sales maximization and oligopoly

Sales Maximization and Oligopoly: A Case StudyAuthor(s): Conway L. Lackman and Jos L. CraycraftSource: The Journal of Industrial Economics, Vol. 23, No. 2 (Dec., 1974), pp. 81-95Published by: Blackwell PublishingStable URL: http://www.jstor.org/stable/2098310 .Accessed: 24/10/2011 06:00

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SALES MAXIMIZATION AND OLIGOPOLY: A CASE STUDY

CONWAY L. LACKMAN and Jos. L. CRAYCRAFT*

THIS study compares the price implications of various models of price theory with the observed prices in a particular industry. The purpose of this comparison is to say something about the reliability of various models in predicting observed prices in a specific cost-demand environment. Empirical estimates of demand and cost relationships were made for the corrugated specialties industry from survey data of the three firms in the industry and their customers. Using a profit maximizing model, an unconstrained sales revenue maximization model, (naive SRM), a constrained sales revenue maximization model (SRM) and a Fellner model, estimates were made of prices, quantities, and rates of return on sales for each model as if the estimated demand and cost relationships were valid. In addition, estimates of bands of prices were made for the Fellner model (integrated model) using assumptions of sales revenue maximization rather than profit maximization.

Section I presents the estimated demand and cost relationships. The various models and resulting estimations are presented in Section II, and Section III presents the integrated models. Conclusions and summary occupy the usual position.

I. ESTIMATED DEMAND AND COST RELATIONSHIPS

A. Industry Demand Curve

Two types of industry demand curves can be derived. First buyers' intentions at various alternative prices may be ascertained at a point in time. These ex ante intentions correspond to theoretical demand curves. Second, the actual sales and prices can produce an empirical demand curve. This ex post approach involves a considerable number of problems with identi- fication, which in turn makes estimates of equilibria subject to error.

The industry demand curve used in this study is ex ante.' It was derived by a survey covering the period I967-69. A large sample of the buyers of corrugated paper specialties products were interviewed. These buyers (classified by market type) were offered a range of eight price level al- ternatives for the product assuming the historical supplier advertising outlay

* The authors would like to acknowledge the assistance of Joseph Gallo, Lloyd Valentine and Harland W. Whitmore of the University of Cincinnati and Donald Dewey of Columbia University who commented on an earlier draft of this paper. Responsibility for remaining errors rest with the authors.

1 All of the analysis in this study was run also using the ex post demand relations rather than the survey data. There was no significant difference in the results.

8I 6

82 CONWAY L. LACKMAN AND JOS. L. CRAYCRAFT

pattern as given, and asked to indicate the quantity (in thousand square feet-referred to as MSF) they would purchase at various price levels- quoted at $/MSF. Two months later the demand data was updated, indicating little bias in the original survey.

B. The Firm Demand Curves

The Firm's demand curves were determined from the same survey. Buyers had indicated in this survey their allocation of demand among their three suppliers (Firms I-3) by price level offered. These individual buyer alloca- tions were summed by price level for each year for each firm to produce the firms' ex ante demand functions for I967-69. Buyers indicated that pro- motional outlays of suppliers influenced their demand, therefore, promo- tional outlays were added to price as a second endogenous variable. The remaining parameters were considered to be exogenous. The general form of the firm's demand curve is as follows:

(1) Xl = a + 13X2(t) + f32X3(t-1) + Ut

where

X = quantity in thousand square feet (MSF) X2 = price per MSF X3 = dollar advertising outlay U = disturbance term

For purposes of developing a general model of the firm, this equation will be used in the following form:

(1') X a + P1IXI(t) + P2X3(t-i) + Ut

The beta estimates, r2's, and standard errors are shown in Table 1.2

The price elasticity of the market and each firm's demand function is presented in Table II. The market demand function becomes somewhat more inelastic over the period studied and the firm's demand curves exhibit an apparent tendency toward unitary elasticity.

