a third year, we would have

FV = $1.21 (1 + 0.1) = $1.331 and so on for future years. Note that the principal sum each year is simply mul406

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

tiplied by (1 +r). In effect, the dollar is initially multiplied by (1 +r), then the resulting product is multiplied by (1 + r), and then the product of that is multiplied by (1 + r) again. Thus for the three-year deposit

FV= PV(14+r)(1 tr)(1 +7) which simplifies to

FV = PV(1 +1r)3 Generalizing for any number of periods into the future, we have

FV = PV(1 +r)!

(17=1)

where t = 1, 2, 3,..., n represents the number of years into the future that the principal sum plus interest will be returned.

EXAMPLE:

Suppose we lend $2,500 for a period of five years at 812% interest. What is the future value of the presently held $2,500? Inserting these figures into Eq. (17—1) we find

FV = $2,500 (1 + 0.085)* = $2,500 (1.085)? = $2,500 (1.50366) = $3,759.15 Thus $2,500 saved at 812% for five years will return the saver $3,759.15 at the

end of the five-year period. The above process is known as compounding the principle sum plus annual interest over the period of the loan. It tells us that $2,500 held today is worth $3,759.15 in five years, if we can obtain 812% interest compounded annually. The compound factor that we use to multiply the $2,500 to obtain $3,759.15 is 1.50366. This compound factor effectively says that $1.00 today is worth $1.50366 in five years, if the interest rate is 812%. Now let us do it in the reverse direction. The present value of a future value can be found by manipulating Eq. (17-1). Dividing both sides by (1 + r)'‘, we find

FV ave ape mr

(=n)

Although we already know the answer, let us compute the present value of $3,759.15 available in five years during which the available interest rate is 812%.

PV

eee)

~ (1 + 0.085)° m3. 2901.5

giselh50366 = $2,500.00 What we have just done is to discount $3,759.15 (future value) back to Capital Investment Under Risk and Uncertainty

407

present-value terms, and to demonstrate that the discounting process is simply the inverse of the compounding process. Whereas future value equals present value multiplied by the compound factor, present value equals future value divided by the compound factor. Alternatively, let us call the reciprocal of the compound factor the discount factor; equivalently then, present value is equal to future value multiplied by the discount factor. The reciprocal of 1.50366 is 0.66504, which is the discount factor when the interest rate is 842%. ($3,759.15 multiplied by 0.66504 equals $2,500.00.) ™N

\

The Opportunity Discount Rate

DEFINITION: The opportunity discount rate is the rate of interest or return the investor could earn in his or her best alternative use of the funds at the same level of risk. Note that we add the caveat that the alternative investment must involve the same level of risk or uncertainty, since many other investment opportunities will be more or less risky or uncertain, and are thus not strictly comparable with the present proposal. The investor must choose the rate of discount quite carefully, since using a wrong discount factor could lead to a bad investment decision when the time profiles of future profit streams associated with alternative investment projects differ markedly. How do we ascertain whether the alternative investment or savings opportunities are of similar riskiness or not? We would calculate the standard deviation of the possible profits or returns associated with alternative opportunities. One of these alternative opportunities would be expected to have a similar value of its standard deviation as compared with the investment project under consideration. The appropriate discount rate for the investment project is thus the rate of interest (or rate of return on investment) available on the alternative savings (or investment) opportunity that has the same or similar value for the standard deviation of its expected returns, as compared with the project under consideration. EXAMPLE:

‘To illustrate, suppose that a firm intends to invest $10,000 in an expansion of its facilities, but might otherwise invest the funds in a bond issue which is perceived to have a similar dispersion of possible outcomes, and which would pay 12% interest compounded annually. The opportunity discount rate to be used when evaluating the future returns from the project under consideration is therefore 12%. It is important to see that the higher the opportunity rate of interest (or opportunity discount rate), and the longer the time period, the lower the discount factor. In Table 17-3 we show the discount factors for several different opportunity interest rates and several different periods of time. Each discount factor is calculated using the expression 1/(1 + r)‘ and we can calculate the discount factor for any other opportunity interest rate and time period using the same expression. Note that the discount factor is inversely related both to the length of the time period and the opportunity interest rate. Discount factors effectively tell us the value of $1.00 at the end of a given period for any opportunity

408

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

interest rate. Thus at 10% opportunity interest rate, $1.00 is worth $0.9091 if received in one year; $0.6209 if received in five years; and $0.0923 if received after twenty-five years, for example. Similarly, with a 20% opportunity interest rate, $1.00 is worth only $0.4019 if received five years from now; $0.0649 in fifteen years; and only a fraction over one cent if received in twenty-five years! TABLE

17-3

Discount Factors for Several Different Opportunity Interest Rates and Time Periods i

Time

Opportunity Interest Rate (%)

Period

(years hence)

fe) 1 2 S 4 5 10 15 20 25

EXAMPLE:

5

10

15

20

1.0000 0.9524 0.9070 0.8638 0.8227 0.7835 0.6139 0.4810 0.3769 0.2953

1.0000 0.9091 0.8264 07513 0.6830 0.6209 0.3855 0.2394 0.1486 0.0923

1.0000 0.8696 0.7561 0.6575 0.5718 0.4972 0.2472 0.1229 0.0611 0.0304

1.0000 0.8333 0.6944 0.5787 0.4823 0.4019 0.1615 0.0649 0.0261 0.0105

This should make us think about what inflation is doing to the present value of people’s life insurance policies and retirement savings plans, for example. It might sound like a lot of money to receive $100,000 in forty-five years time. But if the average rate of inflation is, let us say, only 7% from now until then, and the person’s (real) rate of time preference is 3%, the present value of that $100,000 in 45 years time at a 10% opportunity (risk-free) interest rate, is only $1,371.92! What can $1,371.92 buy today? Exactly what one might expect $100,000 to buy in 45 years time.

Choice among Investments with Multiperiod Profit Streams

Let us now apply all the foregoing to a relatively simple example in which an investor has the choice of two alternative investment opportunities, each of which has an uncertain stream of future profits. When comparing two or more investment opportunities, a different discount rate may be required for each project under consideration. Since the discount rate is chosen by reference to the riskiness of the project, if the projects have different degrees of riskiness (that is, significantly different standard deviations), then higher discount rates are applied to the more risky projects to reflect the opportunity being foregone to invest the funds elsewhere at a higher rate of return. Let us suppose project A has a standard deviation of expected outcomes similar to that of a 12% bond issue, whereas project B has a standard deviation similar to that of a 10% bond issue. Project A should therefore be discounted at 12%, and project B should be discounted at 10%, in order to compare the present value of their expected profit streams on a risk-adjusted basis. Capital Investment Under Risk and Uncertainty

409

In Table 17—4 we show the expected value of the profits from project A and project B in each year over the five-year life of the two projects. Underlying each expected value of profits is a probability distribution of profits in each year. We assume that both projects cost $100,000 initially, but have differing profit streams over the next five years. The discount factors shown for each year of each project are calculated using 1/(1 + r)‘ where r is the opportunity interest rate (presumed to be 12% for project A and 10% for project B). Multiplying the expected profits by the discount factor, we find the expected present value (EPV) of profits for each year. Summing these we fihid the EPV of each project as a whole, and note that project B has the significantly higher EPV of its profit stream. TABLE

17-4

Expected Present Value Analysis of Alternative Investment Projects PROJECT Year

Expected Value of Profits ($)

@) 1 2 3 4 5

—100,000 20,000 50,000 70,000 40,000 10,000

,

A

Discount Factor (at 12%)

Expected Present Value

1.0000 8929 .7972 7118 .6355 5674

—100,000 17,858 39,860 49,826 25,420 5,674 $38,638

— EPV

PROJECT

B

Year

Expected Value of Profits ($)

Discount Factor (at 10%)

Expected Present Value

) 1 2 3 4

—100,000 10,000 40,000 70,000 50,000

1.0000 .9091 8264 .7513 .6830

— 100,000 9,091 33,056 52,591 34,150

5

20,000

.6209

12,418

EPV

NOTE:

$41,306

A couple of interesting features are embodied in Table 17-4. Note that the sum of the future profits (in nominal terms) is $190,000 in each case, excluding the initial outlay of $100,000. The time profiles of the profit streams differ, however, with project A recouping $70,000 over the first two years and project B recouping only $50,000. After the third year, project A’s profits fall off at a faster rate *For simplicity we assume that any scrap value at the end of five years is realized and added into the expected profit calculation. Also we abstract from tax considerations, which should also be considered, since allowances for depreciation against revenues give rise to an opportunity revenue of tax not paid, thereby augmenting the net cash flow in each period. These issues are considered in detail in courses on capital budgeting. See H. Bierman, Jr. and S. Smidt, The Capital Budgeting Decision, 5th ed. (New York: Macmillan, Inc., 1980), chap. 7.

410

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

than project B’s. If both projects had been discounted at the same rate, project A would win every time, since more of its profits are received earlier. Using the 10% discount factors on project A, we find the EPV = $45 ,622—substantially ahead of B’s $41,306. Using the 12% discount factors on project B we find the EPV = $33,766—substantially below A’s $38,638. This demonstrates the differ-

ence that different time profiles have on the EPV calculation. It also illustrates the importance of adjusting for risk in the choice of the discount factor: At equal discount rates project A promises the higher EPV, but when the greater riskiness of A is adjusted for by the use of the appropriate (opportunity) discount rate, project B is superior.?

The Firm’s Long Run Plant-size Adjustment Decision (Reprise) We are now in a position to re-examine the firm’s decision to invest in a larger or

smaller plant size, armed with the concept of expected present value. The firm should invest in the new plant if the EPV of the profit stream with the new plant exceeds the EPV of the profit stream associated with continuing to operate its present plant. Thus, based on the probability distribution of profits associated with each plant (the existing and the proposed plant), the firm must calculate the expected value of these profits in each of the future years up to its time horizon (the end of its planning period). It then multiplies each of these by the appropriate discount factor and totals the products to find the EPV of each plant. If the EPV of the existing plant is higher than the EPV of the contemplated plant, it is not yet time to change plant size. Later, as the existing plant requires progressively larger maintenance expenditures, and as newly available plants incorporate more and more technological improvements, the balance will swing in favor of the new plant, and the decision will finally be taken.

Another factor influencing this decision in the real world is the amortization of the existing plant’s capital cost over several years. Under existing taxation regulations, firms are constrained to a particular rate of depreciation of capital costs against operating revenues. Since charging depreciation against revenues gives rise to an opportunity revenue in the form of tax not paid out, the firm may be motivated to operate the existing plant another year or two until the tax savings are outweighed by the operating economies of the new plant.

IV. SUMMARY In this chapter we considered the firm’s investment decision under conditions of risk and uncertainty. In these circumstances the future profits from an investment decision are not known in advance, and investors estimate probability dis°To be complete we should calculate the standard deviations for each project, plot these against EPV in the investor’s risk-return space, and superimpose the investor’s indifference curves over the points representing the two projects. The investor selects the project allowing the highest level of utility. Calculating the standard deviations is the onerous part. For each year there is a probability distribution of possible profit levels. Suppose there are only five possible profit levels for each of the five years. This means there are 5° = 3,125 possible combinations of profits after five years, each with a miniscule probability of occurring. Calculation of the standard deviation would then proceed on the same basis as in Table 17-2. The previous method of adjusting for risk as perceived by the investor is much more simple. Capital Investment Under Risk and Uncertainty

411

tributions of the possible profit outcomes. A measure of each investment opportunity is the expected value of profits—the sum of the possible profit levels, each weighted by its probability of occurring. A measure of the risk and uncertainty associated with each investment opportunity is the standard deviation of profit outcomes, which is a statistical measure of the dispersion of possible outcomes from the expected value. Individuals may regard risk as a “‘good” or a “bad,” or they may be indifferent toward it. Accordingly we classify individuals as risk preferers, risk averters, or risk indifferents. We expect most investors to be risk averse, and note that the degree ofrisk aversion dictates the choice among alternative investment opportunities.

When investment projects have profits streams extending beyond the present period, we must discount all future profits back to present-value equivalents, in order to properly enumerate and compare alternative investment opportunities. Present-value dollars serve as a common denominator and allow comparability among investment projects, notwithstanding that these commonly have different lives and different time profiles of profit streams over their lives. The appropriate discount rate is the opportunity interest rate, which is the interest rate or rate of return available in the next best savings or investment opportunity of similar riskiness. Using different discount rates for investments of different riskiness allows the investor to adjust for risk and to choose among available investment projects on the basis of the highest expected present value.

DISCUSSION

QUESTIONS

1.

Distinguish among certainty, risk, and uncertainty on the basis of the number of possible events that may follow an act and the assignment of probabilities to each event.

2.

The expected value of a probability distribution is a measure of central tendency similar to the arithmetic mean, except that it weights all expected outcomes appropriately. Explain.

3.

Risk is measured by the dispersion of outcomes on both sides of the mean or expected value. Surely deviations above the mean or expected value would be welcomed. Why are these deviations included in the calculation of a measure of risk?

4.

Define risk aversion. Does a risk averter refuse to take risks? Will a risk

averter ever select the more risky alternative? Explain.

412

5.

Explain why a risk preferer might prefer a high-risk, low-stakes gamble to a low-risk, high-stakes gamble. Are you arisk averter, a risk preferer, or risk indifferent? How do you know?

6.

