SALES MAXIMIZATION VS. PROFIT MAXIMIZATION: ARE THEY INCONSISTENT?

BEVARS DUPRE MABRY BOWLING GREEN STATE UNIVERSITY

What do the leaders of large corporations attempt to maximize-revenue (sales), growth, a target rate of return, or a utility function representing a combination of goals?’ In recent years the appropriateness of the profit- maximizing assumption as a description of the goal sought by leaders of large businesses has been subjected to question. The Baumol challenge to profit maximization, utilizing a well-developed alternative hypothesis of revenue (sales) maximizing, has been widely publicized. In the Baumol model total sales are viewed as a function of output, prices and advertising, and sales increase monotonically as advertising increases.’

To accept.the sales maximizing hypothesis, however, it must be shown that sales maximization behavior is inconsistent with profit maximization behavior. In other words, firms that pursue sales maximization must do so at the expense of maximum profits. Proponents of revenue maximization must show, not that increasing sales occur along with increasing profits- for this may mean that increasing sales are a means to increase profits-but that increasing sales occur at the expense of higher profits.’ Since Baumol argues that the sales maximization goal applies both in the short-run and in the long-run, the inconsistency of sales and profits in both periods must be demon~trated.~

In the following pages, theoretical arguments are presented to demon- strate how sales maximization and profit maximization can be consistent goals of oligopoly-type firms. Next, a related hypothesis-target rate of return maximization-is briefly compared with that of sales maximization. Then,

‘See 111, 121, C31, 161, 181, or 191 respectively. ‘Baumol demonstrates this in the mathematical no te of Chapter 7 of the 1959 edition of his

Bvsiness Behavior, and proof of this is graphically illustrated by R. L. Sandmeyer [ l j , pp. 1073-801. In the 1967 revision Baumol substitutes a sales growth maximization objective for the simple sales maximization goal.

’David Siders and myself have shown that among 120 of the largest American industrial cor- porations, strong empirical evidence exists that suggests that increasing sales lead to increasing profits. C9. pp. 367-771.

‘In the 1959 edition, he asserted, “I believe that sales maximization is management’s objective in the longrun as well as in the short.” I l , p. 521. In a later article, he r&ms his hypothesis “as a static characterization of the current facts of oligopolistic business operation” but in a growth context he modifies the hypothesis to one of maximization of the rate of growth of sales. Also, his profit constraint is reinterpreted in terms of some optimum, but not maximum, growth rate of profit which is consistent with the maximum rate of growth of sales, for “beyond some point profits compete with sales.” He concludes that the logic behind the results of the static and growth models are the same 12, pp. 1078-871.

In terms of this revision, in order to accept the sales growth maximization hypothesis, it must be demonstrated, and not merely asserted. that some higher level of profits md higher rate of profit growth has been foregone in order to obtain a higher rate of growth of sales. Although the analpis presented in this article is primarily concerned with the static model, it has implications for a growth model. See Part 11 below.

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MABRY: SALES MAXIMIZATION 15s

an empirical study that has been cited as support for the static revenue max- imization model is examined and some weaknesses in the reasoning are identified. Finally, conclusions are presented.

I

Two theoretical arguments, one a short-run and the other a long-run argu- ment, can be offered to show that the hypotheses of sales and profit max- imization can be perfectly consistent; in fact, sales maximization will be shown to be a means to secure maximum profits. In Figure 1 assume that an oligopoly firm is faced with a kinked demand curve, A&. The study by Hitch and Hall of British firms [4, pp. 114-18, 120-22, 1251 suggests that such an assumption is not at all unreasonable. Under ARI, the firm is pro- ducing O Q l , and at this output, average total cost is declining. This tinn and others in the industry like it will be under no great pressure to increase price as industry demand increases. The result is a shift to the right in the firm’s demand curve, and price does not change. Certainly, the firm is utiliz- ing maximizing behavior, for MC can continue to intersect the vertical seg- ment of MR as MR moves to the right with AR. In fact, average costs are declining as demand shifts to the position of A& and unit profits are increas-

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ing. However, unit profits may decline as average costs rise when demand shifts to AR,. Pressure to increase price may begin to be felt in the industry as average costs begin to rise when output expands from OQ. to OQI, but profit maximizing behavior continues to be consistent with expanding sales until demand ARI is reached, provided there is no industry agreement in the meantime to raise price?