2 For consistency, the sum of ex ante firm demand curves were benchmarked against the ex post market demand. The technique used to check this consistency was to determine the ex ante price corresponding to the ex post output of each firm. These estimated prices for the three firms are averaged on a weighted basis for each year and compared to the ex ante market demand price corresponding to the expost industry output. If the three firms' weighted (by output) average price for a given year is close to the market price for that year, the estimates are assumed to be consistent. Such a consistency check is needed, since the allocation of demand to the three firms by the buyers surveyed in the ex ante market demand estimate could be subject to error. The calculations are presented below:

Weighted average on Market P/MSF P/MSF

I 967 26.96 27.00 I 968 27.56 25.00 I 969 27.84 25.50

SALES MAXIMIZATION AND OLIGOPOLY 83

TABLE I

SUMMARY ESTIMATES OF FIRMS' DEMAND FUNCTION PARAMETERS-EX ANTE

B B2 7r2

Firm I I967 -51 *14 .99

(.0209) (.0014) I96 -.38 .074 .99

(.0210) (.0074) 1969 -.48 *I25 .99

(.0204) (.0044) Firm 2

I967 -.32 .I2 .99 (.0362) (.005 I)

I968 - .24 .073 .99 (.0338) (.0076)

1969 -.24 .07 *99 (.0341) (.0079)

Firm 3 I967 -.24 *04 .98

(.0434) (.0042) I968 -.24 .o96 .99

(.0469) (.0042) I969 -.20 .o6 .99

(.0510) (.0092) Market

I967 -o.56 *07 *99 (.0I05) (.0103)

I968 -o.67 .005 *99 (.0 I 02) (.0094)

1969 -o.62 .002 .99 (.O0i6) (.OI23)

TABLE II

FIRMS I-3 DEMAND ELASTICITY AT ACTUAL EQUILIBRIUM 1967-69

I967 I968 1969

Firm I - .90 - .97 - I.09 Firm 2 -i.68 -1.52 -I.I6 Firm 3 -I.35 -I.33 - I.08

C. Costs

A non-stochastic cost function has been constructed for each firm with parameters directly assigned from actual cost data from the engineering estimates of each firm based on average variable costs. The costs for each firm were found to be nearly identical at any equivalent output. The cost calculations were expressed as a continuous function by fitting a least square line to the reported cost data.

(2) C(m) = *

+ 11*Xl(t) + 12*X3*(t) where C(,) = average variable cost and X3* = units of labor.


The beta estimates are .i8 and 2.25 respectively and are significant at the I % level. R2 is .92 and autocorrelation is relatively low. This was used as the firm's average variable cost curve. A 'padded' cost curve was calculated reflecting the firm's profit constraint as a markup over average variable costs.

(2') C'(t) 1.2 (C(/)) for firms 1 and 3 C'(t) 1.3(C(t)) for firm 2.3

II. TRADITIONAL OLIGOPOLY MODELS

The simplest model of an oligopolistic firm would be to assume each oligopolist to operate as a monopolist with no dependence among the firm's demand functions. Equations (I') and (2) can be used for such a model.

Profit is at a maximum where:

an AR AC a2Xn2 a2R2 a2 2 - = = - ~ = < o ax ax ax ax ax ax

where TR P *X = R and TC = C *X . These conditions are used to establish the equilibria consistent with profit maximization.

This independent monopoly model would not be expected to be a good predictor of firm behaviour in the corrugated specialties industry as des- cribed previously. As we shall see these expectations are fulfilled.