Demonstrate that the investor’s degree of risk aversion (or preference) is an important element in determining his or her choice among investment alternatives.

FACTOR MARKETS: THE INTERACTION OF PRODUCERS AND RESOURCE OWNERS

7.

Under what circumstances does an investment project with a larger nominal value of its future profit stream, as compared with another project, have a smaller present value of that profit stream? (Note: There are two separate circumstances and the combination of these two.)

8.

What determines the level of the opportunity discount rate to be applied to the future profit stream of an investment project? If it is impossible to obtain the data required, how would you proceed in practice?

9.

Why is it impractical (without the use of a computer) to calculate the standard deviation of the expected present value of a multiperiod profit stream? Given that this could be computed, how would you proceed to make the optimal choice among alternative investment projects? Does the adjustment for risk by differing discount rates necessarily give you the same answer?

10.

Inearlier chapters we concluded that the firm would adjust its plant size in the long run if a lower cost plant was available. In this chapter we have examined the factors underlying the timing of the plant-size adjustment decision. Explain.

SUGGESTED

REFERENCES

BAUMOL, W.J., Economic Theory and Operations Analysis (4th ed.), chaps. 18, 19, 25. Englewood Cliffs, N.J.: Prentice-Hall, 1977.

BIERMAN, H. Jr., and S. SMipt, Macmillan, 1980.

The Capital Budgeting Decision (5th ed.). New York:

BRIGHAM, E.F., Financial Management Theory and Practice, (2nd ed.), chaps. 5, 12, 15. Hinsdale, Il].: Dryden, 1979. DEAN, G., and A. Hatter,

Decisions under Uncertainty. Cincinnati, Ohio: South-West-

ern 971,

FRIEDMAN, M., and L.J.SavaGE, ‘The Utility Analysis of Choices Involving Risk,” Journal of Political Economy, 56 (Aug. 1948), 279-304.

HIRSHLEIFER, J., “Investment Decisions under Uncertainty: Choice-Theoretic proaches,”’ Quarterly Journal of Economics, 79 (Nov. 1965), 509-36.

Ap-

Horow!7z, I., Decision Making and the Theory of the Firm. New York: Holt, Rinehart & Winston, 1970.

Knicut, F.H.,

Risk, Uncertainty and Profit. Boston: Houghton-Mifflin, 1921.

RairFA, H., Decision Analysis: Introductory Lectures on Choices under Uncertainty. Reading, Mass.: Addison-Wesley, 1970.

Capital Investment Under Risk and Uncertainty

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General Equilibrium and Social Welfare

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MR = MC). Since P = MC is necessary for MRT,, = MRS,,, we cannot have general equilibrium or optimal economic efficiency as long as all markets are not purely competitive.

NOTE:

Although the absence of pure competition in all markets removes the possibility of a general equilibrium situation actually existing, this does not mean it is not worthwhile to study the concept of general equilibrium. The model of general equilibrium, like the model of pure competition it is based on, is a simplistic

model useful mostly for pedagogical purposes. It allows us to see how the main players in the microeconomic system interact with each other, and to deduce the conditions necessary to get the absolute maximum out of society’s limited reGeneral Equilibrium Analysis

437

sources. In discovering these intricacies, we expand our analytical capacity, and we are better equipped, having acquired the necessary methodological tools along the way, to solve problems which arise in the more complex real world.

V. SUMMARY In this chapter we drew together the consumption, production, and distribution theory of Chaps. 2, 5, and 14, along with the theory of the purely competitive firm from Chap. 9, to consider the notion of general equilibrium. General equilibrium means that all markets—product and factor markets—are simultaneously in harmony with each other. This requires three conditions to prevail. First, the marginal rate of substitution between any pair of products must be the same for all consumers. Second, the marginal rate of technical substitution between any pair of resources must be the same for all producers. And finally, the common MRS between any two product markets must equal the producers’ common marginal rate of transformation between those two products. The existence of pure competition in all markets ensures that these three conditions can be attained and that a situation of general equilibrium prevails. Using the Edgeworth-Bowley box diagram, we demonstrated the benefits of exchange in both consumption and production. Consumers are able to attain higher indifference curves by exchanging products until their marginal rates of substitution between any pair of products are equalized. Producers are able to attain higher isoquant curves by exchanging capital for labor, or vice versa, in the factor markets, until they equalize the MRTS between those inputs. Given purely competitive markets, consumers, producers, and suppliers of resources, by independently pursuing their own utility, profit, and income-maximizing objectives, move the economy toward a state of general equilibrium. There is no unique general equilibrium situation. A multiplicity of possible general equilibrium allocations exist. Each one is Pareto-optimal, meaning that no consumer or producer can be made better off without simultaneously causing another to be made worse off. Which one of these situations of general equilibrium is the best one? Are they all equally desirable? If not, which particular general equilibrium arrangement of resources and products should society choose? We examine this issue in the next chapter.

DISCUSSION

438

QUESTIONS

1.

Outline the meaning of general equilibrium. What place does ceteris paribus play in general equilibrium analysis?

2.

Define the contract curve. What determines the final location of two parties on the contract curve? Why is the contract curve a locus of Pareto-optimal allocations?

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

What are the conditions for equilibrium in consumption and exchange? Why are these only attainable if pure competition prevails in the product markets? How do producers in effect exchange capital for labor, and vice versa, in the factor markets, and what induces them to do it? Explain how the production possibilities frontier can be derived from the contract curve in factor-input space. Why is the PPF also called the transformation curve? What assumptions underly the convexity (from above) of the production possibilities frontier? Under what circumstances would the PPF be a straight line? Explain the mechanism by which the consumers’ MRS and the producers’ MRT move toward equality. Although there is a multiplicity of general equilibrium allocations of resources and the associated allocations of products, the initial endowment of resources constrains the actual production of goods to a limited part of the PPF. Explain.

There are three conditions required for general equilibrium to prevail. Why are these conditions not satisfied under oligopoly or monopoly, for example? Is it possible that any of the conditions could be satisfied? 10.

Since pure competition does not prevail in all product and factor markets, the economy is in a continuing state of disequilibrium. If pure competition did prevail, and general equilibrium was possible, any change in an underlying element would cause disequilibrium and a resulting equilibration process. Do you suppose pure competition in all markets would allow the economy to be any more tranquil than it is?

SUGGESTED

REFERENCES

‘Existence of an Equilibrium fora Competitive Economy,” Arrow, K.J.,andG, DeBreu, Econometrica, vol. 22, 1954.

Bator, F.M., ‘The Simple Analytics of Welfare Maximization,” American Economic Review, vol. 47, 1957.

BAUMOL, W.J., Economic Theory and Operations Anaylsis (4th ed.), chap. 21. Englewood Cliffs, N.J.: Prentice-Hall, 1977.

HIRSHLEIFER, J., Price Theory and Applications, (2nd ed.), chap. 7. Englewood Cliffs, N.J.: Prentice-Hall, 1980.

JoHNSON, H.G.,

Two-Sector Model of General Equilibrium. Chicago: Aldine, 1971.

KoopMans, T.C., “Is the Theory of Competitive Equilibrium With It?’ American Economic Review, vol. 64, 1974. General Equilibrium Analysis

439

KUENNE, R.E., The Theory of General Economic Equilibrium. Princeton, N.J.: Princeton University Press, 1967.

MANSFIELD, E., Microeconomics: Theory and Applications (3rd ed.), chap. 15. New York, W. W. Norton & Co., Inc. 1979. Quirk, J.,and R. SAPOSNIK, Introduction to General Equilibrium and Welfare Analysis. New York: McGraw-Hill, 1968.

WEINTRAUB, E.R.,

General Equilibrium Theory. London: Macmillan, 1974. yw

440

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

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Welfare Economics

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1. INTRODUCTION In the preceding chapter we saw that there are multiple possibilities for general equilibrium, given the existence of pure competition in all markets. Leaving aside for the moment the fact that there is not pure competition in all markets, we should consider which of these multiple general equilibrium situations is the optimal one from society’s point of view. More broadly, and recognizing that most markets exhibit monopoly elements that preclude general equilibrium, we can investigate the possibility of maximizing the utilities of all members of society regardless of the market types prevailing. We return to the issue of the failure of the economic system to attain a state of general equilibrium, and hence maximum economic efficiency, in the next chapter. DEFINITION: Welfare economics is concerned with the improvement of the welfare of society. The word welfare in this context does not refer to the income-support programs available to the very poor and chronically unemployed people in our society. Welfare is used here in the traditional sense of well-being. We are concerned with the overall well-being, or utility levels, of the members of a society. Naturally, economists want to see the welfare of society, or social welfare, maximized. Which combination of goods and services from the production possibilities frontier and which underlying arrangement of the factors of production should the members of society choose, in order to maximize social welfare? We 441

examine this problem first in a simplistic one-person case, and we then extend the analysis to two persons and finally to an entire society of persons. Interpersonal comparisons of utility are necessary for the construction of a social-welfare function. Our inability to make these interpersonal comparisons is the main stumbling block in the pursuit of maximum social welfare. In order for our elected representatives to move society toward what they believe is a better state of social welfare, they must make value judgments. The value judgments underlying government policy necessarily have an impact upon the distribution of income among members of society. We consider the ‘‘theory of the second best,” which states that in the absence of pure competition in all markets, it may not be an improvement to convert some markets to pure competition. Finally, we examine several criteria for evaluating proposed changes in the economic system, in order that we might determine whether these changes lead to an improvement in social welfare.

Il. MAXIMIZATION OF SOCIAL WELFARE The One-consumer, or Dictator, Case

EXAMPLE:

Suppose that there is only one person in the economy, and therefore that person’s taste and preference pattern dictates the combination of goods and services produced with the economy’s limited resources. This could be Robinson Crusoe (before he met Friday), living alone on an island that provides the resources for the production of goods and services. Alternatively, the one-person case could be a dictator who imposes his preferences on the society that he rules. One might tentatively offer as an example the Shah of Iran, who apparently wanted to lead his country to material well-being by a conscious policy of Westernization. When the Shah was ousted in 1979, the new ruler, Ayatollah Khomeini, essen-

tially reversed the trend, leading the Iranian people’s tastes and preferences back to comply with the traditional Islamic value system. For the case of a single consumer, or a dictator, we simply superimpose that person’s indifference map over the production possibilities frontier to find the combination of the two products that allows the consumer to attain the highest indifference curve. We show this in Fig. 19-1. The single consumer, or dictator, chooses the combination of products represented by Xy and Yo, since this allows attainment of the highest possible indifference curve, Iz. Note that all three conditions for general equilibrium are fulfilled. The MRS,, for all consumers is the same, since there is only one consumer. The MRTS,, is equal for both the producers of X and Y, since the combination Xo, Y) is on the PPF, which in turn is derived from the contract curve in the production sector. Finally, the MRS,, = MRT,,, since the slope of the consumer’s indifference curve I, is the same as the slope of the PPF at point M, the chosen combination. The Utilities Possibilities Frontier

Now suppose that a second person enters the decision-making process to help decide on the social-welfare-maximizing combination of goods and services for society. This is the Mr. A and Ms. B situation we introduced in Chap. 18: Each 442

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

FIGURE

19-1

Maximization of Social Welfare: The Single-Consumer Case

one’s preference structure must be considered to find the combination of products from the PPF that maximizes their joint, or social, welfare. Alternatively, we might suppose that Robinson Crusoe sees a strange footprint in the sand, finds Friday, and invites him to join in the decision-making process. (Crusoe was so lonely by this time that he originated the expression ‘‘Thank God it’s Friday!’’) DEFINITION: To consider the preferences of two persons simultaneously, we must construct a curve knownas the utility possibilities frontier (UPF). The UPF is a locus of the combinations of the two persons’ utilities which satisfies the three conditions for general equilibrium. It is derived from the Edgeworth-Bowley box diagrams in the consumption sector, just as the PPF is derived in the production sector. To understand the derivation of the UPF, consider Fig. 19—2 in which three of the myriad possible general equilibrium situations are shown. The line stretching from Y; to X; is the PPF. Three points on the PPF are identified as 0,, 04, and 0%. These represent combinations of product X and Y that satisfy the Pareto-optimality condition in production (MRTSx, is the same for both producers). Three Edgeworth-Bowley box diagrams are shown: 0, is Mr. A’s origin for all three, and Ms. B’s origin shifts from 0) to 0; to 0;, depending on the combination of X and Y actually produced. Point G on the contract curve 0,0, is a general equilibrium situation, since A’s and B’s indifference curves are tangent, and their common MRS,, equals the MRT,, given by the tangent to the PPF. Looking now at the second Edgeworth-Bowley box with the contract curve 0,0/, point H is a general equilibrium situation, since the common MRS,, at point H is equal to the MRT,, at point 0;. For the third situation, point J on contract curve 0,04 is a general equilibrium allocation of resources and products, since the three conditions are again satisfied. Welfare Economics