This analysis may be applied to a monopoly or oligopoly and interpreted as a long-run phenomenon. Price in the long-run may be regarded as the target price, and the ATC curve may be regarded as a long-run cost curve. A higher price than the one so chosen would encourage entry by increasing long-run profits to such an extent that firms are attracted into the industry, and thereby a sharp increase in the elasticity of the demand curve of the firm above the chosen price would occur. In such a situation, at the point of the target price a kink develops, and the above analysis, with increasing demand, then follows.

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k MR

FIGURE 2

MC’ J I

MR,

‘If i n w i n g factor costs accompany expanding sales, ATC and MC may shift upward with increasing sales. It is possible that the new ATC when combined with the new AR may yield less total profit than was yielded before demand increased and factor prices rose; nevuthclas, profit maximizing behavior has still been followed with the sales expansion.

MABRY: SALES MAXIMIZATION 157

Another approach can be used to demonstrate that long-run profit max- imization is consistent with sales maximization even though in the short-run it may not be. Consider the diagram in Figure 2. Assume the firm is first producing in the short-run and is operating on ATC, and faces MR,. Output is.0Q. The firm may recognize that if it can increase sales, the larger sales will justify the construction of larger, more efficient facilities which in turn will reduce costs. There are Iisks associated with building facilities of larger scale, but increased sales will minimize these risks. Therefore, the firm undertakes a sales promotion campaign. This, of course, raises both the short-run and long-run average and marginal cost curves but MR also shifts to the right. It does not make sense to undertake a sales promotion cam- paign and then to withhold output when increased demand is generated. Consequently, in anticipation of constructing or completing the larger facil- ities represented by ATC,, the firm may attempt to supply OQc output from its smaller plant represented by ATC',, even though it could maximize short- run profit by producing OQ,. However, when the enlarged facilities are placed into operation, production will occur in 2 plant represented by ATCI and sales will be permitted to expand to O e s . In the short-rim, OQI is not a profit-maximizing output when ATG exists, and it very well may appear that sales maximization is the dominant goal. Yet, in the long-run, the in- creased safes permit costs to be reduced and unit and total profits to be increased.

I 1

A variation of the Baumol hypothesis is that firms may seek to maximize sales with the profit constraint being a target rate of return of profit on investment instead of the fixed dollar amount of profit as assumed by Baumol in his static model;* i.e., a firm may seek to earn a target rate of return of ten percent on investment. If sales and investment increase: then profits will also increase. Even though profits yielding a higher rate of return might be earned with a policy of high price, low advertising outlays, and smaller assets, a policy that will only permit the target rate to be earned is chosen in order to expand sales. However, a profit maximizer is not so naive as to imagine he is better off with a higher ratio of profits to assets when the firm is small than when it is large. It is not just a target-rate of return which is sought.

A profit constraint in the form of a target rate of return has been pro- pounded by Lanzillotti 16, pp. 923, 9291. However, Alfred 'E. Kahn 15, pp. 671-761 and Gardiner C. Means 112, pp. 232-481 analyze this phenomenon and make a convincing case that the target rate is in reality a long-run profit maximizing rate set sufficiently low to discourage potential entry.' Indeed, 'In his growth model, he replaces the fixed level of profits with a profit growth rate consistent

with a maximum sales growth rate. The profit growth rate may be interpreted as a target rate of return. In either case, we are faced with the same problem of distinguishing between means and ends. 'The effect of potential entry on the demand curve of an oligopoly &I wps d i s d in k-

tion I.