A number of duopoly-oligopoly models have been developed that would be expected to do a better job of predicting. We used a number of these models to analyze this industry; however, Fellner's models are of particular interest.4

Fellner rejects rigid assumptions about rival firms' reaction functions on the basis that they will be misleading and unrealistic in that they assume away the oligopoly problem. He only assumes a tendency to maximize joint profits.5 In developing his model, he has also found that there are eight factors which can interfere with firm's achievement ofjoint profit maximization. The four most fully developed by Fellner are:

(i) Unwillingness to pool resources and their earnings or to agree on inter-firm compensations, in order to maximize profits in the presence of non-horizontal cost curves. (2) Same unwillingness in the presence of differences between cost curves of the various firms. (3) Same unwillingness in the presence of product differentiation implying unwilling-

3 The I.2 and I .3 values for the coefficients of the 'padded' average variable cost curves are the result of separate interviews with executives of the three companies involved. They indicated target rates of return on sales for their firms. Industry practice is to translate these target rates of return on sales into identical percentage markups on average costs in pricing individual orders.

4 William Fellner. Competition Among the Few. New York: Alfred A. Knopf, I959. 5 Fellner, pp. 33-40.


ness to pool brands, or in the presence of spatial differentiation, implying unwillingness to reallocate output between points with different locations. (4) Incompleteness of coordination concerning future changes in advertising, product quality, and technological methods.6

Qualifications (3) and (4) serve as an incentive for the firms to engage in non-price competition. These forms of competition defend the firm's position against changes in relative bargaining strength and also against aggressive moves of its rivals. To expand upon Fellner's third point, above, firms' product differentiation and advertising result in a distinct demand curve for each firm. These firms would establish several prices depending upon the degree of product differentiation.7 This may cause firms to widen the agreed- upon pricing range. As an example of Fellner's fourth factor, consider two firms sharing a market equally, one having a lower cost of production. The low-cost firm would prefer a lower pricing structure than the other. This results in an unwillingness to adhere to agreed-upon pricing on the part of the firm with lower production costs. That firm could, of course, survive in spite of prices below the agreed-upon range, thus perhaps increasing their share of the market. The effect of this may be a wider agreed-upon pricing range.

Fellner developed more than one model. The one of greatest use to us in analyzing behaviour in the corrugated specialties industry is the 'expanded' Fellner (g-4) model. This model assumes qualifications (I), (3) and (4).

The expanded Fellner model stipulates equal cost firms with joint profit maximizing pricing band. The limits of the pricing range are determined by the highest profit maximizing price and the lowest profit maximizing price. These positions are, in turn, determined by the differences in the firm's demand curves, since this model assumes equal costs. All firms may set other than profit maximizing prices as long as they stay within the pricing range.

The expanded Fellner model doesn't specify whether individual or joint profit maximization must take place, but only that a tendency to maximize joint profits be in effect. Specific, prices and market shares are not specified and a relatively narrow pricing range results. The Fellner model differs in these respects from the earlier traditional oligopoly models. Chamberlin's joint profit maximization produces a single price and the Bertrand-Edge- worth analysis yields an identifiable pricing pattern. Also the Chamberlin and Cournot models predict specific market shares.8 Less rigid assumptions

6 Fellner, pp. I98-9. 7 See Joseph C. Gallo, 'Oligopoly and Price-Fixing: Some Analytical Models', Antitrust

Law and Economics review, Fall, 1970, pp. IOI-I8. 8 The equilibria associated with these models were developed and compared with the

actual prices and outputs. Also a dominant firm-model, Stackelberg model, barometric firm model, Singer model and Nutter model were used to analyze these results. The reason for the use of the Fellner model is that it produced results closest to the actual price and output of all the traditional models. Eugene M. Singer, Antitrust Economics, Englewood Cliffs, N. J.: Prentice-Hall, Inc., I966, pp. 85-8; H. V. Stackelberg, The Theory of Market Economy, London: Oxford Press, 1934; and Warren G. Nutter, 'Duopoly, Oligopoly, and Emerging Competition', Southern Economic journal, April I 964, pp. 343-8.

CONWAY L. LACKMAN AND JOS. L. CRAYCRAFT

concerning the firm's reaction function in the expanded Fellner model demonstrate that seller's learning of mutual dependence can cause the behavioral contraints to deviate from joint profit maximization, but that these constraints are expressable in economically quantifiable terms.

