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

294 INPUT PRICING AND EMPLOYMENT [CHAP. 13
(c)
It pays for this firm to expand its use of input A as long as the MRP a (i.e., the addition to its TR) exceeds P a
(i.e., the addition to its TC) and until the MRP a ¼ P a . Thus, in order to maximize its total profits, this firm
should hire six units of input A. Another way of stating this firm’s profit-maximization point with respect
to input A is
MP a
P a
¼ 1
MC x
¼ 1 P x
or
P a
MP a
¼ P x
Fig. 13-8
Cross-multiplying, we get P a ¼ MP a
. P x ¼ VMP a . Note that in Fig. 13-8, input A is treated as a discrete
variable, while in the text (and in the problems that follow), input A is treated as a continuous variable.
13.5 Assume that (1) the MRP a of a firm is $40 when q a ¼ 4 and $20 when q a ¼ 7 and (2) in the long run,
when all of the firm’s inputs are variable, a fall in P a from $40 to $20 per unit, with all the other input
prices remaining constant, causes this firm’s MRP a curve to shift everywhere to the right by three units.
(a) Derive geometrically this firm’s d a ,(b) explain in detail the internal effect resulting from inputs
which are complementary to input A in production, and (c) explain in detail the internal effect resulting
from inputs which are substitutes for input A. (d ) Until when will these internal effects operate?
(a)
Fig. 13-9
The MRP a curve is drawn on the assumption that the quantity of all inputs other than input A is fixed. It thus
represents the firm’s short-run d a . In this problem, we are told that in the long run, when all inputs are variable
and their prices other than P a are constant, a fall in P a from $40 to $20 per unit causes the firm’s MRP a curve to