443

FIGURE

19-2

Deriving the Utility Possibilities Frontier

Note that we can show Mr. A’s indifference curves, Ao, Ai, and A, as com-

mon to all three production possibilities. Mr. A’s curves are in product space, his origin does not move as the actual production situation changes, and thus we can depict a single set of indifference curves for A that allow comparison of the three general equilibrium situations from A’s point of view. Thus A prefers the situation atJto that at H, and prefers H to G. Mr. A can therefore rank the

three general equilibrium situations shown, in terms of the utility he expects to derive from the combination of products he would consume. It follows that he could rank all the general equilibrium situations that are associated with all the output combinations shown on the PPF. We turn now to Ms. B’s side of the social-welfare- maximization decision. Her indifference curves, B, B’, and B” shown in Fig. 19—2 are not comparable,

since they each relate to a different origin (0,,0,, and 0%, respectively). In order for B’s indifference curves to be comparable, they must all relate to the same point of origin. A way to do this would be to switch A and B, letting B have the lower left-hand corner of the Edgeworth-Bowley box, and A the upper righthand corner. Then we can see Ms. B’s ranking of the three general equilibrium situations shown in Fig. 19—2 and can rank any other general equilibrium situations in the same way. I will presume that you can follow the logic of this without illustrating it diagrammatically. It would be much like Fig. 19—2, except that point G would be much higher in the first box, being relatively distant from B’s origin, and so on. Now lets bring A and B together. Each has ranked all the general equilibrium situations in terms of his or her expected utility from each situation. The utility possibilities frontier is the locus of the pairs of utilities associated with each general equilibrium situation. In Fig. 19-3 we show the UPF that is derived from Fig. 19-2. The points G, H, andJ in utility space in Fig. 19-3 relate to the 4a4

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

FIGURE

19-3

The Utility Possibilities Frontier

B’s Utility

(U,)

A's Utility

(U,)

same points shown in Fig. 19-2 in product space. Point G represents relatively low utility for Mr. A, whereas it simultaneously affords Ms. B relatively high utility. (Note from Fig. 19—2 that Ms. B has the greater share of both products at point G.) Point H has Mr. A better off, whereas Ms. B is worse off as compared with point G. Similarly, point Jhas Mr. A even better off, and Ms. B even worse off, as compared with the other two points. Which point on the utility possibilities frontier is optimal? Which combination of A’s and B’s utilities maximizes social welfare? To answer this we must postulate the existence of a social-welfare function. The Social-Welfare Function

DEFINITION: The social-welfare function expresses society’s welfare as a function of the utilities of the constituents of that society. In the simple case of Mr. A and Ms. B, the social-welfare function (SWF) can be defined in general terms as some function of A’s and B’s utilities. That is

SWF = f(U,, U,) The social-welfare function would therefore rank all combinations of U, and U, and show which combinations of U, and U, society as a whole prefers to other combinations of U, and U,, and which combinations it considers equal to

each other. The SWF therefore gives rise to social or community indifference curves, each one being the locus of combinations of U, and U, that society regards as equivalent to each other. The usual assumptions of indifference curves

apply: Higher community indifference curves are preferred to lower community indifference curves; they are presumed to have negative slope throughout; they Welfare Economics

445

are convex to the origin; and they neither cross nor intersect. A set of community indifference curves is shown in Fig. 19-4. FIGURE

19-4

Community Indifference Curves

Community indifference curve Cy shows two explicit points that society (Mr. A and Ms. B) regard as being equivalent. At point L, Ms. B enjoys utility of B,, and Mr. A receives only Ay units of utility. Suppose Ms. B says she is very happy and Mr. A says he is miserable. At point M the situation is about the opposite—A receives A, units of utility and pronounces himself very happy and B receives only By units and says she is miserable. Considering both situations, let us suppose they agree that their total utility (social welfare) is the same at points L and M, and hence these points are on the same community indifference curve. Other points on the same curve lie to the right of M (where A progresses through ecstasy to euphoria, while B moves through melancholia to purgatory) and to the left of L (where the opposite situations are experienced by each party). Points like N on indifference curve C, and P on indifference curve C, are unambiguously preferred to points L and M on curve Co, since at least one party is better off and neither party is worse off. There are other points on C, and C, where either A or B would be substantially worse off, while the other would be better off. These points are, nevertheless, considered by Mr. A and Ms. B to reflect the same total (social) welfare as either point N or point P, respectively. By superimposing the community indifference curves on the utility possibilities frontier, we can find the combination of A’s and B’s utilities that serve to maximize social welfare and, underlying these, the combinations of X and Y

and the combinations of K (capital) and L (labor). We show this in Fig. 19-5, in which A and B attain community indifference curve C;, which is just tangent to the UPF at point Q. Ms. B gets more utility than Mr. A, but they agree that this situation makes them better off in total than any other point. 446

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

FIGURE

19-5

The Maximization of Social Welfare

Interpersonal Comparisons of Utility

The notion of a social welfare function, whether involving only Mr. A and Ms. B, or involving millions of consumers within a society, necessarily requires interpersonal comparisons of utility to be made. For example, in Fig. 19-4 A and B effectively agree that moving from pointL to pointM left them jointly indifferent, because B’s loss of utility (from B, to By) is just balanced by A’s gain of utility (from A, to A,;). Thus they compared the utility they each expected to lose or gain. Such interpersonal comparisons of utility are acceptable between consenting parties, of course, but become impossible to keep track of as the number of persons in the society increases.

Complete democracy, where every voice is heard and given equal weight, is difficult to achieve. Instead, for efficiency, we elect representatives who make decisions that influence social welfare. These decision-makers are frequently caught in a situation where they judge that society would be better off as a whole if a change were made that benefits one group of people but makes other people worse off.

EXAMPLE:

Examples include the decision to build a hydroelectric generating station in a particular location. This makes residents of nearby cities better off, but reduces the utility of farmers and rural communities whose land is expropriated and who must move away before their land is flooded. Similarly, new expressways benefit commuters but raise noise levels and increase air pollution for local residents. In each of these cases the decision-makers have decided that society is better off with the change, which is to say that the utility gain of the beneficiaries outweighs the utility loss of the people made worse off by the decision. Of course decision-makers cannot look inside the brains of consumers and Welfare Economics

447

measure the utility gained by some consumers and the utility lost by others. Instead they are forced to make value judgments that one group’s loss of utility is less than another group’s gain of utility as the result of a proposed change. These are called value judgments, because they depend upon the decision-makers’ value systems. For example, they may think that farmers and rural communities are not very important compared with city dwellers or they might have other biases, prejudices, or views that underlie their decision. Value judgments are opinions, and we all make them. For example, Montreal is a nicer city than Chicago and Burt Reynolds is better looking than Robert Redford. Value Judgments, Politics, and Income Distribution

In actual practice, then, decisions that influence social welfare are made by people who must exercise value judgments involving interpersonal comparisons of utilities. These decision-makers, at least at the government level, are elected by the people. Suppose we could divide society into two main groups—the workers and the property owners. A political party represents each group—call these the Labor Party and the Conservative Party. Elections are held periodically to determine who gets to make the value judgments and the decisions influencing social welfare. Suppose the Labor Party is elected. We might expect policies to be introduced that make workers better off at the expense of property owners, such as higher taxes on middle and high incomes, with the increased tax revenues paying for socialized health care, expenditure on low-cost housing, and so forth. The community indifference curves envisioned by these decision-makers exhibit arelatively low MRS between workers’ utility and property owners’ utility. Oppositely, the party representing the property owners envisions a relatively high MRS between workers’ utility and property owners’ utility. The reader should appreciate that the different slopes of the community indifference curves envisioned by different decision-makers lead to different optimal points on the UPF. In Fig. 19-6 we show two different sets of community indifference curves superimposed on the UPF for workers and property owners. The property owners’ envisioned SWF gives rise to community indifference curves Po, P,, and P, and in their view social welfare is maximized at the utility combination represented by point R. The workers, on the other hand, envision a SWF giving rise to indifference curves Wo, W,, and W,. They feel social welfare

is maximized at the combination of utilities represented by point S. It is clear that such a divergence of opinion would lead to significantly different policies, depending on which party gets elected to govern the society. NOTE:

Different visions of the social-welfare function by different political parties have profound implications for the distribution of income among members of society. In the example given above, the Labor Party would be expected to institute changes that increase the workers’ share of total output, whereas the Conservative Party would be expected to make changes to improve the property owners’ share of total output. This in turn would mean different total supplies of the goods and services produced and different combinations of capital and labor in

448

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

FIGURE

19-6

Value Judgments and the Optimal Social Welfare Situation Workers’ utility

Property owners’ utility

each production process, as we trace the effects of the different SWF back through the UPF, the PPF, and the Edgeworth-Bowley box diagram of the production sector. The different MRTSx, in the production sector would, in turn,

have implications for the prices of labor and capital services, and thus for the distribution of income between these two groups of suppliers of inputs to the production process. The Theory of the Second Best

Given the policy-makers’ ability to institute changes within the economic system, is it feasible to change the structure of markets that presently contain monopoly elements, so that all markets exhibit pure competition? If this could be done, then economic efficiency could be increased to its theoretical maximum.

In fact it is neither feasible nor desirable to change all markets into purely competitive markets. This would require the absence of all product differentiation in the product markets and the absence of all skill or quality differentials in the factor markets. These differences contribute to the quality of life for many people and would not be given up very readily. Monopolies are likewise considered desirable in some markets. National defense is better kept in the hands of a central administration, rather than be farmed out to hundreds of separate peacekeeping firms. Communications and other industries benefit from such massive economies of plant and firm size that it would most likely raise prices and reduce efficiency to split these industries into many small firms. Still there may be some markets that are presently monopolistically competitive that could conceivably be changed to become purely competitive. An Welfare Economics

449

example is an industry of firms that produce and sell the same product in different locations, so that the product is differentiated by the greater or lesser convenience for purchase by consumers. Government policy could cause these firms to be relocated to one large shopping mall, thus equalizing the ease of purchase offered to consumers. Would this move society closer to the point of optimal economic efficiency? NOTE:

The theory of the second best says that if optima] economic efficiency (the firstbest solution) is unattainable because of monopoly elements, product differentiation, or other imperfections in some product or factor markets, changing any one market into a purely competitive system may not improve the situation at all. The three conditions for general equilibrium and for optimal economic efficiency are necessary conditions in any one market, only if they simultaneously prevail in all other markets. Given that these conditions are unattainable or undesirable in some markets, the existence of these markets changes the requirements for the second-best situation. The actual requirements for the second-best solution depend upon the nature and extent of the imperfections existing in the economic system.!

Ill. WELFARE CRITERIA FOR EVALUATING PROPOSED CHANGES Society’s decision-makers are constantly faced with proposed changes in the structure of society, or modifications to market forms, or other changes that have an impact upon the utility functions of consumers, the profit functions of producers, and the income functions of resources. How do they evaluate these proposals and decide which ones appear to be best for social welfare purposes? Although intuition and instinct are useful, an explicit criterion is better. Let us consider some of the criteria that have been suggested. Pareto-optimality

In the foregoing we have introduced the notion of Pareto-optimality. A situation is Pareto-optimal if any change from that situation causes any party to be worse off. The Pareto criterion for evaluating a proposed change is, accordingly, that the change should be made if it is expected to benefit at least one person and hurt no one. Note that the Pareto criterion is rather restrictive, and it would have prevented many developments in society that are generally considered to be in the overall best interests of that society.

EXAMPLE:

For example, re-zoning a pig farm on the outskirts of town as “residential property” hurts the farmer but benefits the actual and potential residents of the town to a far greater extent. Similarly one cannot evaluate a proposition to reduce property taxes, California’s proposition 13, for example, using the Pareto criterion. 'R. G. Lipsey and K. Lancaster, “The General, Theory of the Second Best,”” Review of Economic

Studies, 24 (1956-1957), 11-32.

450

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

The Kaldor-Hicks Criterion

The Kaldor-Hicks criterion attempts to solve this problem.? Nicholas Kaldor and John Hicks argue that the potential gainers and losers could evaluate their gains and losses in monetary terms, and that the change should be made if the gainers’ gains outweigh the losers’ losses. Thus the gainers could compensate the losers by an amount at least equal to the value of the latters’ losses, and all parties would be better or no worse off after the change. Difficulties abound, of course,

in the implementation of this criterion. The losers are likely to inflate their losses shamelessly, and the gainers may be unwilling to actually hand over the compensation, particularly in cases involving moral, aesthetic, or environmental considerations. Moreover, the Kaldor-Hicks criterion depends upon interpersonal comparisons: It implies that a dollar has the same psychic value to everyone. Is the increment to utility enjoyed by a rich person who gains $1,000 necessarily greater than the reduction in utility suffered by a poor person who loses $995? If we cannot be sure about this, then we cannot be sure that a change that passes the Kaldor-Hicks criterion necessarily improves the welfare of society, since the gainers may not be able to compensate the losers adequately. Bergson’s Criterion Abraham Bergson’s criterion for evaluating a proposed change depends on an explicit formulation of the social welfare function. The policy-makers must specify the elements of the SWF based on the preferences and value judgments of the members

of the society. Once constructed, the social welfare function

could be fed the new values of all variables influenced by the proposed change, and the total value of social welfare (under the proposed changes) could be compared with the status quo. Those changes that increase social welfare as measured by the agreed formulation of the SWF would pass Bergson’s criterion and be instituted. One can appreciate that construction and updating of the social welfare function would be a monumental task. Yet, with the aid of computers,

this difficulty would not invalidate it. A more serious concern is that it may be impossible to develop an SWF that reflects all individual preferences. Arrow’s Impossibility Theorem

Kenneth Arrow, who shared the 1972 Nobel Prize for Economics with John Hicks, has shown that it is impossible to derive a social welfare function without

violating one or more principles that the individual consumer considers inviolate.4 He took the following four main considerations to be necessary features of 2N. Kaldor, ‘‘Welfare Propositions in Economics and Interpersonal Comparisons of Utility,” Economic Journal, 49 (Sept. 1939), 549-52. J. R. Hicks, ‘‘The Foundations of Welfare Economics,”’ Economic Journal, 49 (Dec. 1939), 696-712. 3A. Bergson, “A Reformulation of Certain Aspects of Welfare Economics,” Quarterly Journal of Economics, 1937-1938, pp. 310-34.