III. THE BAUMOL SALES REVENUE MAXIMIZATION MODEL

An alternative to the models examined in the previous section is an oligopoly model assuming independent or autonomous behavior among firms. The Baumol Sales Maximization Model (or SRM) is a prime example.9 The Baumol SRM substitutes sales maximization, with a minimum profit constraint for profit maximization as the goal of the oligopolist. A naive form of the SRM would assume sales maximization without a profit constraint in the shortrun. This substitution is based on the assertation that a firm with

increasing volume of sales will have an advantage in attracting capital under more favorable terms, in producing a positive image with consumers, personnel and distributors.1° Furthermore, executive compensation seems to have a higher correlation with sales than with profits.1l

The determination of the profit constraint is crucial in the SRM model; however, Baumol devoted surprising little time and attention to the problem. It would seem that the long run equilibrium of the sales revenue maximizer would require an optimum path of firm growth. Baumol translated that into a stable stock price.12 Baumol does not develop further the rationale for the

profit constraint calculation. He never considers directly the possibility that the profit constraints, representing firm target revenue growth or SRM

equilibria, may be merely a proxy objective for long run equity or wealth maximization.

Baumol claims that the oligopolist is in equilibrium at that price and output where realized profit is equal to the minimum acceptable profit. Using equations (I') and (2') as a model and AR = AC + n as the equilibrium conditions, the SRM equilibria for the corrugated specialties can be

empirically approximated. 9 William Baumol. Business Behavior, Value and Growth. New York: Harcourt, Brace and

World, 1959. 10 Baumol, pp. 45-6. 11 See J. W. McGuire, J. S. Chin, and A. O. Elbring, 'Executives Incomes, Sales and Profits', American Economic Review, September 1969, pp. 40-6. Other studies which support the correlation between executive compensation and variables other than profits include David R. Roberts, 'A General Theory of Executive Compensation Based on Statistically Tested Propositions', Quarterly Journal of Economics, May 1965, pp. 276 ff; Herbert A. Simon, 'The Compensation of Executives', Sociometry, March I957, pp. 32-5; David R. Roberts, Executive Compensation (Glencoe: Free Press, I959); Oliver E. Williamson, 'Managerial Discretion and Business Behavior', American Economic Review, December 1963, pp. I040-7. A contrary view has been expressed in a recent study by Wilbur G. Lewellen and Blaine Huntsman. Using multi-variate analysis, they found a high degree of correlation between executive compensation and reported profits and equity market value, but no relationship to sales. See their 'Managerial Pay and Corporate Performance', American Economic Review, September I970, p. 719. 12 Baumol, pp. 35-40.

86

SALES MAXIMIZATION AND OLIGOPOLY

The basic static oligopoly model was presented by Baumol as in Figure I. The SRM equilibrium is AR = AC + Xt (Point C) following the Sandemeyer interpretation.1 3

If the firm were a profit maximizer, it would produce Q,n units of Q. Baumol SRM attempts to maximize sales or total revenue subject to a profit constraint. Assuming that the minimum acceptable profit per unit is in

$/MSF

7/ 2 +AVC

//\ _S^,\r +AVC

M_ M

/--'""" \ _<LAVC

MR i D

0 Q, QO Qs MSF/t

FIGURE I.

and the corresponding 'padded' cost curve is nt1 + AC, the firm in the shortrun produces output QA where total receipts are maximized (naive SRM

