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.
5. Price-Output Determination: Sales Maximization
Saks maximization under a profit constraint does not mean an attempt
to obtain the largest possible physical volume (which is hardly easy to
define in the modern multi-product firm). Rather, it refers to maximization
of total revenue (dollar sales) which, to the businessman, is the obvious
measure of the amount he has sold. Maximum sales in this sense need not
require very large physical outputs. To take an extreme case, at a zero
price physical volume may be high but dollar sales volume will be zero.
There will normally be a well-determined output level which maximizes
dollar sales. This level can ordinarily be fixed with the aid of the well-
known rule that maximum revenue will be obtained only at an output at which
the elasticity of demand is unity, i.e., at which marginal revenue is zero.
This is the condition which replaces the "marginal cost equals marginal
revenue" profit-maximizing rule.
But this rule does not take into account the profit constraint. That
is, if at the revenue-maximizing output the firm does, in fact, earn enough
or more than enough profits to keep its stockholders satisfied then it will
want to produce the sales-maximizing quantity. But if at this output
profits are too low, the firm's output must be changed to a level which,
though it fails to maximize sales, .does meet the profit requirement.
We see, then, that two types of equilibrium appear to be possible: one
in which the profit constraint does not provide an effective barrier to
sales maximization, and one in which it does. This is illustrated in Figure
2, which shows the firm's total revenue, cost, and profit curves as
indicated.
The profit- and sales-maximizing outputs are, respectively, OQP and
OQ,. Now if, for example, the minimum required profit level is OP\, then
the sales-maximizing output OQ, will provide plenty of profit, and that is
the amount it will pay the sales maximizer to produce.
His selling price will then be set at Q,R,/OQ,. But if the producer's
required profit level is OP2, output OQ,, which yields insufficient profit,
clearly will not do. Instead, his output will be reduced to level OQC,
which is just compatible with his profit constraint.
It will be argued presently that in fact only equilibrium points in
which the constraint is effective (OQC rather than OQ,) can normally be
expected to occur when other decisions of the firm are taken into account.
The profit-maximizing output, OQP, will usually be smaller than the
one which yields either type of sales maximum, OQ, or OQC. This can be
proved with the aid of the standard rule that at the, point of maximum
profit marginal cost must equal marginal revenue. For marginal cost is
normally a positive number (we can't usually produce more of a good for
nothing). Hence marginal revenue will also be positive when profits are at
a maximum, i.e., a further increase in output will increase total sales
(revenue). Therefore, if at the point of maximum profit the firm earns more
profit than the required minimum, it will pay the sales maximizer to lower
his price and increase his physical output.
2. Перевод текста с языка оригинала
Фирма и её цели
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