4K, J. Arrow, Social Choice and Individual Values. (New York: John Wiley & Sons, Inc., 1951). Welfare Economics

451

an acceptable SWF. First, social preferences must be transitive—that is, if A is preferred to B and B is preferred to C, then A is also preferred to C. Second, social preferences must respond in the same direction as any individual’s preferences—that is, ifa change makes any individual better off, it makes society better off as well. Third, social preferences must not be imposed upon consumers or dictated by any particular consumer. Fourth, social preferences between two alternatives must be independent of irrelevant alternatives—for example, soci-

ety’s preference for A over B is unaffected by the availability of another alternative C. Arrow has shown, in his famous impossibility theorem, that it is impossible to make a consistent set of choices among all sets of alternatives without violating at least one of the above features. Thus the SWF must be either democratic or consistent; it cannot be both.

IV. SUMMARY Social welfare is a term that represents the aggregate welfare, or utility, of society. Given that hedonism is an entrenched principle in society, economists have investigated the notion of maximizing social welfare, so that the resources of the economy are utilized to the maximum benefit of society. The social welfare function is a theoretical construct that would, if measurable, allow policy-makers to choose the best situation for society and to institute changes designed to move society toward this best point. Construction of a social-welfare function requires interpersonal comparison of utilities, a step of dubious methodological and ethical validity. Thus we rely on the value judgments of our elected representatives and accept the consequences of these for income distribution. Since pure competition does not prevail in all markets and, indeed, is undesirable in at least some markets, general equilibrium and optimal economic efficiency seem to be unattainable. The theory of the second best cautions us against transforming monopoly, oligopoly, or monopolistic competition markets into purely competitive markets in the search for increased economic efficiency, since the second-best solution may require monopoly elements— product differentiation, skill differentials, for example—in all markets. Changes from the status quo that are intended to enhance social welfare may be evaluated using the Pareto criterion; the Kaldor-Hicks criterion, involving compensation of the losers by the gainers; or the Bergson social welfare criterion. Arrow’s impossibility theorem suggests that no social-welfare function can be derived that is at the same time democratic and logically consistent. General equilibrium and welfare analysis may be a little too far removed from the real world for the tastes of some, but remember that we are as much concerned with pedagogy as we are with explanation and prediction. The simplistic models used here do serve a valuable purpose: They aid the understanding of how the agents in the microeconomic system interact and they help develop one’s analytical power for use elsewhere. 452

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

DISCUSSION

QUESTIONS

1,

Explain the derivation of the utilities possibilities frontier. In the example used in the text, why are Mr. A’s indifference curves comparable and Ms. B’s curves incomparable?

2.

What is the social welfare function? Is it analogous to the individual’s utility function? How does it involve interpersonal comparisons of utility?

3.

A policy-maker’s underlying value judgments should be stated explicitly. Discuss this statement.

4.

Explain a politician’s attitude to gun control in terms of the value judgments he or she makes, with respect to society’s marginal rate of substitution between the right to bear arms and the right to die of old age.

5.

Explain how different value judgments about social welfare by political leaders can lead to changes in the distribution of income. Suppose one party wants to put space stations in orbit, whereas the other wants to promote cultural development.

6.

In what circumstances is pure competition neither feasible nor desirable in a particular market? If it is feasible and desirable in specific markets, will it improve social welfare to convert these markets to pure competition? Explain.

7.

Discuss the limitations of the Pareto criterion for evaluating proposed changes in the economy.

8.

Why is the Kaldor-Hicks criterion superior to the Pareto criterion? Why is it also not completely satisfactory?

9.

Discuss Bergson’s criterion for evaluating a proposed change. What are the major difficulties with this criterion? Which of the three criteria is superior?

10.

Arrow’s impossibility theorem says that the social-welfare function must be either democratic or consistent, but it cannot be both. Explain.

SUGGESTED Arrow, K.J.,

REFERENCES

Social Choice and Individual Values. New York: John Wiley & Sons, Inc.,

1951.

Bator, F.M., ‘‘The Simple Analytics of Welfare Maximization,” American Economic Review, 47 (March 1957), 22-59. BERGSON, A., ‘A Reformulation of Certain Aspects of Welfare Economics,” Quarterly Journal of Economics, 1937-1938, pp. 310-34.

Hicks, J.R.,

‘‘The Foundations of Welfare Economics,” Economic Journal, 49 (Dec.

1939), 696-712. Welfare Economics

453

KaLpor,

N.,

‘‘Welfare Propositions in Economics

Utility,’ Economic

and Interpersonal Comparisons

of

Journal, 49 (Sept. 1939), 549-52.

Lipsey, R.G., and K. LANCASTER, ‘‘The General Theory of the Second Best,”’ Review of Economic Studies, 24 (1956-1957), pp. 11-32. Littie, I.M.D., A Critique of Welfare Economics University Press, 1957.

(2nd ed.). Oxford, England: Oxford

MANSFIELD, E., Microeconomics—Theory and Applications New York: W. W. Norton & Company, Inc.,1979. ~ ‘

MISHAN, E,J.,

‘‘A Survey of Welfare Economics,

(June 1960), 197-265.

454

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

(3rd ed.), chaps. 15, 16.

1939-1959,” Economic Journal, 70

leatlid Pa aaa” ae is

Externalities

and Public Goods

1. INTRODUCTION In Chap. 18 we saw that the microeconomic system can fail to generate the conditions necessary for optimum economic efficiency if there are elements of monopoly in the system. These monopoly elements most readily arise as a result of product differentiation, whether due to inherent differences, locational differ-

ences, the consumers’ lack of knowledge of the prices, or the availability of competing products. In the production sector, the nonhomogeneity of inputs similarly prevents the system from generating the required marginal conditions for optimum economic efficiency.

DEFINITION: The term market failure is often used to describe the inability of the microeconomic system to automatically gravitate to the conditions required for optimum economic efficiency. In this chapter we are concerned with two other phenomena that similarly cause market failure. The first concerns the external costs and benefits that may be associated with both the consumption and production of goods and services. These external effects, or externalities as they are known collectively, cause the microeconomic system to produce either too many or too few of the products that generate the externalities, in each case compared with the amount of each product that would allow the attainment of maximum social welfare. In the next

455

section we examine these externalities and the means by which their incidence

can be either inhibited or encouraged, so that social welfare may be improved.

The second major topic of this chapter concerns public goods. The entire general equilibrium and underlying consumption and production sector analysis presupposed the private ownership of all factors of production and all goods and services produced. Some inputs to some production processes, such as air and water, are owned by no one in particular and everyone in general. Since these goods are free to anyone who wants to use them, they tend to be overutilized by the market system, with resultant air and water pollution in our example. Similarly some goods and services, once produced, can be consumed by everyone, all at the same time and without the necessity of first paying for one’s share. The usual result is that these public goods are underproduced, since individuals tend to be willing to provide fewer units of these goods and services than would be socially desirable. Hence there is a role for governments (at various levels) to provide these public goods, so that social welfare may be enhanced. Thus the purpose of this chapter is to examine the impact of externalities and public goods on the microeconomic system, and the means at our disposal for at least partially correcting the failure of the system to gravitate to the optimal allocation of resources and the subsequent social-welfare-maximizing production of goods and services.

Il. EXTERNAL COSTS AND BENEFITS We begin by making the distinction between private and social costs. We then define external costs as the difference between private and social costs. Private Costs, Social Costs, and External Costs DEFINITION:

Private costs are comprised of the labor cost, material cost, and all other var-

iable and fixed costs (all valued at their opportunity cost) that are incurred (or imputed) by the producer in the production process. Throughout our analysis of production and cost in the preceding chapters, we limited our analysis to the private costs of production. It is often the case, however, that the production of goods and services imposes costs on other people or firms not directly involved with the production of those goods and services. EXAMPLE:

If a pulp and paper mill upstream from a brewery discharges wastes into the river, necessitating the purification of the water before it can be used in the production of beer, the brewery incurs the cost of water purification as a consequence of the production of pulp and paper. Similarly, if air pollution from a steel foundry means you and I must use more shampoo and soap, this is a cost imposed by the producer of the iron and steel.

DEFINITION: These imposed costs are known as the external costs of production, as distinct from the private, or internal, costs of production incurred by the producer alone. These external costs are not limited to air and water pollution. Any cost 456

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

incurred by a person or firm as a consequence of the activities of another person or firm is an external cost of the latter person’s or firm’s activities. A firm that locks out its unionized workers and therefore disrupts its supply of materials to other firms will most likely impose a cost on those other firms. Similarly, a firm that previously allowed other firms’ trucks to take a short cut across its property will impose an external cost on those other firms by denying access to this shortcuts

DEFINITION: The social cost of production is therefore the total of the private cost of production plus the external costs imposed on other persons or parties as a consequence of that production. There are external costs in consumption as well. Persons littering the highway or parks with empty food and beverage containers impose a cost on the municipality or highway authority, which must hire people to clean up the litter. Traffic noise, a by-product of people consuming transportation services (or of firms producing goods and services) may induce the owner of a building or office complex to install more soundproofing material and thicker glass than would otherwise be necessary. The additional cost in this case is an external cost, imposed by the consumers and producers who create the noise.

External costs need not be simply monetary, but may be, psychic as well. Environmental pollution imposes very definite psychic costs, as well as monetary costs, in many instances. Unpleasant sights, smells, noises and tastes as a result of someone else’s consumption or production activity reduce the utility (or psychic satisfaction) that may be derived from consumption when these unpleasantries cannot be avoided. Hikers hate dirt bikes the same way skiers despise snowmobiles. The noise produced by these machines, as well as their destruction of plant life and the natural habitat, reduce the utility of (or impose disutility on) others who are involved in a separate consumption activity. A similar psychic cost is imposed by the construction of a new building that blocks the view of people living or working nearby. Inflation, as we noted in Chap. 15, is a process involving external costs. Wage demands by unions or increased prices set by the firm benefit the workers or the firm directly, but impose a cost on society due to the effect these wage or price increases have on the general price level. When a wage settlement is followed by higher prices, all consumers of the firm’s product are afflicted with a higher cost of living. These consumers are in turn inclined to ask for higher wages and salaries, fueling the inflationary process further and creating a new set of external costs for other members of society. Private Benefits, Social Benefits, and External Benefits

On the other side of the coin we have benefits conferred upon persons or firms as a result of the production or consumption activities of others. The private benefits of production are measured by the profits to the owners of the firm, whereas 1L ater in this section we shall distinguish between pecuniary external costs and technological external costs. The first group actually facilitates the working of the microeconomic system, whereas the maxsecond group prevents the system from generating the combination of goods and services that imizes social welfare. Externalities and Public Goods

457

the private benefits of consumption are indicated by the utility derived by the consumer. Social benefits may exceed private benefits if a production or consumption activity simultaneously

generates profits or utility for persons in-

volved in other production or consumption activities.

EXAMPLE:

The traditional example of this is the benefits provided to each other by the beekeeper and the orchardist.? In the production of his fruit the orchardist produces blossoms as a by-product. These blossoms are utilized by the beekeeper as a raw material in the production of his honey. Oppositely, the beekeeper provides the orchardist with a service, namely the cross-pollenation of his fruit

trees. Without the blossoms (and their nectar) there could be no honey, and without the bees (and their hairy legs) there would be no fruit. Each firm augments the production and hence the profits of the other as a consequence of its own production process. It is interesting to note that in some places where bees are relatively scarce, the orchardist pays the beekeeper, and in other places where blossoms are relatively scarce, the beekeeper pays the orchardist.? Other external benefits in production are provided by forest products companies, which often permit other vehicles to use the roads through their forests and tree plantations. Automobile rallies, wildlife service projects, and recreational use are often allowed in these private areas. Access to these roads confers external benefits on the “‘outside”’ users when they derive profit or utility as a consequence of their use of these roads. Similarly, a hydroelectric dam that controls the rate of flow into the river downstream, thereby keeping the river from drying up in summer, confers an external benefit on the farmers, fishers, and recreational users downstream. External benefits in consumption are familiar to you. Surely you have benefited as a consequence of your friend having a car and giving you a ride on the way to his or her own destination. Alternatively, suppose you buy a yellow sweatshirt and later find out that yellow sweatshirts are being worn by all the avant-garde on campus. You might derive an external benefit as a result of their collective consumption activity. Alternatively, you might never wear your sweatshirt in public again; thus the avant-garde imposed an external cost on you. Finally, suppose your neighbors paint their house or beautify their apartment. This makes your home a nicer place to live, or it may raise the value of the property, thus conferring external benefits. NOTE:

In our previous treatment of consumer behavior, we proceeded on the assumption that consumers’ tastes and preferences are independent of each other’s consumption patterns. The existence of external costs and benefits in consumption means, of course, that consumers’

tastes and preferences are interdependent.