13 R. L. Sandmeyer, 'Baumol's Sales Maximization: Comment', American Economic Review, December I964, p. 1077. The shape of the 'padded' cost curve (average cost plus minimum per unit profit) in Figure I does not correspond to the shape used or suggested in Baumol, op. cit., p. 64. He used a profit constraint where the total profit was constrained. Thus R-C 2 K where K is expressed in terms of a fixed dollar amount. Thus the 'padded' cost curve would be hyperbolic and asymptotic to the LAVC curve. Minimum profits per unit would be equal to Kf Q (1 = K Q) and at equilibrium P = AC + 7-. As Baumol suggested, this view of the constraint is not likely to be commonly felt in the business com- munity. A minimum rate of return on investment or on sales or minimum percentage mark up over costs is more likely to the form of the constraint as felt by the businessman. Each form of this constraint generates a different 'padded' cost curve. If the constraint is in the form of a minimum percentage return on sales such that R-CIR > K where K is some minimum percentage, then the minimum per unit profit (g) will equal f * P. The 'padded' cost curve (AC + 1i) would approach the LAVC curve as p falls and would become coincident if the demand curve cut the Q axis. If the constraint is in the form of a minimum percentage mark up over costs such that R-C/C > K where K again is some minimum percentage, then the minimum per unit profit (i7) will equal K . AC. The 'padded' cost curve (AC + g) would lie further and further above the LAVC curve as AC increased. The 'padded' curves shown in Figure I are based upon this form of the budget constraint. Cf. Baumol, op. cit., p. 64 ff.

87


equilibrium). With an output of QA, the firm earns X13 profits, which are greater than the minimum (t1) required by the stockholders. The SRM manager will allocate these sacrificable profits to expand sales until stopped by the profit constraint (point C).14

Thus with it1 + A VC as a profit constraint, Point M is the profit maximizing equilibrium, Point Q is the naive-SRM equilibrium, and Point C is the SRM equilibrium.

Had the minimum acceptable profit been n2, rather than t1, the firm would have had to stop at QS units of output, where total revenues could not be maximized. The price-quality adjustment ignores the reactions of rivals. The SRM firm is assumed to have an independent price policy which he uses or could use to maximize sales if not constrained from doing so by the minimum acceptable profit.

IV. INTERIM RESULTS

Some comparisons can now be made. The actual prices and outputs are known. The profit maximizing, naive SRM, and SRM equilibria can be approximated from the models. The Fellner band of prices can be approximated from the model by using the highest and lowest profit maximizing prices. Table III presents this information in relative form using the actual price, outputs, and rate of return for the base of the relative. Table IV then presents the unweighted averages of those relatives for each firm for the three years.

Without exception the actual rate of return on sales was less than rate predicted by the profit maximizing or Fellner models but larger than that predicted by the SRM model.

There appears little doubt, however, that the firm's price-quantity adjustment is consistent with the naive model of the shortrun adjustments of a Sales Revenue maximizer. (See Table IV.) This interpretation is rein- forced by the data contained in Table II. One could interpret Table II as indicating a tendency of the firms in this industry to seek the unitary elastic portion of their demand curve. This, of course, corresponds to the maximum point on the total revenue function. This would be consistent with a naive statement of the shortrun equilibrium in the SRM model.

V. INTEGRATED MODEL

The traditional oligopoly models are concerned with inter-firm relations with respect to pricing, output, market shares and profits. The Baumol

14 There is an extensive literature on the nature of the adjustment process producing a point such as C (p = AC + it) as a final SRM equilibrium. See Baumol, Business Behavior, Value, and Growth; Sandmeyer, 'Baumol's Sales Maximization: Comment', American Economic Review, June 1970; M. Z. Kafoglis and R. C. Bushnell, 'The Revenue Maximization Oli- gopoly Model: Comment', American Economic Review, June I970; and C. J. Hawkins, 'The Revenue Maximization Oligopoly Model: Comment', American Economic Review, June 1970.


TABLE

III

COMPARISON

OF

FIRMS

ACTUAL

EQUILIBRIA

IN

RELATIVE

TERMS

(ACTUAL

=

IOO)

I967-69

r967

1968

r969

Firm I

P/MSF

Q

(MSF)

ROS

P/MSF

Q

(MSF)

ROS

P/MSF

Q

ROS

Profit

Max.

