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

CHAP. 13] INPUT PRICING AND EMPLOYMENT 295
shift to the right to MRP 0 a (see Fig. 13-9). Thus, point A and point C are two points on the firm’s long-run d a .
(The movement from point B to point C is the internal effect of the change in P a .)
(b) Starting from the profit-maximizing point A, a fall in P a from $40 per unit causes the MRP a to exceed the new
and lower P a . Thus the firm, in its attempt to maximize its profits with respect to input A, expands its use of
input A (a movement down its unchanged MRP a curve). However, as the firm uses more of input A, the MP,
and thus the MRP curve of inputs complementary to input A, shifts up and to the right. Thus, the new and
higher MRP for these complementary inputs exceed their unchanged prices. So this profit-maximizing firm
expands its use of these complementary inputs, but this causes its MP a and thus its MRP a curve to shift up
and to the right.
(c) On the other hand, as the firm uses more of input A because of the fall in P a , the MP and thus the MRP curve of
each input which is a substitute for input A shifts down and to the left. Thus, the new and lower MRP for a
substitute input is now smaller than its unchanged price. As a result the firm will reduce its use of these substitute
inputs, but this causes the firm’s MP a and thus the MRP a curve to shift even further to the right.
(d ) These shifts in the firm’s MRP curves (of input A, their complements and substitutes) and the corresponding
changes in the firm’s utilization of all of these inputs will continue until the firm has once again reestablished
its profit-maximizing position with respect to all of its variable inputs. The more and better is the availability
of inputs which are complementary and substitutes for input A, the further to the right the firm’s MRP a curve
shifts and the more elastic is the firm’s long-run d a .
13.6 Suppose that the external effect of the fall in P a from $40 to $20 per unit causes the d a of each of 100
identical firms demanding input A to shift from the d a in Fig. 13-9 everywhere to the left by two units.
(a) Derive D a geometrically and (b) explain how this external effect of the change in P a operates on each
firm. (c) What are the determinants of the price elasticity of D a ?
(a)
Fig. 13-10
(b)
(c)
Starting from the profit-maximizing point A, ifP a falls (because, for example, S a increases), the MRP a . P a
for each firm using input A. Thus, each firm expands its use of input A. But as all firms expand their use of
input A, the S x increases (i.e., shifts down and to the right). Given D x , this causes a fall in P x . Since the d a of
each firm was drawn on the assumption of a given and constant P x , when P x falls, the MRP a curve of each firm
shifts to the left and causes the d a of each firm also to shift to the left (from d a to da 0 in Fig. 13-10). It is the
quantity demanded on these lower da 0 curves that are added in order to get a new QD a (and thus another point
on D a ) when P a falls.
D a is more price-elastic, the more price-elastic D x , the more and better the availability of substitutes and
complements of input A, the more price-elastic the supply curve of these other related inputs, and the
longer the period of time under consideration.
13.7 Given the D a in Fig. 13-10(b) and QS a ¼ 40P a (with P a given in dollars), determine geometrically the
market equilibrium P a and Q a . How much of input A would each of 100 identical firms use?