That is, one consumer’s utility depends not only on that person’s purchases, but also upon the simultaneous purchases of other consumer’s. The effects of other ?J.E. Meade, “External Economies and Diseconomies in a Competitive Situation,” Economic Journal, 62 (March 1952), 54-67.

3Sveven N.S. Cheung, “The Fable of the Bees: An Economic Investigation,” Journal of Law and Economics, 16 (April 1973), 11-33.

458

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

consumers’ purchases on the consumption decision of an individual consumer have been called the bandwagon and snob effects.4 Bandwagon and Snob Effects in Consumption

For many individuals the quantity of a particular product or service that they purchase depends to some degree upon the quantity of that item that other people are simultaneously demanding. For example, in the clothing industry, anew style becomes fashionable as more and more people adopt that style. In many cases the widespread market acceptance of a style causes individuals to demand more than they would have demanded had it not been so popular. DEFINITION: The tendency to change one’s taste and preference pattern in favor of a particular product in some positive relationship with the total demand for that product is known as the bandwagon effect. Consumers jump onto the bandwagon, in effect, so that they are where the crowd is. They allow their tastes to be influenced positively by the tastes of others, and derive additional utility from the knowledge that their consumption behavior is similar to, and endorsed by, that of their peers or other groups of consumers. In terms of external benefits, the

individual receives an external benefit (derives utility) as a consequence of the consumption of others. DEFINITION: The opposite relationship between individual consumer demand and total market demand is known as the snob effect. In this case the individual reduces his or her consumption of the product when it becomes apparent that the product is gaining wider market acceptance. Such a person presumably derives utility from being part of a relatively select group of people consuming the product and derives disutility from being associated with the great unwashed masses. In terms of the attribute analysis of consumer behavior, the individual exhibiting the bandwagon effect derives utility from the attribute social conformity, whereas the individual exhibiting the snob effect derives utility from the attribute exclusivity. And finally, whereas the bandwagon effect implies the conferring of an external benefit, the snob effect implies the imposition of an external cost upon the individual, in each case as a result of the consumption activity of others.

Technological Externalities versus Pecuniary Externalities It is important to distinguish between pecuniary and technological externalities. Technological externalities are imposed or conferred directly upon another party, whereas pecuniary externalities involve the imposition of costs and revenues indirectly, via the market system.

EXAMPLE:

If there is a severe cold period during the growing season for Florida oranges that causes the price of frozen orange juice to be increased, we expect subsequent price changes for other products that compete with orange juice for the con4See Harvey Leibenstein, “Bandwagon, Snob and Veblen Effects in the Theory of Consumer Demand,” Quarterly Journal of Economics, May 1950, pp. 183-207. Externalities and Public Goods

459

sumer’s dollar. The consumers of Hawaiian fruit drinks may find that the price

of this product has increased, due to a shift to the right of the demand curve for

that product (as consumers leave the frozen orange juice market and enter the fruit drink market). The additional cost of their drink to the regular drinkers of Hawaiian fruit drink is a pecuniary external cost imposed on them by the combined forces of nature and the producers of frozen orange juice. More generally, inflation is a process whereby individuals, groups of individuals, firms, and other institutions impose external pecuniary costs on each other indirectly through the market system. Oppositely, pecuniaty benefits may be conferred on individuals or firms by other individuals or firms via the market system. An example is the reduced cost of bus fares to bus travelers as a competitive response to a reduction in rail fares. DEFINITION: Technological externalities are costs imposed or benefits conferred directly upon a person or firm by another person, group of persons, or a firm.-These are called technological because they enter the technology of the consumption and production functions of the injured party (in the case of technological external costs) or of the beneficiary (in the case of technological external benefits). That is, the utility of the consumer depends not only upon his or her consumption of goods and services, but also upon some other party’s consumption or production activity. For example, consumer A’s utility function may be expressed in general terms as follows:

U, =f(X, Y, Z, B)

(20-1)

where U, represents A’s total utility, the X, Y, Z variables represent the goods and services that A purchases, and B represents the consumption or production activity of some other party. Alternatively, for the producer of product X, the production function may include a ‘‘foreign’’ term, as follows:

Q, = f(K, L, W)

(20-2)

where the output of product X is a function of capital and labor as before, but is also dependent on some variable W that is controlled elsewhere. This variable may represent, for example, the emissions of waste products from a neighboring plant, which cause nausea and headaches among the workforce of firm X, thus

reducing their productivity and hence the output of product X.

NOTE:

Pecuniary externalities are part and parcel of the microeconomic system and are therefore part of the mechanism that ensures the goods and services are produced and delivered to those willing to purchase these goods and services. Technological externalities, on the other hand, represent an impediment to the efficient functioning of the microeconomic system. These directly imposed externalities cause market failure, in the sense that their presence prevents the attainment of the optimal social welfare. Let us see why. —

460

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

The Overproduction and Overconsumption of Activities Generating External Costs When a production or consumption activity generates external costs, it tends to be overproduced or overconsumed relative to the level that maximizes social

welfare. We demonstrate this with the aid of Fig. 20-1, which may be interpreted as representing either a production or a consumption activity. The curve MB, represents the private marginal benefit derived by the individual or firm engaged in the activity. (In consumption activity, MB, is the marginal utility curve, whereas in production it is the marginal revenue curve.) In the absence of any external benefits resulting from this consumption or production activity, social marginal benefits (MB,) are equal to private marginal benefits, and thus the MB, and MB, curves are coextensive. The MC curves shown represent the marginal costs incurred as a result of the consumption or production activity. MC, is the private marginal costs incurred by the individual or firm engaged in the activity. M€., represents the external marginal cost imposed on other parties as a result of the activity. MC, is the social or total marginal cost of the activity, and as such it is simply the vertical summation of MC, and MC,.

FIGURE 20-1 The Overproduction or Overconsumption Problem When Social Costs Exceed Private Costs

Social, private, and external costs and benefits

Private production or consumption activity

Now, the private party engaged in the consumption or production activity maximizes his or her own utility or profits by equating MC, and MB,, which occurs at activity level A,. Note that this ignores the external marginal costs that

Externalities and Public Goods

461

cause social marginal cost to exceed the social marginal benefits at that activity level. Social welfare is maximized if the activity is carried only to the level A*, where MC, = MB,. That is, from the point of view of all parties involved, collective utility or profits are greater and are maximized if the consumption or production activity is reduced from the privately optimal level A, to the socially optimal level A*. Thus the existence of external costs tends to cause the consumption or production activity to be carried beyond the socially optimal level. %

\

The Underproduction and Underconsumption of Activities Generating External Benefits

Now let us show that activities generating external benefits are underproduced and underconsumed from the viewpoint of society as a whole. In Fig. 20-2 we show the private and social marginal cost curves (MC, and MC,) as being coextensive, representing a private consumption or production activity that imposes no external costs. The private marginal benefits are shown by the curve MB,. To maximize its own utility or profits, the consumer or firm selects activity level A,, where private marginal costs equal private marginal benefits. But since this activity simultaneously confers external marginal benefits, social marginal benefits exceed the private marginal benefits of the consumer or firm engaged in the activity. Adding MB, vertically to MB, in Fig. 20—2, we find MB,, and note that social marginal benefits equal social marginal costs at activity level A*. Thus the private activity is not carried far enough for the maximization of social welfare when there are external benefits conferred on other parties. EXAMPLE:

462

As an example of underconsumption of an activity that confers external benefits, suppose the chairperson of the economics department is recruiting new faculty members. Having already a high quality group of professors, the department is able to attract better candidates than other departments can. The chairperson, being a particularly persuasive person, has a high success rate for signing up new professors. Any other department with less notable academics and less effective recruiting efforts benefits from the hiring of these superior candidates by the economics department. These external benefits derive from the favorable image and good publicity the economics department brings to the university as a whole. The Nobel Prize for Economics is awarded each year, and the winner or joint winners are always identified by their university affiliation. This kind of publicity helps other departments at that university to hire better professors, get research grants, maintain student numbers and quality, and receive various other benefits. The economics department, looking only at its own budget, and its own teaching and research needs, typically does not take these external benefits into account. It therefore hires less of these superior candidates, as compared with the number that would maximize the welfare of the university community as a whole. :

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

FIGURE 20-2 The Underproduction or Underconsumption Problem When Social Benefits Exceed Private Benefits Social, private, and external costs and

benefits

Private production or consumption activity

We have seen that activities imposing external costs tend to be overproduced or overconsumed, whereas activities conferring external benefits tend to be underproduced or underconsumed. Let us now examine some ways and means by which these activities can be reduced back to, or raised up to, the levels that would maximize social welfare. Internalization of the External Costs

The imposition of external costs upon other consumers or firms does not seem fair or just, and so we investigate the means by which individuals or firms imposing these costs on others may be induced to avoid, or at least to reduce, this

practice. Our objective is to equalize private and social costs by the elimination of all external costs. To do this we mustensure that the person or firm engaged in the consumption or production activity is responsible for, and pays for, the total or social costs of that activity. When the firm or the individual is forced to pay for these external costs, they become private, or internal, costs. Our objective is therefore to internalize all external costs, so that private costs are the only component of social costs. Voluntary Internalization. Ina world of reasonable men and women we could ask the firm or individual to restrict the imposition of external costs voluntarily or, alternatively, to compensate all parties upon whom an external cost is imposed. Thus the firm or individual has several choices and combinations of these

Externalities and Public Goods

463

options. First it could forego profits or utility by ceasing the production or consumption activity or by reducing that activity to a level that no longer imposes

external costs. For example, if the stereo in the next apartment is too loud, the

neighbor can be asked to either turn it down or turn it off completely. A second option is for the offending party to incur costs to eliminate the external costs while continuing the production or consumption activity. Thus a firm that is polluting the environment may voluntarily install the appropriate filters and purification systems, so that it no longer,imposes external costs upon other users of the environment. Similarly, users of dirt bikes and snowmobiles might install more effective exhaust mufflers on their machines to at least remove the aural offence they create. The neighbor with the loud stereo system might be induced to either soundproof his or her apartment, or buy an expensive pair of headphones that will give the same volume and quality of sound without waking up the neighborhood. A third option is for the offending party to compensate the offended party for the cost imposed. Thus, if you are the offendee, you might agree to tolerate the imposition of the external cost in return for a payment that you feel adequately compensates you for bearing the imposition. If this payment is less than the cost the offender must otherwise incur to eliminate the external cost, or if it is less than the profits (or monetary value of the utility) that would be foregone by reducing or ceasing the production or consumption activity, the offending party prefers to make the payment to compensate the offended party for the cost incurred. In effect this would be a bribe to induce the recipient of the external costs to put up with the cost, inconvenience, or unpleasantness imposed.

NOTE:

In each of the above cases the individual previously imposing the external costs effectively internalizes those costs by increasing his private costs. Given voluntary internalization, these increased private costs are either the opportunity cost of foregone profit, the actual cost of eliminating the externality, or the compensation required to bribe the recipients to continue bearing the externality, whichever is the lesser amount.

Legal Recourse. In the absence of voluntary internalization of external costs, the offended party might take legal action to obtain either the restitution of his or her rights or compensation for profits or utility foregone because of the externality. The courts are literally full of law suits that involve one firm against another or an individual against a firm or another individual, because of some external cost imposed by one upon the other that is not resolved voluntarily. It is obvious that when an issue is clear cut and is supported by adequate jurisprudence and legal precedent, it is more efficient simply to outlaw certain practices that typically cause the imposition of external costs. Thus we have laws and regulations constraining firms and individuals to internalize what would otherwise be external costs. Airplanes and motor vehicles are subject to maximum noise and air pollution levels. Firms are prohibited from discharging into the environment waste material with a concentration above so many parts per million. Individuals are not allowed to ‘disturb the peace,” and so on. The existence of these laws and regulations places the onus on the firm or individual 464

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

to internalize all costs, or at least to internalize more costs than they might otherwise wish to. It therefore allows the courts to concentrate on violations of these

laws or what appear to be exceptions to the laws, rather than the repetitive processing of similar grievances.

Fees and Penalty Charges. Governments, whether municipal, state (provincial), or national, might impose fees or penalty charges on firms or individuals who habitually impose external costs upon others. Such fees are often based on the quantity of the offense, with a per-unit charge reflecting the external costs imposed per unit of the offending practice. Suppose a firm discharges chemical waste into a river, causing water pollution and consequent losses to farmers and fishers downstream. A means of reducing the firm’s discharge of the waste is to charge it an effluent fee of so much per gallon, this fee reflecting some estimate of the aggregate external costs imposed per gallon of the discharge. If this fee is high enough the firm finds it cheaper to install filters and purification systems rather than continue to discharge the untreated waste. If the firm finds it cheaper to continue to pollute, and the fees collected adequately compensate all parties for all external costs imposed, then society as a whole is better off if the firm continues polluting and simply compensates (through the fees levied against it) all injured parties. This may seem like a strange result, but it is not. In most cases the socially optimal level of pollution is positive, not zero. The Optimal Level of Pollution or Other External Cost. Typically society is better off with, and is willing to tolerate, some positive level of pollution rather than to press for its total elimination. This result is obtained primarily because it becomes progressively more expensive to eliminate pollution (and other external costs) as the level of the problem is reduced. There comes a point when it would cost society more to reduce pollution one more unit than society is willing to pay. The benefits of a further reduction in pollution or other external costs are outweighed by the cost of obtaining that further reduction. Thus the noise level produced by automobiles may be legally restricted to, let us say, 80 decibels, which is still loud enough to be offensive to many people. The cost of reducing this maximum noise level to a more comfortable 60 decibels would be quite high, and there would appear to be insufficient public support (recognizing the subsequent increase in the cost of automobiles) for lowering the noise levels further.