133

67

130

134

68

150

120

80

125

SRM

51

130

42

80

120

55

62

140

43

Naive

SRM

104

97

I06

103

98

108

99

107

I06

Actual

100

100

100

100

100

100

100

I00

100

Fellner

Band:

Upper

133

70

128

142

64

I66

120

80

133

Lower

113

92

107

129

74

145

107

97

117

Firm 2

P/MSF

Q

ROS

P/MSF

Q

ROS

P/MSF

Q

ROS

Profit

Max.

120

73

I26

115

81

127

132

63

117

SRM

83

123

76

87

125

77

94

108

97

Naive

SRM

94

109

85

90

125

58

97

108

85

Actual

100

100

100

100

100

100

100

100

100

Fellner

Band:

Upper

140

46

152

128

65

146

146

52

189

Lower

120

73

I30

II6

81

131

13I

68

172

Firm 3

P/MSF

Q

ROS

P/IASF

Q

ROS

P/MSF

Q

ROS

Profit

Max.

II9

73

140

120

77

141

128

70

171

SRM

85

II9

55

82

123

53

9I

110

68

Naive

SRM

go

118

67

96

115

68

95

107

84

Actual

100

100

100

100

100

100

100

100

100

Fellner

Band:

Upper

139

45

I69

123

77

142

146

58

195

Lower

118

73

140

113

87

125

125

75

I67


TABLE

IV

UNWEIGHTED

AVERAGE

OF

RELATIVES-FIRMS

ACTUAL

PRICE

AND

OUTPUT

(I967-69

AVERAGE)

Firm I

Firm 2

Firm 3

P/MSF

Q

(MSF)

ROS

P/MSF

Q

(MSF)

ROS

P/MSF

Q

(MSF)

ROS

Profit

Max.

129

72

135

I26

72

I23

122

73

151

SRM

64

130

47

88

I99

83

85

117

59

Naive

SRM

I02

98

I07

93

II4

76

92

113

73

Actual

00

100

100

100

1 00

100

100

100

100

Fellner

Band:

Upper

limit

I32

70

142

I38

54

I63

139

6o

I68

Lower

limit

II6

87

I23

I22

74

I44

II9

78

144

SALES MAXIMIZATION AND OLIGOPOLY 9I

SRM discussed is not concerned with inter-firm relations, but rather with the objective function of the individual firm. Recognizing that these approaches are not mutually exclusive, we have integrated the Baumol objective functions into the traditional oligopoly models. Hopefully this integrated model will be a better predictive model than either the SRM or the traditional oligopoly models. Using the Fellner model we have examined the effect of the SRM assumptions on the resulting price, output and profits of the firms. The limits of the integrated Fellner band are determined by the firms' highest and lowest SRM price rather than profit maximizing prices. Integration, therefore, introduces a different range of price-output equilibria; however, the objective function is economically quantifiable. The equilibrium is therefore identifiable. In such a model, in contrast to the SRM, firms may set other than sales maximizing prices as long as they stay within the pricing range.

The original Fellner (g-4) model establishes a profit maximizing price band between P1 and P2 (Figure 2).

Since we have used two SRM objective functions, each will be used in integration with the Fellner model. In what we have called the naive-SRM, the firm is assumed to maximize total revenue, i.e., operate at the point of unitary elasticity where MR = o. A Fellner-naive SRM band is established by the highest and lowest total revenue maximizing prices among the firms (P1' to P2" in Figure 2). The other SRM objective function is related to the longrun adjustments in the Baumol model. We have identified it as the SRM equilibrium and is specified by the intersection of the demand curve and the 'padded' AC curve (p = n: + AC). A Fellner-SRM band is established by the highest and lowest SRM prices among the firms (P1' to P2' in Figure 2).

