Предыдущая страница реферата | 1  2  3  4  5  6  7 | Следующая страница реферата

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.

2. 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.

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 OQm will this area have reached its maximum size—profits will encompass the entire area TKMP.

But at output OQm 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 OQt as well as at OQm. But at OQt the firm obtains only the net loss (negative profit) represented by heavily shaded area RTC. A move in either direction from point Qt 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 OQt 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.

3. Application: Pricing and Cost Changes

The preceding theorem permits us to make a number of predictions about the behavior of the profit-maximizing firm and to set up some normative
"operations research" rules for its operation. We can determine not only the optimal output, but also the profit-maximizing price with the aid of the demand curve for the product of the firm. For, given the optimal output, we can find out from the demand curve what price will permit the company to sell this quantity, and that is necessarily the optimal price.
In Figure 1, where the optimal output is OQm we see that the corresponding price is QmPm where point Pm is the point on the demand curve above Qm
(note that Pm is not the point of intersection of the marginal cost and the marginal revenue curves).

It was shown in the last section of Chapter 4 how our theorem can also enable us to predict the effect of a change in tax rates or some other change in cost on the firm's output and pricing. We need merely determine how this change shifts the marginal cost curve to find the new profit- maximizing price-output combination by finding the new point of intersection of the marginal cost and marginal revenue curves. Let us recall one particular result for use later in this chapter—the theorem about the effects of a change in fixed costs. It will be remembered that a change in fixed costs never has any effect on the firm's marginal cost curve because marginal fixed cost is always zero (by definition, an additional unit of output adds nothing to fixed costs). Hence, if the profit-maximizing firm's rents, its total assessed taxes, or some other fixed cost increases, there will be no change in the output-price level at which its marginal cost equals its marginal revenue. In other words, the profit-maximizing firm will make no price or output changes in response to any increase or decrease in its fixed costs! This rather unexpected result is certainly not in accord with common business practice and requires some further comment which will be supplied presently.

4. Extension: Multiple Products and Inputs

The firm's output decisions- are normally more complicated, even in principle, than the preceding decisions suggest. Almost all companies produce a variety of products and these various commodities typically compete for the firm's investment funds and its productive capacity. At any given time there are limits to what the company can produce, and often, if it decides to increase its production of product x, this must be done at the expense of product y. In other words, such a company cannot simply expand the output of x to its optimum level without taking into account the effects of this decision on the output of y.

For a profit-maximizing decision which takes both commodities into account we have a marginal rule which is a special case of Rule 2 of
Chapter 3:

Any limited input (including investment funds) should be allocated between the two outputs x and у in such a way that the marginal profit yield of the input, i, in the production of x equals the marginal profit yield of the input in the production of y.

If the condition is violated the firm cannot be maximizing its profits, because the firm can add to its earnings simply by shifting some of г out of the product where it obtains the lower return and into the manufacture of the other.

Stated another way, this last theorem asserts that if the firm is maximizing its profits, a reduction in its output of x by an amount which is worth, say, $5, should release just exactly enough productive capacity,
C, to permit the output of у to be increased $5 worth. For this means that the marginal return of the released capacity is exactly the same in the production of either x or y, which is what the previous version of this rule asserted.3

Still another version of this result is worth describing: Suppose the price of each product is fixed and independent of output levels. Then we require that the marginal cost of each output be proportionate to its price, i.e., that [pic]where Px and MCX are, respectively, the price and the marginal cost of x, etc.

In this discussion we have considered only the output decisions of a profit-maximizing firm. Of course, the firm has other decisions to make. In particular, it must decide on the amounts of its inputs including its marketing inputs (advertising, sales force, etc.). There are similar rules for these decisions, as discussed in Chapter 11 and in Chapter 17, Section
6. The main result here is that profit maximization requires for any inputs г and j

[pic]where MPt represents the marginal profit contribution of input г and Pi is its price, etc.

Having discussed the consequences of profit maximization, let us see now what difference it makes if the firm adopts an alternative objective, one to which we have already alluded — the maximization of the value of its sales (total revenue) under the requirement that the firm's profits not fall short of some given minimum level.

Рекомендуем скачать другие рефераты по теме: школьные рефераты, скачати реферат, тесты бесплатно.



Предыдущая страница реферата | 1  2  3  4  5  6  7 | Следующая страница реферата

Поделитесь этой записью или добавьте в закладки