associationprofit maximization under monopolistic competition

8/13/2019 AssociationProfit Maximization Under Monopolistic Competition

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PROFITMAXIMIZATION UNDER MONOPOLISTICCOMPETITIONCurrent theory nominally recognizes that the individual firm maximizes profits, notthrough output adjustments alone, but also by determining price, the attributes of theproduct and selling effort. In this article the role of product variation and the interrelationsof these three variables are emphasized. Diagrammatics analogous to those customarilyused in price-output problems are developed and these are later employed to demonstratethat the incidence of relevant techno'logical innovations upon the quality of the productof the firm are independent of abnormal profits or of monopolistic advantage. Finally, thejoint determination of output, product and promotion is considered. Normally, the ex-ploitation of every profit possibility until marginal costs and receipts were equated wouldbe expected. Available funds may, however, be limited and certain policies may earnlosses unless more intensively pursued. In this case certain profit possibilities mustbe passed over in favor of others, the marginal net return on working capital will vary

with different employments, and as the amount of such funds available changes the mannerof their expenditure may differ markedly.Entrepreneurs must determine, inter alia, the price and output of theirproduct, its specifications, and the amount and type of selling effort.' Thelogic and illustrative diagrammatics of the entrepreneurial determinationof output and price are familiar. Similar methods, developed below, areapplicable to the problems of determining the optimum degree of dura-bility and of other product attributes. The procedure used is shown to berelevant to a consideration of the incidence of improved technology on

prices and quality. Finally, the joint determination of price, product,2 andpromotion3 is attempted. In the following discussion it is assumed that theproducts of immediate rivals are heterogeneous and are considered byconsumers to be close but not exact substitutes: they are differentiated onefrom another either because the product (or service) is tangibly different,or because it has been made to seem so, or because of location. The timeperiod relevant to the considerations of this paper is not the long run, buta short period in which there is, however, sufficient time for some ratherfundamental adjustments by entrepreneurs: the product of each firm is heldcapable of considerable modification, but the possibility of changing overto a radically different type of product with altogether dissimilar uses andattributes is excluded. The location of the enterprise is considered given,but distribution facilities or delivery services may be modified. The reason-ing throughout assumes that entrepreneurs desire profits, have perfectknowledge, and act rationally.

1 If the firm has a less than infinitely elastic demand schedule, and one assumes thatoutput and sales will be equated, then a price decision simultaneously determines output(or vice versa) and this theoretically comprises but one decision.2 Product throughout includes the material good plus all associated intangibles exceptthose resulting from promotion and the peculiar site of the place of sale. Thus differentia-tion due to location or advertising is excluded: all other types are included.' Promotion throughout includes all selling effort, whether advertising or personalsalesmanship. Although advertising is only a particular form of promotion it will be usedsynonymously.

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318 Stephen Enke [JuneI

The relationship of price, promotion, and product, as it might be viewedby management, is set forth in the schema in Figure 1. Management is seenconstantly attempting to alter, in its favor, the balance between total re-ceipts and costs. Output is assumed always to equal sales, and gross receiptsto be the product of price and sales. While promotion and piroduct affecttotal costs directly, they determine total receipts only indirectly via sales orprice.

TotalReceipts

FIGURE 1Theoretically, the relationship between any two of the variables indi-cated may be considered while the remainder are held temp-orarilyconstant.Suppose the rate of expenditure on promotion to be increased and that thisincreases the acceptance of the unchanged product by the public so thatdemand is increased in the schedule sens-eand a higher price or greater salescan be realized. If the entire effect is upon price, both sales and outputcosts will be unchanged; and the cost of promotion can readily be set againstincreased receipts. However, if price is unaltered, sales will increase and perunit costs will probably be changed; the additional advertising will then be

of advantage to the firm only if there are increasing returns with augmentedoutput sufficient to outweigh the cost of promotion. Whether the increaseddemand is exploited through sales or price will depend upon the magni-tudes and slopes of the marginal costs and receipts curves. A further possi-bility is that management does not wish to increase either the price or sales



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1941] Profit Maximization 321there is reason to suppose that, as the number of colors increases, totalcosts of producing the given output will increase at an increasing rate. Assales and output are assumed constant, the receipts and costs curves repre-sent either totals or averages.In this case the costs curve has been assumed convex from the x-axisand the receipts curve concave. fHad the reverse been assumed, there wouldhave been no stable equilibrium adjustment. Had we assumed a cost curve

n A.RA.R. - 1930

F F //. R .- ~~1940 14()

Lli~l

lxO INDEXOF QUALITY

FIGURE 3concavefrom below, with marginalcosts falling, there would be a deter-minate solutiononly if the concavityof the receiptscurvewere morepro-nounced.7

What will be the inicidence f an improvedtechnologyon costs, prices,andproducts?We mightsupposethatbecause he cost of makinga specificproduct s reduced,priceswill be reduced f competition s effective;or wemight argue that a more acceptableproduct, and one which previouslywould havecost more to fabricate,will now be sold at the customarypricelevel. For example,althoughtechnicalprogaressas continuedapace n theautomobile ndustryduring the last decade, the price of a certain repre-sentativecar in the low-pricefield was almost identicalin 1940 with that

'The preceding analysis ignores the rare product change which does not affect bothcosts and receipts in the same direction.