With the Fellner-SRM model, a firm's prices will be less than the prices in the originial Fellner model for both firms. The range between P1 and P2 in the original model would be modified to P1' P2' (Fellner SRM) and P1' P2" (Fellner naive-SRM) in the integrated models. The firms' output would be Ql' and Q2' (Fellner-SRM) and Ql" and Q2" (Fellner naive- SRM). 15

The total market is larger in the integrated models than in the original Fellner model. Both Firm A's and Firm B's output increased. Firm B with its more elastic demand curve experiences a relatively larger increase in output in each integrated model. These results conform to those found in the original Fellner model.

Combined profits of firms in the integrated models are less than those 15 With the demand elasticities used in Fellner's original model, the range produced by

the integrated models will be narrower. However, if Firm A's demand became more elastic, and Firm B's demand becomes less elastic, the range of indeterminancy would widen until it exceeds that of Fellner's (g-4) model. The compromise price range will become narrower as Firm A's demand becomes less elastic and Firm B's demand becomes more elastic. In this case, the higher price would maximize Firm A's sales while the lower price would maximize Firm B's sales.


$

Firm A

$

Firm B

P2

e->

_____

>

___

~~~~~~~~~~AC r

A ~

~

~

A+

pi

I

-

Q

Q,

QjQ5

Q/t

Q

Q2

Q/t

FIGURE

2.


found with the original model. In the case of the Fellner-SRM model, profits for Firm A with the less elastic demand curve would increase with a higher profit constraint. Profits for Firm B with its more elastic demand curve would decrease with a higher profit constraint (assuming its price elasticity is greater than unity within the relevant bargaining range, P1' - P2'or or P2"). The converse holds for firms' profits assuming a lower profit constraint. The firm with the less elastic demand would lose profits, while the other firm would gain profits.

VI. RESULTS OF THE INTEGRATED ANALYSIS

A. The Expanded Fellner-SRM Model

Of all the integrated models examined the expanded Fellner model best fits the characteristics of the corrugated specialties industry hence it was selected for our analysis. As in the expanded Fellner model, this industry has equal cost firms (qualification I), product differentiation (qualification 3) and lack of coordination in advertising, product quality, and technology (qualification 4). The upper and lower bounds of the price band are determined by the SRM equilibria of each firm, which position is in turn determined by differences in the demand curves and the profit constraints. The result is a lower price band in which the firms bargain and usually lower profits and higher outputs compared with the original Fellner model. (Figure 2.)

We must differentiate between the SRM and the Fellner-SRM models. In the SRM models, each firm must be individually in SRM equilibrium. In the Fellner-SRM models if the upper and lower limits are set by the high and low profit constraint firm SRM equilibrium, respectively, then all firms can price off their SRM equilibrium as long as they stay within the pricing band.

The actual pricing range (Table V) in the corrugated specialties market is midway between the joint profit maximization range in the expanded Fellner model (P1 - P2, Figure 2) and the joint optimality range in the Fellner- SRM model (P1' - P2') 16 This integrated model establishes a joint sales revenue maximization range where a compromise price agreement might result. In such an agreement the firm with the comparatively lower profit constraint (i.e., Firms I and 3) would price above their SRM equilibria toward their profit maximizing equilibria. The firm with the comparatively higher profit constraint (i.e., Firm 2) influences the joint sales revenue maximization compromise agreement toward the profit maximizing equilibria of the lower profit constraint firms (Table V).

The Fellner-naive SRM price band encompassed all the observed prices in I967 and nearly does in I969. In I968 Firm 2 overpriced this band by $.84 while Firm 3 exceeded the band by $I.84. These small discrepancies might

16 The actual agreed range for pricing was about $2 for I967 and $4 for I968 and $5 for I 969.


TABLE V

COMPARISON OF TRADITIONAL, FELLNER, BAUMOL SRM, FELLNER-SRM EQUILIBRIUM, PRICING BANDS AND ACTUAL