EXAMPLE:

Consider Fig. 20-3 in which we show the private, external, and social costs of noise pollution. Note that the private costs of noise control are inversely related to the level of noise pollution. Thus, to have a very quiet automobile or commercial aircraft involves very high costs being incurred by the owner and user of the automobile and the aircraft. Oppositely, very loud automobiles and aircraft require a smaller private expenditure on noise control. The external costs of noise pollution are positively related to the level of noise pollution. The louder the automobiles and aircraft, the more money people have to spend on ear plugs, medical expenses, sound insulation, and so forth. The social costs curve, or the sum of the private and external costs, is found by the vertical addition of the Externalities and Public Goods

465

private and external cost curves. Note that since it is the sum of a falling curve and a rising curve it is necessarily U-shaped. Thus, the total, or social, costs of noise pollution is minimized at, for the sake of this example, an 80-decibel max-

imum noise emission limit. FIGURE 20-3 The Optimal Amount of an External Cost: The Noise Pollution Example &

\

Total costs

of noise

Total (Social) Cost of Noise External Costs

(of noise pollution) TCrin-

—

—

—

—

—

Private Costs (of noise control) Level of noise

20

40

60

80

100

:

(decibels)

In summary, external costs in production and consumption cause a reduction in the profits or utility of others not directly involved in the production or consumption activity that generates those external costs. This is neither fair nor just and reduces social welfare below the level where it would be if all costs were privately incurred. Inducing, or forcing, firms and individuals to internalize the external costs of their production or consumption activity raises that party’s private cost of engaging in that activity. This in turn, due to the law of demand, reduces the production and consumption of items that tend to impose external costs. Other items thus become more attractive in consumption (or more profitable in production) and so the allocation of resources is modified in a way that enhances social welfare. Internalization of the External Benefits

To encourage the production and consumption of goods and services that generate external benefits, we must induce the recipients of the external benefits to

compensate the private consumer or producer responsible for generating those benefits. The beneficiaries might be induced to make payments directly or indirectly via the tax mechanism. EXAMPLE:

An example of the internalization of external benefits is seen in government, business, and alumni support of universities and colleges. The production of educated people confers external benefits on society as a whole, since it tends to

466

GENERAL EQUILIBRIUM AND sotwetran ANALYSIS }

make people more socially conscious, less bigoted, less likely to become involved in crime, more likely to do great things for society, and so forth. In recognition of these external benefits, society as a whole helps to support the university and college system through payment of income taxes that are later remitted to universities to help pay for their production of graduates. Similarly all property owners in a particular school district are required to pay school taxes, whether or not they have children attending school. Education is also supported by business firms, wealthy individuals, and the alumni of particular colleges and universities. Each of these groups make voluntary payments to educational institutions, presumably in recognition of the benefits that they, as individuals and as members of society, derive as a byproduct of the institution’s production process, namely, the education of stu-

dents. The additional financial support the universities and colleges receive from government,

business, and private sources ensures that their output of

graduates is increased toward the socially optimal level. In many instances when external benefits are conferred, it is difficult to internalize the external benefits, thus the activity may not be increased to the

socially optimal level. Recipients of external benefits may prefer to continue receiving these benefits without paying for them. If forced to pay, they might tend to understate the value of the benefits received, in order to receive them for

less money than they would otherwise have to pay. Such persons are known as free riders; they are discussed in the following section. It suffices to say here that as long as the consumer or producer of an activity that confers external benefits is not fully compensated for those external benefits, the activity remains restricted at a level below that which would maximize social welfare.

lll. PROPERTY RIGHTS AND PUBLIC GOODS The discussion of private and social costs leads us to a consideration of property rights and the classification of products as either private, public, or mixed goods. The free rider problem with public and mixed goods is then discussed. After examination of Coase’s Theorem we finish by examining the class action lawsuit as a solution to the problem of high transaction costs for individuals seeking restitution of rights or compensation. Private versus Communal Property

DEFINITION: Any object or thing is your private property if you have the right to use it, dispose of it, or take legal action for someone else’s misuse of it. You have these property rights over your own person (within limits, however, for suicide is illegal) and for items you have purchased or received or earned as remuneration for services rendered. Thus you might own acar, a stereo, books, sporting equipment and apparel, a piece of land, ten shares in IBM, and two tickets to Saturday’s game. If these are stolen or damaged by someone you can sue that individual for the restitution of the value of these articles. Externalities and Public Goods

467

DEFINITION: Items of communal property, or public goods, are defined as goods and services we have a right to use (or consume), but our right does not extend to the exclusive use of that product. The air we breathe is acommunal, or public, good. Everyone breathes the air and no one may deny others the use of air. The road system, beaches, state forests, and the main street in our home town are similar

examples. Immediately we can see that there are limits to our use of these public goods: If our use restricts other people’s use, endangers other people, or involves an illegal activity, then our actions may be constrained. Public goods may be simultaneously consumed by several people or parties, and the consumption of one party does not detract from or prevent the simultaneous consumption of others. This property of public goods is called jointness, meaning that more than one consumer can jointly consume the product at the same time. Some public goods also have the property of nonexclusion, meaning that one person’s consumption of the good cannot exclude any other person’s consumption of the good.

EXAMPLE:

A bridge over a river is typically a public good. Hundreds or even thousands of people may cross the bridge simultaneously up to the point at which the bridge is operating at its full capacity, without any one person’s bridge crossing being less effective. (At full capacity the nonexclusion property of the bridge disappears.) Defense services provided by the military are another public good. We all simultaneously consume an item called ‘‘protection from invasion”’ or at least we enjoy the security provided by having major deterrents to invasion without any one person’s consumption of that service limiting any other person’s consumption. Note that defense has the properties of jointness and nonexclusion.

DEFINITION: Mixed goods are those that are both private and public goods. These are the products that confer external benefits as a by-product to their private consumption or production. EXAMPLES:

Examples we have considered above include the orchardist’s blossoms, the university’s graduates, and the faculty’s hiring of top academics. Other examples include a musician practicing in the park, athletes performing their sport, or a person with a well-trained dog. While each is privately pursuing utility or profit maximization, their production or consumption activity simultaneously allows other persons or firms to derive utility or profit by observing or in some other way benefiting from that production or consumption activity.

Public Goods, Mixed Goods, and Free Riders

DEFINITION: A free rider is someone who benefits from a public or mixed good without paying his or her share. Moral and ethical considerations aside, why should the individual pay for using a public or mixed good? By definition, these goods are available simultaneously to other consumers whether or not the individual pays for or uses that product or service. Someone who jumps over the turnstiles at the 468

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

entrance to the subway station can ride the train without detracting from the service provided to others. A person who evades taxation may continue to benefit from the services of government, including national defense, without detracting from anyone else’s use or enjoyment of these services. Similarly, without breaking any laws, a person may watch Public Broadcasting Station television broadcasting without sending an annual donation to help support this broadcasting. What, then is the problem of free riders? In the case of public goods, if everyone is a free rider or if there are too many free riders, there would be no one, or not enough people, paying for the services provided. In the short run this service might continue, but there has to be sufficient financing to replace or repair the facilities. In the long run, then, these public goods are either eliminated if everyone wants to be a free rider, or underproduced if some people take .. free rides. We have already seen that the existence of free riders causes mixed’ goods to be underproduced, if the private consumer or producer is not adequately compensated for the external benefits provided. The same is true of public goods provided by governments, such as bridges, highways, police services, and national defense. The existence of free riders consuming these goods and services similarly leads to less than the socially optimal amount of these products being provided. EXAMPLE:

Using the example of the subway train service, suppose that 10% of all riders use fake passes or counterfeit tokens and coins or simply jump the barrier and run into the crowd waiting for the train. The subway authority may underestimate demand for its services by as much as 10%, since it bases its estimates on

ticket or token sales or by turnstile counters. Moreover the profitability of providing the service is less than it should be, since 10% of the users did not pay. Thus the subway authority is unlikely to provide enough capacity to comfortably handle peak period demands for the service, not only because it underestimates peak demand, but because such capacity does not seem justified in terms of revenues from paying customers. If it raises fares, it only serves to send marginal users to alternate transportation services, and these are almost certainly paying customers! Clearly the subway authority has an interest, as does the paying customer, in eliminating the free rider problem. EXAMPLE:

In other areas as well, the ability to take a free ride causes the underproduction of a product or service, unless the problem is recognized and compensated for. Defense is an obvious example. Without society’s collective insistence on adequate defense and national security, which is reflected in the election of governments who stand for a particular defense posture, defense expenditure would be substantially less. Imagine for a moment a defense budget supported by voluntary contributions from those concerned enough to pay: It would surely lead to a defense capability only a fraction of what we actually have. Provision of defense by national governments allows for a more equitable distribution of the cost of that public good across all consumers. Supported by general tax revenues, defense is effectively paid for by all who pay taxes, rather than by nervous Externalities and Public Goods

469

or patriotic people who would contribute under a voluntary system. The free rider problem is then controlled by the effective enforcement of the tax laws.

EXAMPLE:

Public television programming, which tends to contain more educational and cultural material than commercial television programming, is also no doubt underproduced for the maximization of social welfare. If all viewers could be assessed a fee, PBS stations would undoubtedly generate substantially more revenue and therefore be able to provide more and better programs in the same spirit. The only recourse of PBS stations is to limit the details of their programming to subscribers by a monthly newsletter and program. Nonsubscribers must rely on the programs published in newspapers and other TV program guides, to which some PBS stations provide only program titles, rather than details as well. In the future, with the probable widespread adoption of pay-TV programming in the home, free riders in this area may be substantially reduced. When the TV set becomes simply the audio-visual output terminal of a complete home information service, individual cable links (like telephone service now available) will allow people to request particular programs whenever they want to see them, and in so doing will activate the electronic funds transfer to pay for the information or program received. If your credit is bad, the system would not deliver, and so the potential free rider is forced to pay for receipt of these benefits. Given the great cost of establishing such a system, the broadcasting and cable TV companies are moving toward pay-TV to provide programming and information services that are not for the masses or that are otherwise specialized in some way. This eliminates the free rider and allows the socially optimal amount of these services to be produced. Eventually we might expect all television programming to be sold in this way.

Property Rights and Coase’s Theorem

As stated above, property rights are conferred on the owner of private property, who in turn may take legal action to restore these rights if they are denied. With public goods or communal property, we cannot sue if the bridge is too crowded or if we cannot find a space on the beach. With many public goods, it’s a case of first come, first served, especially at peak periods of consumption, due to the inability of that good to meet total (or peak) demand for its services. This is often the result of underproduction of the public good, which we have seen to be a consequence of incomplete internalization of external benefits and the free rider problem. While individuals may own their land and buildings, they do not typically own the air space above that land, nor the minerals or other valuables in the earth below it. Nor do individuals typically have a property right to the view from their house or piece of land. As long as zoning laws and other construction standards are met, our neighbors may block our view by the erection of new SPeter W. Bernstein, ‘‘The Race to Feed Cable TV’s Maw,” Fortune, May 4, 1981, pp. 308-18.

470

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

buildings, by planting trees, or whatever. Our neighbors have the property rights to their property and need not consult us at all. The problem is that our property rights are incomplete. It is usually not specified that we have a right to a place on the beach, to an uncongested bridge, to a view from our land, to the minerals below our land, or to clean air and water. In fact, the problem usually is that someone else usually owns the right to prevent us from obtaining the benefits mentioned above. Ronald Coase has shown that the economic system can take care of this problem.® EXAMPLE:

Consider the following case. Suppose you own a tract of land in a semidesert region and graze cattle on this land. A mining exploration firm approaches you for the right to dig on your property for minerals that they speculate will be found. This firm is willing to pay you a sum of money (up to the amount they expect to earn from digging on your property) for the right to begin excavation. They do not offer this sum immediately, of course. Instead, they offer you a smaller sum of money indicating that this is their best offer. If this amount compensates you for the loss of income from your cattle grazing operation, as well as for the aesthetic aspects of having your property trampled and excavated, you accept the offer. If not, they will raise the offer and approach you again. The minimum price of your property right is the value you feel justly compensates you for loss of income and utility. The maximum price is the amount the mining firm expects to make as a result of acquiring the right. If the former is less than the latter, a deal is struck and the property right changes hands. Note that society as a whole is better off, since you receive a payment that at least compensates you for your profit and utility lost, and the mining firm pays less than it expects to earn. Thus the two parties to the transaction are either both better off, or one is better off without the other being made worse off, and there has been a Pareto-optimal change made. Coase’s Theorem shows that it does not matter who initially owns the property right: It will change hands if the value of it to the prospective owner exceeds the value of it to the initial owner. To illustrate, suppose now that the mining firm has the right to dig anywhere on your property. The mining firm may have originally owned the land and sold it to someone with the stipulation that they retain the rights to any excavation and mining activity on that property. When you purchase the land that stipulation remains part of the deed unless the mining firm is now willing to sign it away. If you don’t want them digging on your land, you might approach them and offer them a sum of money to revoke the right they currently hold. The maximum you would offer is the monetary equivalent of the profits and utility you expect to lose as a result of their use of their right. If this exceeds the value they expect to derive from the right, the mining firm will sell the right to you. If not, they will continue to hold the right, just as in the preceding case you would have kept the right if the mining firm were not willing to pay your price. 6R. Coase, ‘‘The Problem of Social Cost,” Journal of Law and Economics, Oct. 1960, pp. 1-44. Reprinted in E. Mansfield, ed., Microeconomics: Selected Readings, 3rd ed. (New York: W. W. Norton & Go, inc),).

