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

CHAP. 13] INPUT PRICING AND EMPLOYMENT 301
13.16 (a) Plot, on the same set of axes, the VMP a , MRP a , and S a schedules for the firm in Problem 13.15.
(b) How many units of input A should this firm use in order to maximize its total profits? (c) What
is the amount of monopolistic exploitation when this firm is in equilibrium?
(a)
Fig. 13-17
Note that when we have monopoly or other forms of imperfect competition in the product market, the MRP a
curve represents the firm’s short-run d a , and the MRP a curve or d a lies below the corresponding VMP a curve.
Also, since this firm pays the same P a for various quantities of input A it purchases, the firm behaves as a
perfect competitor in the market for input A and thus the S a it faces is infinitely elastic at P a ¼ $8.80.
(b) This firm is in equilibrium (i.e., it maximizes its total profits with respect to input A) when MP a /
P a ¼ 1/MC x ¼ 1/MR x or (MP a )(MR x ) ¼ MRP a ¼ P a . Thus, this firm should hire four units of input A
(see point B in Fig. 13-17).
(c)
Monopolistic exploitation in this case is $4 (given by $12.80 – $8.80, or BB 0 in Fig. 13-17). The name “monopolistic
exploitation” is somewhat misleading since the difference between the VMP a and the corresponding
MRP a is not pocketed by the firm, and the input receives the entire increase that it contributes to the TR of
the firm.
13.17 Assume that (1) the MRP a for the monopolistic producer of commodity X is $40 when q a ¼ 3 and $20
when q a ¼ 5 and (2) a fall in P a from $40 to $20 per unit, with the prices of all other inputs remaining
constant in the long run, causes this firm’s MRP a curve to shift everywhere to the right by two units.
(a) Why does this firm’s MRP a curve shift to the right when P a falls? (b) Derive this firm’s long-run
d a geometrically.
(a)
Starting from the profit-maximizing point A, a fall in P a will induce the firm to expand its use of input A (i.e.,
to move down its MRP a curve). However, when this occurs, the MRP curve of factors complementary to input
A shifts to the right and the firm uses more of them. This causes the firm’s MRP a curve to shift to the right. On
the other hand, when the firm uses more of input A (because P a has fallen), the MRP curve of factors which are
substitutes for input A shifts to the left and the firm uses less of them. This causes the firm’s MRP a curve to
shift even further to the right. However, as the MRP a curve shifts to the right and more of input A is used, the
MRP curves of complementary inputs again shift to the right and the MRP curves of substitute inputs again
shift to the left. This in turn causes a further shift to the right in this firm’s MRP a curve, and the process is
repeated until the firm reaches another profit-maximizing position [see Problem 13.13(c)]. The entire shift
to the right of the firm’s MRP a curve is called the internal effect on the firm resulting from the change in P a .