PRICING BANDS

I967 I968 I969

Actual Prices Firm I 27.65 25.20 32.00 Firm 2 26.59 28.oo 26.68 Firm 3 26.I3 29.32 27.88

Profit-Maximizing prices Firm I 37.80 33.80 38.31 Firm 2 32.56 32.68 34.36 Firm 3 31.64 35.93 35.14

Naive SRM prices Firm I 28.30 25.90 3I.45 Firm 2 23.30 24-52 25.29 Firm 3 23.24 25.84 26.88

SRM prices Firm I I 9.50 20.I9 20.45 Firm 2 21.46 24.28 24.76 Firm 3 22.00 24.68 25-24

Chamberlin price P2 32.00 33.80 34.80

Fellner Band of Prices Upper limit 37.80 35.93 38.3I Lower limit 3I.64 32.68 34.36

Fellner-Naive SRM band Upper limit 28.30 25.90 31.45 Lower limit 23.24 24.52 25.29

Fellner-SRM Band of prices Upper limit 22.00 24.68 25.24 Lower limit I.950 20.19 20.45

be attributable to error. Clearly, the Fellner-naive SRM produced better predictions than other models tested.

B. Other Integrated Oligopoly Models

Other oligopoly models were integrated and their predictive capacity examined. The Cournot model could not be integrated in any manner which would provide useful and specific prices and outputs capable of predicting behavior in the corrugated specialties industry.'7 The remaining models were integrated; however, either the resulting models were not interpretable with respect to this market (Nutter) or the Fellner integrated models were clearly superior. 1 8

VII. CONCLUSIONS

The empirical analysis of the corrugated specialties industry resulted in predictions which were at variance with both the traditional oligopoly

17 C. Lackman and J. Gallo, 'An Integration of the Baumol-SRM into Oligopoly Theory', Working Paper, July 1971.

18 Supra, fn. 8.


models and the Baumol Sales Revenue Maximizing Model (SRM); that is, the price bands predicted by these models encompassed none of this industry's prices and outputs. The observed firms' prices and outputs fell midway between predicted SRM and profit maximizing equilibria. An exception in I969, when, for two of the firms, actual prices and outputs approached SRM predictions. The naive-SRM produced the closest estimates of the actuxal prices and outputs; however, significant discrepancies were still apparent. None of the firms exhibited the behavior expected of a monopolist.

Low predictive capacity on the part of the traditional oligopoly models indicated need to explore the integration of the more recent behavioral models of the firm, such as the SRM, into the reaction function of firms in an oligopoly in an attempt to find a model with greater predictive capacity. Integration of the SRM assumptions into several oligopoly models made by the Lackman and Gallo study was used to test the predicting capacity of the integrated models. Fellner-SRM integrated model produced somewhat better predictions, although the observed prices did not coincide with the joint optimality price band predicted by the integrated model. The Fellner- naive SRM produced price ranges encompassing most of the deserved prices.

The results indicate that the neoclassical, profit maximizing, oligopoly models, if integrated with assumptions providing for goals other than profit maximization in the firm's reaction function, probably would have better predictive capacity. A major unresolved question beyond the scope of this study is the extent to which profit-maximization models should be equity maximization models. Corollaries of this question are: Is the profit constraint of the Baumol model, equity maximization in disguise? What would be the relative predictive capacity of a traditional oligopoly with equity maximization and a SRM model casting the profit constraint in terms of equity maximization? Would these models become identical or would integration as attempted in this paper still produce improved predictions?

The authors were surprised to find the apparent superiority of the naive- SRM model over the Baumol-Sandmeyer interpretation. This may have resulted from the short time span studied. As indicated in the previous paragraph, we do not advocate disregarding the concept of the profit constraint and its significance in both SRM and traditional oligopoly models. We do encourage, however, anyone using an SRM in empirical work to subject their analysis to a naive-model test as we have done. They too may be surprised by the results.

RUTGERS UNIVERSITY, AND

UNIVERSITY OF CINCINNATTI

sales maximization and oligopoly

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