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even if the target-rate hypothesis is typical of the behavior of oligopolists, it would be difficult to verify that this is in accord with the sales maximiza- tion hypothesis. To establish that a sales maximization hypothesis is being pursued would require (1) a demonstration that the firm could have earned a higher rate of return but did not in order to expand sales, and (2) that any potential higher rate of return was not so high as to induce entry. Unless these points can be established, saIes maximization as an objective cannot be accepted over the long-run profit maximization explanation of Means and Kahn. The burden of proof seems to lie upon the proponents of the sales maximization hypothesis.

Furthermore, given a fixed target rate of return, to the extent that sales expand without an increase in investment, profits need not increase. Sim- ilarly, a contraction in demand that reduces sales, assuming that the target rate of return is a minimum profit constraint, might induce behavior to main- tain profits at this minimum level, assuming that investment is fixed in the short-run. Sales can vary without changes in profits, and this can be con- sistent with profit maximizing behavior if the target rate of return is con- sistent with long-run profit maximization.

111

Empirical support for the Baumol hypothesis has been offered by McGuire, Chiu, and Elbing [ l l , pp. 753-611, who report a series of correlation tests between executive incomes and sales, between executive incomes and profits, and between lagged relationships of incomes and sales and profits. The motive behind this test lies in an assertion by Baumol that “executive salaries appear to be far more closely correlated with the scale of operations of the firm than with its profitability” [ 1, p. 461. McGuire, Chiu, and Elbing there- fore sought to determine if this was true. Finding that sales and executive incomes do correlate more highly than do profits and executive incomes, they have concluded that the Baumol thesis is supported [ 11, p. 7581. Their conclusion, however, does not follow from their findings; a higher correla- tion between executive incomes and sales than between income and profits does not imply that executives seek to maximize sales rather than profits.

The McGuire study computes executive income for 45 of the largest 100 industrial corporations in the United States from 1953 through 1959. Execu- tive incomes were obtained from annual reports published in Business Week and wherever stock contributions constituted a part of the executive’s in- come, it was evaluated at the market price as of December 31 of the re- spective year. Gardiner C. Means [ 12, pp. 281-861 reports that two of the leading forms of executive incentive compensation are the following:

1. The cash bonus system where the amount of the bonus is determined by setting aside a s u m equivalent to a fixed percentage of the dividends paid on common stock-say 60/0-each year for top management. 2. The stock-option plan which rewards executives by bestowing upon them gratis company stock or by giving them the option to purchase stock at less than market value.

MABY: SALES MAXIMIZATION 1 S9

There are other bonus systems, but these are sufficient to cast doubt on the significance of the correlation findings. In either of the above cases, execu- tive compensation is likely to be a linear function; in case (1) it will be a linear function of dividends; in case (2) it will be a linear function of what- ever basis is used to distribute the stock options. The constant in the linear equation is the base salary of the executive and the slope value is his bonus.

Assume plan (1) is being used to reward executives. The issuance of new stock is a common practice in American industry and provides an increasing volume of outstanding shares of common stock for most large American firms. It is well-known that American firms pursue a dividend payment policy that seeks to stabilize the rate of dividends paid per unit of stock. This does not say that the dividend payment will be constant, but that it will fluctuate less than corporate earning. Therefore, an increasing quantity of common stock and stable dividend payments assure an increasing amount of total dividends. If the cash bonus fund is a fixed percent of total dividends, it too will increase. As Moody’s data shows, sales have had a strong tendency to trend upward since 1953 for most corporations. However, this is less true of profits.8 Some profits trend upward, others are steady, arid others trend downward. Therefore, sales and executive compensation both tend to have a strong upward bias, but profits may fluctuate widely in both directions. As a result, sales and executive incomes can be expected to have a higher correlation than profits and executive incomes. This is not due to a causal relationship between sales and executive income, but rather to an upward trend bias in the data being correlated. Indeed, executives--like workers, merchants, and college professors-do not like to have their incomes re- duced. Consequently, the type of cash-bonus plan tied to an upward moving base is exactly the type of program that a rational person is likely to con- struct to protect his earning position. However, the income is no more re- lated to sales than to profits. Indeed, to the extent that the capitalization of a firm is expanded through retained earnings which may increase the market value of the stock and its dividend payment, there is more reason to suppose the bonus plan is related to long-run profits than tan sales. In addi- tion, executives may not be punished for failing to earn satisfactory profits by having their incomes cut. Discharge or replacement may be the usual method and a far more satisfactory one. So, a simple correlation between profits and income will not reveal what may be a far more fundamental motive to earn profits-that of maintaining one’s job.

