Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

292 INPUT PRICING AND EMPLOYMENT [CHAP. 13
(b)
(c)
A profit-maximizing firm will employ an input as long as the extra income from the sale of the output produced
by the input is larger than the extra cost of hiring the input. If the firm uses only one variable input,
the extra income or marginal revenue product of the input (MRP) is given by the marginal product of the
input (MP) times the marginal revenue of the firm (MR). If the firm is a perfect competitor in the product
market, price P ¼ MR and MRP equals the value of the marginal product (VMP).
Because the firm produces in stage II of production (where the law of diminishing returns operates), as more of
the input is used together, with fixed quantities of the other input(s), the MP declines. This causes the MRP to
decline as more units of the input are hired, even though MR remains constant. The declining portion of the
firm’s MRP schedule for the input is the firm’s demand schedule for the input.
13.2 For a perfectly competitive seller of commodity X and a perfectly competitive buyer of variable inputs
A and B, (a) indicate the profit-maximizing level of output of commodity X for the firm, (b) state the
condition for minimizing the cost of producing any level of output, (c) explain why MP a /P a ¼ 1/MC x ,
and (d ) state the condition for profit maximization for the firm.
(a)
(b)
(c)
The profit-maximizing level of output of commodity X is given by MR x or P x ¼ MC x and MC x is rising,
provided that at this level of output, P x 5AVC x (see Chapter 9).
MP a
P a
¼ MP b
P b
(See Chapter 8.)
When P a remains constant, an additional unit of input A will add P a to the firm’s total cost and contributes
MP a to the firm’s total product. Thus, P a /MP a is the change in the firm’s total costs per unit change
in its total product or output. This is the definition of marginal cost. Thus, P a /MP a ¼ MC x . Similarly,
P b /MP b ¼ MC x . So the best (least-cost) input combination to produce any level of output can be rewritten as
P a
MP a
¼ P a
MP b
¼ MC x
or
MP a
P a
¼ MP b
P b
¼ 1
MC x
(d ) In order for the firm to maximize its total profits, it must not only use the best (least-cost) input combination,
but it must also use the correct absolute amount of each input to produce its best level of output of the final
commodity. This occurs when
MP a
P a
¼ MP b
P b
¼ 1
MC x
¼ 1 P x
13.3 With reference to Fig. 13-7, indicate whether the firm is using the least-cost input combination and
producing its best level of output at points H and E.
Fig. 13-7