Externalities and Public Goods

471

NOTE:

Thus property rights change hands if someone else values them more highly than the present owner of the property right, and social welfare is increased asa result of the transaction. One important proviso to this argument, however, is that the costs of the transaction must not be so large as to offset the gain to the prospective purchaser. These transaction costs include the time and expenses of both parties involved in the negotiation process and the legal expenses associated with the transfer of the property right. If these are zero or quite small, the preceding argument holds. If, on the other hand, they are relatively large, they might negate the incremental profits or utility expected to be derived by the party purchasing the right; this party would then refuse to buy the property right, since after transaction costs he or she is not better off.

EXAMPLE:

To give anumerical example of the preceding scenario, suppose that the landowner expects to derive $100,000 worth of profits and utility (in expected net present-value terms) from his or her private use of the land. Suppose that the mining company expects to derive $150,000 profits by digging on the land (again in expected net present-value terms). It is clear that whoever initially owned the right to dig on the land, the mining company will end up with it in this case, as long as transaction costs do not exceed the $50,000 differential between the two valuations of the property right.

Collective Property Rights and Class Action Suits

Although public goods are owned by everybody in general and no one in particular, individuals or firms do not have the right to abuse their share of the public good or to use it in a way that is detrimental to others’ simultaneous consumption of the same product or service. The obvious example is environmental pollution: Consumers and producers do not have the right to bestow external costs upon other consumers and firms, as a consequence of their using air and water in their private consumption or production activity. That is, their usage of the air and water should not reduce the quality of these public goods, so that others suffer as a result. The remaining consumers and producers have the right to expect the public good to remain unspoiled after its joint consumption by others. It is often difficult and expensive to insist upon one’s rights, however, especially if these property rights are not clearly defined. The individual consumer or firm may find itself the lonely voice against the titans of industry that create the environmental pollution. Legal costs for the individual are typically so great that one’s utility-maximizing strategy is to put up with the inconvenience rather than to wage a legal battle at great cost and personal inconvenience. Essentially, the transaction costs involved (in forcing the offending consumer or firm to compensate the offended parties) are so high, that the market system fails to make the Pareto-optimal change, which could otherwise be made. One means of reducing these transaction costs for the individual is the class action suit, which allows people with a similar complaint to press their claim for compensation jointly, thus spreading the legal and other costs over dozens or even thousands of plaintiffs. The rationale is that if the offence is found to have been committed 472

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

against one of the plaintiffs, the remaining cases are similarly proven due to the basic similarities of all the cases. Collective or class action law suits represent an important new strategy to

enforce the recognition of individual’s rights without these claims being inhibited by mammoth legal costs. The victims of the thalidomide drug, which caused deformities in babies, took class action against the chemical company responsible. Relatives of victims of air crashes often group together to simplify and share the ensuing legal proceedings. Individuals suffering from a common problem due to environmental pollution or hazardous work conditions, such as the lung disorders common to asbestos workers, may find the class action suit the only way they can assert their collective property right and obtain compensation. Attitudinal Shifts Concerning Property Rights

Attitudinal shifts, assisted in some cases by legislation, have aided individuals to obtain recognition of their property rights. A good example is that of nonsmokers. Ten or more years ago, before it was widely publicized that smoking is statistically linked to lung cancer, the nonsmoker was often forced to look at life through the haze of other people’s cigarettes. Now that smoking is widely recognized as a filthy habit, it is the smoker who timidly asks if we mind his or her smoking, rather than the nonsmoker requesting that there be no smoking. The smoker is like the polluting firm, causing a deleterious effect on the public good as a result of his or her joint consumption of it. This attitudinal shift has had an impact—for instance, larger nonsmoking sections on aircraft and the appearance of no smoking regulations in such places as elevators, restaurants, theaters, and the like. A similar example is presented by the almost universal acceptance of antipollution devices on automobiles. A decade ago many people were motivated to remove or de-activate the antipollution equipment, on the grounds that small amounts of pollution from their automobile would not make any significant difference in the overall quality of the environment and that the automobile would run better without it. It is true that a properly readjusted engine runs better without the constrictions imposed by antipollution equipment, but motorists are now much less likely to interfere with this equipment—it was, from the start, illegal to do so. I believe that motorists as a group are now much more conscious that without this equipment they impose external costs on other members of society, and that they have no right to do this. Seeing the attitudinal shifts involved in the cases of the smoker and the polluting motorist, one should take heart that the fight against one of today’s largest problems, inflation, will benefit by a widespread shift in attitude. Recognition of the fact that selfish profit-seeking by firms and selfish income-seeking by individuals has external pecuniary effects that exacerbate the problem of inflation, might induce more socially responsible behavior from profit seekers and income earners. If this is forthcoming, one could conjecture that we might see the removal of a major element in the inflationary process. The tax-based incomes policy, outlined in Chap. 15, explicitly recognizes that inflation is a Externalities and Public Goods

473

process involving external costs, and operates to reduce excessive wage claims and price hikes, by taxing those people and firms imposing the external costs. In effect it is similar to an effluent fee levied against a polluter: it is designed to cause the individual to reduce the activity which imposes the external cost as a profit or income maximizing response.

IV. SUMMARY *

\

In this chapter we have examined the concepts of externalities and public goods, both of which contribute to the failure of the market system to produce the socialwelfare-maximizing combination of goods and services. Production and consumption processes that impose external costs tend to be taken to a level beyond that which is socially optimal. As long as the external costs are not internalized, the product is effectively too cheap in production and consumption. Therefore more of it is produced and consumed than is socially desirable. Inducing, or forcing, the internalization of all external costs, so that private costs equal social costs, raises production and consumption costs and thereby inhibits these activities. External benefits in production and consumption are measured by the increases in profits or utilities that some persons or firms enjoy as a consequence

of the production or consumption activities of others. Compensating the consumers and producers who generate external benefits increases the level of those activities to socially optimal levels. The bandwagon effect in consumption was seen to be an external benefit accruing to individuals as a result of the simultaneous consumption of the same product by others. The snob effect is the converse: It represents an external cost imposed by the simultaneous consumption

of others. Public goods, or communal property, and mixed goods are products or services that may be simultaneously consumed by more than one consumer. Public goods are owned by everyone in general and no one in particular. A general problem with public and mixed goods is that they tend to be underproduced, compared with the amount that would maximize social welfare. Free riders, who use public goods and avoid paying for the cost of providing these goods, contribute to the underproduction problem by not allowing the market system to provide producers with the appropriate demand and profit signals. Measures to reduce free riding and government actions to further social interest are necessary to bring the provision of public goods up to the level required for maximum social welfare. Coase’s Theorem says that a property right changes hands if it is worth

more to the potential owner than to the existing owner, as long as transaction costs do not wipe out the difference. Thus despite the existence of externalities, there can be a Pareto-optimal re-allocation of goods and services assisted by the market mechanism. Class action lawsuits are a means toward the social-welfare optimum. Col-

474

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

lective legal action to restore property rights or to obtain compensation helps to circumvent the transaction cost obstacle to Pareto-optimal adjustments, allowing people to achieve a net gain in income or utility that they would otherwise be unable to attain. Finally, we noted the increasing awareness of externalities by consumers and producers. In this light, it may be politically feasible to implement the taxbased incomes policy to control inflation.

DISCUSSION

QUESTIONS

What is market failure, and what causes it to happen? Does it mean that the markets cannot function and should perhaps be replaced by a bureaucratic price and output determination process, as in some communist economic systems?

Why does the existence of external costs reduce social welfare? Do you think that external benefits outweigh external costs? If so, would the situation be optimal? If external costs and benefits in consumption are simply psychic, how can these be evaluated for the purposes of a law suit, for example. What problems are likely to arise? Think up some new examples of external costs in production, external costs in consumption, external benefits in production, and external benefits in consumption. Explain the bandwagon and snob effects in consumption, in terms of the externalities conferred upon others in a consumption process. Can the “keep-up-with-the-neighbors” syndrome be explained in similar terms? What means exist to internalize the external costs in production and consumption? Why does the internalization of external costs cause the problem to be at least partly rectified?

What are the essential characteristics of a public good? Does this mean that they would get very crowded? Why don’t entrepreneurs build bridges and charge everyone for each crossing?

What is Coase’s Theorem? Does this mean that you can buy the right to an unobstructed view of the lake from your house? What problems might arise?

Why do free riders cause a problem in the economic system? What is the nature of that problem and how might it be rectified? 10.

How do class action law suits contribute to the improvement of social welfare? When are they the only feasible means of restoring one’s property rights?

Externalities and Public Goods

475

SUGGESTED Bator, F.M.,

REFERENCES

‘The Anatomy of Market Value,” Quarterly Journal of Economics,

72

(Aug. 1958), 351-79.

BUCHANAN, J.M., Nally, 1968.

The Demand and Supply of Public Goods. Chicago, Ill.: Rand Mc-

,and W.C. STUBBLEBINE,

“Externality,’’ Economica, 29 (Nov. 1962), 374. \

BAUMOL, W,J., “On Taxation and Control of Externalities,” American Economic Review, vol. 62, June 1972. , Economic Theory and Operations Analysis (4th ed.). Englewood Cliffs, N.J.: Prentice-Hall, 1977. CHEUNG, S.N.S., ‘The Fable of the Bees: An Economic Investigation,” Journal of Law and Economics, 16 (April 1973), 11-33. Coase, R.H.,

‘The Problem of Social Cost,’ Journal of Law and Economics,

3 (Oct.

1960), 1-44.

Davis, J.R., and J.R. HULETT, An Analysis of Market Failure: Externalities, Public Goods, and Mixed Goods. Gainsville: The University Presses of Florida, 1977. DEMSETZ, H.,

‘Toward a Theory of rey

(May 1967), 347-73.

DoRFMAN, R., andN.DORFMAN,

Rights,’’ American Economic Review, 57

Economics of the Environment. New York: W. W. Nor-

ton & Co., Inc., 1977.

FURUBOTN, E., and S. PeyovicH, ‘Property Rights and Economic Theory: A Survey of the Recent Literature,” Journal of Economic Literature, 10 (Dec. 1972), 1137-62. LEIBENSTEIN, H., ‘Bandwagon, Snob and Veblen Effects in the Theory of Consumer Demand,” Quarterly Journal of Economics, May 1950, pp. 183-207. MEADE, J.E., “External Economies and Diseconomies in a Competitive Situation,’’ Economic Journal, 62 (March 1952), 54-67.

MISHAN, E.J., ‘“The Relationship between Joint Products, Collective Goods, and External Effects,” Journal of Political Economy, 72 (May-June 1969), 349. SCHALL,L.D., ‘On Taxation and Control of Externalities,” American Economic Review, vol. 62, June 1972.

WoRCHESTER, D.A.,

‘Pecuniary and Technological Externality, Factor Rents, and Social

Costs,’ ‘American Economic Review, 59 (Dec. 1969), 837—85.

476

GENERAL EQUILIBRIUM AND SOCIAL WELFARE ANALYSIS

A Review of Analytic Geometry and Calculus: Functions, Graphs, and Derivatives

1. FUNCTIONS AND GRAPHS A function is an expression of the dependence of one variable upon one or more other variables. The general form is

Y =f(X) and it is read as the value of Y is a function of, or depends upon, the value of X. Y is known as the dependent variable, and X is the independent variable. The value of Y may depend on more than one independent variable, of course, so that we might express the functional relationship in general form as: Y =f (X;, Xo, Xz, xy

a)

In this multivariable function the value of Y depends upon the value of several independent variables, where n is the number of these independent variables. For example, the sales of umbrellas may be a function of the price of umbrellas, the income of consumers, the rainfall levels, the advertising expenditures of umbrella manufacturers, the price of taxi fares, and so on.

The form of the functional dependence of Y upon the independent variables X;, wherei = 1, 2,...,n, remains unspecified in the preceding expressions. To find the exact nature of the dependence, we must examine the specific form of the function. This may take a variety of mathematical forms: For example, Y may be a linear, quadratic, cubic, quartic, or higher order function of X (or the 477

X’s), or it may be a power function, an exponential function, a hyperbolic function, or some other form. Let us examine these in turn. Linear Functions

The general form of a linear function is

Y=a+ bX ~

\

where a and b are constants. If, for example, a = 4 and b = 0.5, we could array the value for Y, given the values for X as shown in Table A-1. These values indicate the specific dependence of the variable Y upon the variable X. When X is zero, the second term (bX) is zero and drops out, and Y is simply equal to the parameter a. Each time the variable X is increased by one unit, the value of Y increases to the extent of the parameter b. TABLE

A-1

Values of Y for Various Values of X for Y = 4 + 0.5X

Values of X Values of Y

OO: ALO) tk.