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322 Stephen Enke [Juneten years before, the benefits of scientific invention for the consumer havingtaken the form of an improved rather than a less expensive automobile.There has been controversy over whether this outcome is owing to theallegedly monopolistic position of the largest units in the industry, as evi-denced by a high rate of return on invested capital in certain cases, orwhether this entrepreneurial reaction is also compatible with keen compe-tition between rival producers.In Figure 3 variations in quality, expressed in terms of some hedonicindex,8 are measured along the X-axis: aggregate receipts (or price) aremeasured, together with aggregate costs (or average costs), on the Y-axis.Output and sales are assumed equal and constant. And again, unfortunately,all disturbing factors must be impounded in ceteris paribus.Hypothetical receipts and costs curves for Corporation X are shown for1930. The receipts curve is positively inclined, but, reflecting the decreas-ing marginal utility of additional quality, rises asymptotically. Aggregatecosts will also certainly tend to increase with additional quality, but at firstthe increase in costs will be moderate. As technical limits are reached, how-ever, each improvement (e.g., another mile per gallon without sacrificingother performance characteristics) will be realized only with increasingdifficulty and cost. Profits are shown as being maximized with a qualitydetermination of OX.9Ten years later in 1940, after further invention and innovation, theconsumer has modified his scale of values and now expects rather more forhis money, and accordingly the price which the market will pay for a givenquality has decreased. There is reason for supposing that this reductionwill be greatest for the lower qualities. The market places a premium onthose quality features (e.g., sealed-beam headlights, column gear-shifts,hydraulic drives, etc.) which are new or have not yet been universallyintroduced.10Mr. Jones is also eager to enjoy features formerly to be hadonly on the explensivecar of Mr. Bucks. But previous improvements, suchas safety glass, four-wheel brakes, and self-starters, are taken for grantedand all cars have them. We can ignore the factor of styling because the1940 fashions probably looked no better last year than the 1930 ones didthen. So we assume that the receipts curve becomes lower and more positivein inclination in 1940 than it was in 1930. Compared with the cost curve

8 Cf. A. T. Court's paper, 'Hedonic Price Indexes with Automotive Examples, pre-sented at a joint meeting of the American Statistical Association and the Econometric So-ciety in Detroit, Michigan, December 27, 1938. Perhaps this index might include milesper gallon, acceleration, retardation, maximum speed, ratio of sprung to unsprung weight,etc.9 The marginal curves are omitted to simplify the diagram. At OX the vertical distancebetween the receipts and costs curves is at a maximum.1 While all new models may have these features the majority of automobiles, whichare several years old at any given date, do not have them.



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1941] Profit Maximization 323in 1930, however, the cost curve in 1940 is also lower but probably lejspositively inclined. It is reasonable to suppose that there are diminishingreturns in the solution of any problem, particularly after it has been fairlysatisfactorily solved; and industrial invention is characteristicallyconcerned,not with making simple things easier, but hard things less difficult. The1940 adjustment (see Figure 3) shows that CorporationX has now selectedOX1 degree of quality, for this will realize maximum profits.It is clear from Figure 3 that, if a consumer representative were givenentrepreneurial authority subject to the limitation that price must not beless than cost, the quality determination in the 1940 case would again beOX1 and the price and costs would be Oy, thus eliminating profits. Thereceipts curve is by definition an indifference curve for the consumer; 1similarly, if prices must equal costs, the costs curve becomes an indifferencecurve from the point of view of the corporation. The distance between thecurves might be likened to a surplus, i.e., cash profits for the corporation,if the price exceeds Oy, or free utility for the consumers if the price fallsshort of 0Y1. If we assume that the corporation always charges the maxi-mum that it can for each degree of quality, its determination of qualityper se is of no consequence for the consumer. Injury to the consumer, in sofar as it may exist, would seem to result from the fact that the corporationcan command a price in excess of costs for each several quality: this may bedue to peculiarly low costs or to limited rivalry in the industry.The optimum determination of quality will depend upon the twist giventhe curves by each new innovation and not upon the resulting mean changein their vertical positions, although the latter will of course determineprices, costs and profits, once the degree of quality is known. If we canassume the receipts curve to become more positive and the cost curve lesspositive, then, irrespective of what happens to price, costs, and profits,technical progress will result in increased quality of product. lThe newprice (0Y1) may be greater than, less than, or equal to the old pirice (OY).Whether or not relevant technological advances result in an improvedproduct has nothing to do with the existence of monopoly elements, orabnormal profits or losses, but depends upon the twists given the receiptsand costs curves.12The product will be improved if the receipts curve be-comes more positively inclined relatively to the costs curve (or the latterless positively inclined relatively to the former). For a change in quality it

The combination of price and quality is a matter of indifference to the consumer,provided it can be represented by a point on the receipts curve. The position of this curveis, of course, based in large measure upon the valuation placed by the consumer on substi-tute goods and the prices charged for them. A reduction in the price of a rival makewill lower the receipts curve of Corporation X, particularly over the range of qualityequivalent to that of the competitor's product.

