Alternative Objectives of the Firm

There is no simple method for determining the goals of the firm (or of its executives). One thing, however, is clear. Very often the last person to ask about any individual's motivation is the person himself (as the psycho­analysts have so clearly shown). In fact, it is common experience when interviewing executives to find that they will agree to every plausible goal about which they are asked. They say they want to maximize sales and also to maximize profits; that they wish, in the bargain, to minimize costs; and so on. Unfortunately, it is normally impossible to serve all of such a multiplicity of goals at once.

For example, suppose an advertising outlay of half a million dollars minimizes unit costs, an outlay of 1.2 million maximizes total profits, whereas an outlay of 1.8 million maximizes the firm's sales volume. We cannot have all three decisions at once. The firm must settle on one of the three objectives or some compromise among them.

Of course, the businessman is not the only one who suffers from the desire to pursue a number of incompatible objectives. It is all too easy to try to embrace at one time all of the attractive-sounding goals one can muster and difficult to reject any one of them. Even the most learned have suffered from this difficulty. It is precisely on these grounds that one great economist was led to remark that the much-discussed objective of the greatest good for the greatest number contains one "greatest" too many.

It is most frequently assumed in economic analysis that the firm is trying to maximize its total profits. However, there is no reason to believe that all businessmen pursue the same objectives. For example, a small firm which is run by its owner may seek to maximize the proprietor's free time subject to the constraint that his earnings exceed some minimum level, and, indeed, there have been cases of overworked businessmen who, on medical advice, have turned down profitable business opportunities.

It has also been suggested, on the basis of some observation, that firms often seek to maximize the money value of their sales (their total revenue) subject to a constraint that their profits do not fall short of some minimum level which is just on the borderline of acceptability. That is, so long as profits are at a satisfactory level, management will devote the bulk of its energy and resources to the expansion of sales. Such a goal may, perhaps, be explained by the businessman's desire to maintain his competitive posi­tion, which is partly dependent on the sheer size of his enterprise, or it may be a matter of the interests of management (as distinguished from shareholders), since management's salaries may be related more closely to the size of the firm's operations than to its profits, or it may simply be a matter of prestige.

In any event, though they may help him to formulate his own aims and sometimes be able to show him that more ambitious goals are possible and relevant, it is not the job of the operations researcher or the economist to tell the businessman what his goals should be. Management's aims must be taken to be whatever they are, and the job of the analyst is to find the conclusions which follow from these objectives—that is, to describe what businessmen do to achieve these goals, and perhaps to prescribe methods for pursuing them more efficiently.

The major point, both in economic analysis and in operations-research investigation of business problems, is that the nature of the firm's objec­tives cannot be assumed in advance. It is important to determine the nature of the firm's objectives before proceeding to the formal model-building and the computations based on it. As is obviously to be expected, many of the conclusions of the analysis will vary with the choice of objec­tive function. However, as some of the later discussion in this chapter will show, a change in objectives can, sometimes surprisingly, leave some significant relationships invariant. Where this is true, it is very convenient to find it out in advance before embarking on the investigation of a specific problem. For if there are some problems for which the optimum decision will be the same, no matter which of a number of objectives the firm happens to adopt, it is legitimate to avoid altogether the difficult job of determining company goals before undertaking an analysis.

The Profit-Maximizing Firm

Let us first examine some of the conventional theory of the profit-maximizing firm. In the chapter on the differential calculus, the basic marginal condition for profit maximization was derived as an illustration. Let us now rederive this marginal-cost-equals-marginal-revenue condition with the aid of a verbal and a geometric argument.

The proposition is that no firm can be earning maximum profits unless its marginal cost and its marginal revenue are (at least approximately) equal, i.e., unless an additional unit of output will bring in as much money as it costs to produce, so that its marginal profitability is zero.

It is easy to show why this must be so. Suppose a firm is producing 200,000 units of some item, x, and that at that output level, the marginal revenue from x production is $1.10 whereas its marginal cost is only 96 cents. Additional units of x will, therefore, each bring the firm some 14 cents = $1.10 — 0.96 more than they cost, and so the firm cannot be maximizing its profits by sticking to its 200,000 production level. Similarly, if the marginal cost of x exceeds its marginal revenue, the firm cannot be maxi­mizing its profits, for it is neglecting to take advantage of its opportunity to save money—by reducing its output it would reduce its income, but it would reduce its costs by an even greater amount.

C

We can also derive the marginal-cost-equals-marginal-revenue proposi­tion with the aid of Figure 1. At any output, OQ, total revenue is rep­resented by the area OQPR under the marginal revenue curve (see Rule 9 of Chapter 3). Similarly, total cost is represented by the area OQKC immediately below the marginal cost curve. Total profit, which is the dif­ference between total revenue and total cost is, therefore, represented by the difference between the two areas—that is, total profits are given by the lightly shaded area TKP minus the small, heavily shaded area, RTC. Now, it is clear that from point Q a move to the right will increase the size of the profit area TKP. In fact, only at output OQ_m will this area have reached its maximum size—profits will encompass the entire area TKMP.

	OUTPUT

But at output OQ_m marginal cost equals marginal revenue—indeed, it is the crossing of the marginal cost and marginal revenue curves at that point which prevents further moves to the right (further output increases) from adding still more to the total profit area. Thus, we have once again estab­lished that at the point of maximum profits, marginal costs and marginal revenues must be equal.

Before leaving the discussion of this proposition, it is well to distinguish explicitly between it and its invalid converse. It is not generally true that any output level at which marginal cost and marginal revenue happen to be equal (i.e., where marginal profit is zero) will be a profit-maximizing level. There may be several levels of production at which marginal cost and marginal revenue are equal, and some of these output quantities may be far from advantageous for the firm. In Figure 1 this condition is satisfied at output OQ_t as well as at OQ_m. But at OQ_t the firm obtains only the net loss (negative profit) represented by heavily shaded area RTC. A move in either direction from point Q_t will help the firm either by reducing its costs more than it cuts its revenues (a move to the left) or by adding to its revenues more than to its costs. Output OQ_t is thus a point of minimum profits even though it meets the marginal profit-maximization condition, "marginal revenue equals marginal cost."

This peculiar result is explained by recalling that the condition, "mar­ginal profitability equals zero," implies only that neither a small increase nor a small decrease in quantity will add to profits. In other words, it means that we are at an output at which the total profit curve (not shown) is level—going neither uphill nor downhill. But while the top of a hill (the maximum profit output) is such a level spot, plateaus and valleys (minimum profit outputs) also have the same characteristic—they are level. That is, they are points of zero marginal profit, where marginal cost equals marginal revenue.

We conclude that while at a profit-maximizing output marginal cost must equal marginal revenue, the converse is not correct—it is not true that at an output at which marginal cost equals marginal revenue the firm can be sure of maximizing its profits.