Now let us assume that executive bonuses are based on plan (2)-the stock-option plan. Assume that executives have constructed a relatively stable stock-option bonus plan. It may even fluctuate mildly up and down with profits. Yet, so long as the market value of stock reflects an upward trend, the weighted value of the stock acquired through all of these plans will also tend to have an upward trend. Given the upward trend of sales, and to the

‘See C9. pp. 371-731.

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extent that the value of stock on December 31 does not move in line with profits of that year, we should expect executive compensation so valued to correlate more strongly with sales than with profits, even though there is no necessary relation between sales and executive income.

Therefore, unless we know specifically the type of bonus plans on which executive compensation is based, we cannot conclude that the correlation between sales and income is meaningful. Particularly, we cannot draw from such a correlation the inference that because sales and profits differ sig- nificantly in their correlation with income, the sales maximization hypothesis is therefore supported. Such a difference in correlation neither supports nor refutes the Baumol hypothesis.

IV

The conclusions from the paper are as follows: 1. Under certain conditions, it can be demonstrated theoretically that

profits and sales can move inversely to one another but that profit maximiz- ing behavior is nevertheless still being pursued.

2. If target pricing is practiced in order to earn a target rate of return, it can be shown that this practice is consistent with long-run profit maximizing behavior. Yet, under target pricing, sales can vary without corresponding changes in profits.

3. A higher positive correlation between sales and executive incomes does not support the sales maximization hypothesis. There is strong reason to believe that biased forces in the forms of executive compensation produce this result. Upon analysis, the validity of the correlations and the conclusions drawn from them are open to question.

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REFERENCES William J. Baumol. BIdJinCJJ Bebauior. Valve and Growth. New York 1959. 1967.

, “On the Theory of Expansion of the Firm,” Am. EEon. Rcv., Dec. 1962, 52, 1078-87. William Fellner, Proability and Profit. Homewood 1965. R. L. Hall and C. J. Hitch, “Price Theory and Business Behavior,” Oxford Stvdicr in #6r Price Mechanism, eds. T. Wilson md P. W. S. Andrcws. Oxford 1951.

A. E. Kahn, “pricing Objectives in Large Companies: Comment,” Am. Ecor. R w , Sept. 1959, 49, 670-78. R. P. Luuillotti, “Priaag Objectives in Large Companies.” Am. &on. Rev., Dec. 1958, 48, 920-40.

, Pricing Objectives in Large Companies: Reply,” Am. Econ. Rcv., Sept. 1959, 49. 679-86. HI& Leibmstein, Economic Tbeory and Organiuttiond Analysir. New Yo& 1960. &van D. Mabry and David L. Siders, “An Empirical Test of the saks Mnrimizntion Hypothesis,” Sonrbcrn ECOR. /ow. , Jm. 1967.33. 367-77. Robin Marris, ‘Tbe Economic Tbcory of ManaKerial Capitalism. New York 1964. J. W. McGuire, J. S. Y. Chiu, and A. 0. Elbing. “Executive Incomes. Sales and Profits,” Am. Econ. Rcv., Sept. 1962,52, 753-61. Gardiner C. Means. Pricinz Powcr and tbr Pnblic Interest. New York 1962. R. L. Sandmeger, “Baumol’s Sales-Maximization Model: Comment,” Am. am. RH., &. 1964. s4, 1073-ao.