2 What happens to price is another matter. For example, lessened competition mightraise the entire receipts curve in 1940. Such possibilities have been disregarded.



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324 Stephen Enke [Juneis not necessary, as supposed above in the automobile case, that the changesin slopes be opposite in an absolute sense. The more general requirementis simply that the changes in slopes be relative.

IVFinally, if the entrepreneur knows the relations of marginal costs andreceipts to variations in (1) output and sales, (2) the quality of the prod-uct, and (3) the extent and kind of selling effort, this knowledge must beemployed in the simultaneous determination of these three strategic var-iables.As a general principle the entrepreneur will, taking account of his own

means . . . push the investment of capital in his business in each severaldirection until what appears in his judgment to be the outer limit, ormargin, of profitableness is reached '3 To give concreteness, we can con-ceive of the management of an existing enterprise, controlling a certainfund of circulating capital, deciding in which of the three directions men-tioned above it will invest. Of course there are many alternative means bywhich these ends may be sought: there may be M ways of augmenting out-put, N ways of improving the product, and 0 ways of increasing promotion.However, just as we do not usually bother about the less efficient ways inwhich the factors can be combined to give a certain output, so in this caseare we concerned only with the most economical way of improving theproduct or of increasing promotion by a given amount.14The marginal net return on an additional dollar of working capital in-vested to augment output (MNPo) can be readily calculated if the custo-mary relations of marginal costs and receipts to changes in output and salesare known. The increase in output resulting from an additional dollarexpended will be the reciprocal of the marginal cost at that output range,and the value of this output will be given by the prevailing marginalrevenue: for the investment to be profitable the increment of expenditure(or the cost of the last unit produced) must be recovered.15If marginalcosts increase soon and rapidly, and the price elasticity of demand is ap-proaching zero, the marginal output possible for each increment of expendi-ture will be decreasing and the revenue from the extra output will be fall-ing: thus, in time, additional investment for output will no longer be re-coverable.16In exactly the same way working capital may be expended to enhancethe acceptance of the product by altering its specifications. Given the rela-

13 Alfred Marshall, Principles of Economics, 8th ed., Book V, iv, 4.14 In each case a longer run envelope curve is fitted to the subsidiary relationships.16 Symbolically, MNPo = (MRo/MCo) -I where MR. and MC. are marginal costs andreceipts for the appropriate output. It follows that MNPO is zero when MC. and MR. areequal.16 Interest on the investment can be included as a cost.



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326 Stephen EnkeINPS) would at first be negative, but later would rise to a maximumpositive value and then commence to descend.20In these instances a certain

minimum investment, sufficient to cancel earlier losses, must be made beforethere can be net additioins to profits, and adjustments will necessarily bediscrete instead of continuous. Thus in Figure 4 we have supposed thefirm to be in equilibrium when spending $700,000 for output, $300,000improving the piroduct,and $1,000,000 for promotion. Had the total capitalavailable for investment been only $700,000, this would all have gone foroutput: investment in another direction would be unprofitable unless on ascale sufficient to offset initial losses incidental to improving the product orundertaking selling effort. If various policies can prove profitable onlywhen supported by a certain minimum rate of expenditure (because themarginal net profit will otherwise be negative), then the availability toeach firm of adequate surplus capital furndsbecomes important.It is recognized by the writer that these different curves are in practiceinterrelated and that any change in the determination of one variable maychange the positions of the other two curves. In the simple case here con-sidered the range of variation is of course far too great. For small changesin any one variable, however, this interdependence might frequently beignored. Another difficulty is that the increased receipts resulting from animprovement in the product, or from promotion, may not arise from higherprices being charged but from increased sales-which in turn means achange in output, unit costs, and price. Notwithstanding the many diffi-culties, this theoretical procedure illustrates the logic of the entrepreneurialdetermination of oiutput,product and promotion. It also indicates the limitedrole which output adjustments may play in profit maximization under con-ditions of monopolistic competition.

STEPHEN ENKEHarvard University20It will cross the X-axis twice--when MC equals MR-but only in the second casewill the equilibrium be stable. See Curve S, Figure 4.

associationprofit maximization under monopolistic competition

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