Let us plot the function on a graph that has X on the horizontal axis and Y on the vertical axis. Using the pairs of observations for X and Y as coordinates, we are able to plot the equation Y = 4 + 0.5X, as shown in Fig. A-1. The graph of this equation would extend into three of the four quadrants, but we show only the northeastern quadrant, where both variables have positive values, since for most economic applications these are the only meaningful values of the function. Notice that the graph intercepts the Y axis at the value of 4; hence the parameter a is known as the intercept parameter. Similarly the graph slopes upward and to the right at the rate of one half unit of Y for each one unit increase in X. The slope of the line (the vertical rise over the horizontal run) is thus equal to 0.5, precisely the value of the b parameter. Accordingly, b is often called the slope parameter. Thus by observing the value of the a and b terms in a simple linear function, we are able to envisage the graphical form of that function. For multivariable linear functions, we simply extend this analysis to a case of additional explanatory variables, such as: Y=a@

+

DyX,

+ boX,

+ baX3

+

hate

+bpX,

Where the X; (i = 1, 2, 3,...n) represents several independent variables, and the b; coefficients represent the influence that a one-unit change in the value of

each independent variable has on the value of Y. A simple example of a multi-

variable linear equation is Y = 2 — 0.4X, + 0.3X,. Substituting values for X, and X, into this expression allows us to obtain the values for Y as shown in Table

A-2. 478

APPENDIX

FIGURE

A-1

Graph of a Linear Function with Only One Independent Variable

rise

b="-—~ = slope run

Ff WO NW DN Aor

TABLE

A-2

Values of Y for Various Values of X, and X,When Y = 2 — 0.4X, + 0.3X,

ee ee

ee

Values of X,

The values in the body of Table A—2 represent the value of Y for the values of X, and X, given by the coordinates of that value. For example, Y = 2.4 when X, = 2 and X, = 4. Graphing the values of Y against the values of X, and X;, we obtain Fig. A—2, in which it can be seen that the equation is that of a plane. Note that the parameter a is again an intercept value, or equal to the value of Y when the values of the independent variables are zero, and that the b coefficients represent the slope of the function as we move one unit in the direction of a particular independent variable. Note too, that the sign of b, is negative, indicating that the value of Y declines as additional units of X, are added. Quadratic Functions

The linear relationships noted above represent what are known as first-degree functions, since each of the independent variables are raised to the first power only. We move now to quadratic, or second-degree, functions, in which one or A Review of Analytic Geometry and Calculus: Functions, Graphs, and Derivatives

479

FIGURE A-2 Graph of a Linear Function with Two Independent Variables

¥ =a —b4X,+ 9X9

‘

xX,

more of the independent variables are squared or raised to a second power, such as | Y=a+bX+cX?

Hence Y is a function of the constant a plus the constant b times the independent variable X, plus the constant c times the square of that independent variable. Suppose we let a = 5, b = 3, andc = 2. We may calculate the values of Y for various values of X as shown in Table A-3. TABLE

A-3

Values of Y for Various Values of X When Y = 5 + 3X + 2X”

Values of X Values of Y

ey

Nh

Ww

aS

oO

ao

Plotting these values on a graph, (Fig. A—3) it can be seen that the graphical representation of a quadratic function is curvilinear, whereas a linear function is rectilinear. Notice that the parameter a remains the intercept term, and that the slope depends not only upon the value of X, but also upon the square of the value of X. In Fig. A-3 we show a second quadratic function Y = 15 + 10X — 2X?, and it can be seen that the curvature of this function is concave from below, 480

APPENDIX

whereas the curvature of the first function is convex from below. This concavity is the result of the negative sign in front of the second-degree term in the latter expression. (Notice that concavity and convexity are always stated in relation to a particular aspect. A line that is concave from below is, of course, simultaneously convex from above.) FIGURE

A-3

Graph of a Quadratic Function with Only One Independent Variable

Y =15+10X — 2x?

FIGURE

A-4

Graph of a Quadratic Function with Two Independent Variables

Y=a+bX,—

2 2 cx, +dX,—eX5

xy A Review of Analytic Geometry and Calculus: Functions, Graphs, and Derivatives

481

When there are multiple independent variables and the relationship between these variables and the independent variable is quadratic, we may express the function as follows: Y =a

+ bX, + cX? + dX, + eX}

This is a simple case in which there are only two independent variables, X, and X,. This relationship is graphed in Fig. A-4, in which it can be seen that the negative signs preceding the second-degree terms indicate that the surface representing the function is convex from above. Onte again the parameter a is the intercept on the Y axis and takes a positive value. In other cases, of course, the parameter a may be zero or negative, just as the other coefficients may have positive values, zero, or negative values. Cubic Functions

We turn now to the third-degree terms in the functional relationship. Cubic functions may have first-, second-, and third-degree terms, such as the following: Y=a+bX

+cX? + dX?

When all the coefficients have positive signs, it is clear that the values of Y in-

crease by progressively larger increments as the value of X increases. When the signs of the coefficients differ, the graph of Y may display both convex and concave sections, may have hills and valleys, or simply exhibit a monotonically increasing or decreasing shape, depending upon the values of the coefficients. As an example, consider the function Y = 25 + 10X — 5X? + 2X°. In Table A-4 we calculate the values of Y for several values of X. TABLE

A-4

Values of Y for Various Values of X When Y = 25 + 10X — 5X? + 2X3

Values of X

, Calculations Values of Y

25 =) 1oce) Zax X=

(6)

iL

2

3

25 120

25 10 a5 2 32

25 20 ote 16 41

25 30 BRAG 54 64

6 3

4

25 40 ~ 28H «128 113

5

25 50 fsa8 250 200

Plotting the values of Y against the value of X as in Fig. A-5, we see that the function is monotonically increasing yet exhibits convexity from above at first, changing at the inflection point to concavity from above. In the same figure we show the graph of the equation Y = 100 + 5X — 10X? + 2X? and note that it has sections of both positive and negative slope. This indicates that the values of the parameters are instrumental in determining the shape of the graphical relationship. The distinguishing feature of a cubic function, as compared with a quadratic function, is that the former may have an inflection point—where slope 482

APPENDIX

changes from convexity in one direction to concavity in that direction or vice versa—whereas the latter does not. FIGURE

A-5

Graph of Cubic Functions with Only One Independent Variable

200

Y =25+ 10X — 5X2 + 2x3

150 Y = 100 +5X — 10x? + 2x3 100

50

FIGURE

A-6

Graph of Cubic Function with Two Independent Variables

7) 3 2 Y =a +b,X1+ 0X4 —dXj +eXq+ FXo9X73

xy Derivatives A Review of Analytic Geometry and Calculus: Functions, Graphs, and

483

Cubic functions in two independent variables produce a three-dimensional surface when graphed, as in Fig. A-6. Again the value of the parameters and the signs of these parameters and coefficients operate to determine the shape and placement of the surface depicting the functional relationship. We could continue the examination of functional relationships with fourth-degree terms and higher influencing the value of the variable Y, but these are not necessary for an understanding of the microeconomic analysis in this textbook. Rather we turn to some other types of functions that may be useful to us, although not all of these are used in this text: Other Functional Forms

Exponential functions take the form

Y=a+b* As we look at this specific form of the functional relationship, we should appreciate that the value of Y increases monotonically as X increases, since the second

term in the function assumes progressively higher degrees. An exponential function, among others, is shown in Fig. A—7. Power functions take the form , Y=ax?

and can be seen from Fig. A—7 to exhibit the general parabolic shape, as do the exponential and quadratic functions. Hyperbolic functions take the general form

Y=a In this case as X grows larger, the value of Y diminishes and approaches zero asymptotically, as shown in Fig. A~7. Note that hyperbolic functions are in fact FIGURE

A-7

Graphs of Other Functional Relationships between Y and X

Y=a+t b* (Exponential)

Y=ax?

a Y = —

xb

(Power)

(Hyperbolic)

Xx

484

APPENDIX

power functions in which the parameter b has a negative sign. A special case of the hyperbolic function is the rectangular hyperbola Y = a/X, in which the parameter b has the value unity. Hence YX equals a at all points on the curve. In verbal terms the product of the two variables is a constant at all levels of the two variables indicated by points on the curve. The rectangular hyperbola has applications in microeconomics, such as the representation of the average fixed costs curve, since total fixed costs are a constant amount equal to the number of units of output times the average fixed costs at each output level.

Il. DERIVATIVES

OF FUNCTIONS

Derivatives and Slopes

The size of the coefficient to the independent variable indicates the extent to which a marginal change in that variable influences the dependent variable. Examination of the marginal impact of one variable upon another is commonly referred to as marginal analysis. Economists make extensive use of marginal analysis when establishing normative rules for decision making. If Y is to be maximized, for example, the impact on the value of Y for a marginal change in the value of X is sought in order to decide whether to increase, decrease, or hold constant the value of the independent variable X. In general terms we want to know whether it is worthwhile (in terms of the increment to Y) to increase or decrease X. In terms of the graphical representations above, we are interested in the slopes of the functions. A mathematical technique that generates the slope of functions is to take the first derivative (differential) of the function. The derivative of a function shows the change in the value of the dependent variable Y, given an infinitesimally small change in the variable X, and is written as dY/dX, where d connotes the increment or decrement to each variable. For marginal analysis it is imperative that we consider small increases in the independent variable, since larger increases may incorrectly indicate the extent of change in the dependent variable. In Fig. A-8 we depict a changing marginal relationship between Y and X. Suppose that the values of X and Y are as indicated by pointA in that figure. The marginal relationship, or the slope of the function, is given by the slope of a tangent to the curve at pointA. But this is only a correct representation of the slope of the function for an infinitesimally small change in the variable X. For larger changes, such as to levels X, or X;, the slopes of the arcs AB and AC are not accurate representations of the slopes of the function over those values of X and Y. They are, in fact, approximations (averages) over the wider range of X and Y values. For decision-making purposes, we are typically concerned with the incremental units of output (or some other variable), and hence we require the more accurate marginal relationship between variables. It is therefore important that we understand the rules of differentiation for use in optimization procedures. A Review of Analytic Geometry and Calculus: Functions, Graphs, and Derivatives

485

FIGURE

A-8

Change in Slope as AX Is Increased

Rules of Differentiation

Constants. Since the derivative shows the amount by which the dependent variable changes for a change in an independent variable, and since a constant by definition does not change, it is clear that the derivative of a constant must be zero. Therefore, if

‘

then

Y=@

dy ax_

The Power Rule. When the function includes a term that is raised to the firstdegree or higher, we use the power rule, which may be stated as follows: Y = aX? if then

dY ne ox

bax b-1

To illustrate this let us begin with a first-degree function, such as Y = aX. Since X is implicitly equal to X', it is clear that the application of the power rule reduces the X term to X°, which equals 1, and the derivative of Y = aX is simply the coefficient of the X term. Thus if Y = aX, then

ala:

xt

=l-a-xo

= leg

=a 486

APPENDIX

For higher degree terms, the power function is applied similarly. Suppose Y =a + bX?, then dy ear Sy 2bX 2-1 OX =D = 2bX

To demonstrate the power rule in the context of terms of various degrees, consider the function Y = 5 + 3X + 2X? + 5X°. Treating one term at a time, dY/dX = 3 + 4X + 15X?. (Is this correct? Confirm it for yourself, using the steps above.)

The Function ofa Function Rule. In the case where Y and X are related through an intermediate variable Z, to find the change in Y due to a variation in X, we need first to ascertain the impact on Z of the change in X, and then multiply this by the impact of a variation in Z upon Y. Thus, if

Y=2Z)

Vanda

Z= if)

CYC Y: S02 pelts fatale p aes’ OK Olax

then

For example, if Y= 4 + 6Z? and Z = 8 + 3X3, then

= 108Z(X?) The Chain Rule.

Where Y is the product of two variables, X and Z, which are

themselves related, and we wish to find the derivative of Y with respect to X, we must consider both the direct influence on Y of a change in X and the indirect influence on Y of the change in Z, which the change in X provokes. Thus if

Yo= 7X;

where

Z.= F(X)

th

an

dy =

aX

Vi. ab XdZ

dX

Partial Derivatives

When a function has multiple independent variables, and consequently each independent variable is only one of a number of variables that effect the value of the dependent variable Y, we take what is known as the partial derivative of the function for each independent variable. This is equivalent to the ceteris paribus assumption in economics: That is, we examine the influence of one of the indeA Review of Analytic Geometry and Calculus: Functions, Graphs, and Derivatives

487

pendent variables upon the dependent variable, while holding all other variables constant. The partial derivative thus shows the impact upon Y of an infinitesimally small change in one of the independent variables, while all other independent variables are held constant. By convention and to distinguish it from the derivative of functions with only one independent variable, we depict the partial derivatives by the lower case delta, 0, rather than the lower case d as used above. Thus if Y is a function of several variables such as

Y=a+bX+cX?+dZ+e22 + fQ? then OY

si meer

le Sap goar OZ OY norte Af(\2 a0 3fQ

Each partial derivative shows the marginal impact of one of the independent variables upon the dependent variable, while holding constant the impact of the other independent variables. Maximum and Minimum Values of Functions

In the above we have been concerned with first derivatives, which show the slope of the function as the independent variable (or one of the independent variables) is varied by a small amount. The first derivative thus shows the rate of change of the dependent variable relative to the specified independent variable. With curvilinear functions that rate of change varies for different starting points in the value of X. In Fig. A—9 the quadratic function Y = —10 + 30X — 3X? is FIGURE

A-9

Changing Value of the First Derivative

60

40

20

488

APPENDIX

dy dX

—