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

284 INPUT PRICING AND EMPLOYMENT [CHAP. 13
EXAMPLE 1. In Table 13.1, column (1) shows the units of input A (the only variable input) used by the firm. Column (2)
gives the total quantities of commodity X produced. Column (3) refers to the change in total output per unit change in the use of
input A. The MP a declines because we are in stage II of production (the only relevant stage), where the law of diminishing
returns is operating. Column (4) gives MR x ;MR x ¼ P x and remains constant because of perfect competition in the commodity
market. Column (5) is obtained by multiplying each value of column (3) by the value in column (4). The MRP a declines because
the MP a declines. Column (6) gives the price at which the firm purchases input A; P a remains constant because of perfect competition
in the input market. In order to maximize profits, the firm will hire more units of input A as long as the MRP a . P a and
until MRP a ¼ P a . Thus, this firm will hire seven units of input A. When columns (5) and (1) of Table 13.1 are plotted, we get this
firm’s MRP a curve. This is the firm’s demand curve for input A, d a (see Problem 13.4).
Table 13.1
(1)
q a
(2)
q x
(3)
MP a
(4)
MR x ¼ P x
(5)
MRP a ¼ VMP a
(6)
P a
3 6 . . $10 . . $20
4 11 5 10 $50 20
5 15 4 10 40 20
6 18 3 10 30 20
7 20 2 10 20 20
8 21 1 10 10 20
13.3 THE DEMAND CURVE OF THE FIRM FOR ONE OF SEVERAL VARIABLE INPUTS
When input A is only one of several variable inputs, the MRP a no longer represents the firm’s demand
curve for input A. The reason for this is that, given the price of the other variable inputs, a change in the
price of input A will bring about changes in the quantity used of these other variable inputs. These changes,
in turn, cause the entire MRP a curve of the firm to shift. The quantities of input A demanded by the firm at
different prices of input A will then be given by points on different MRP a curves.
EXAMPLE 2. Suppose that a firm is initially producing its best level of output with the least-cost combination of variable
inputs and is using three units of input A at P a ¼ $8 (point A on the MRP a curve in Fig. 13-1). If, for some reason, P a falls
from $8 to $4 in the face of constant prices for other variable inputs, the firm will want to hire more units of input A, since
the MRP a . P a now. But as this occurs, the MP curve (and thus the MRP curve) of variable inputs complementary to input A
will shift to the right, and the firm will hire more of these complementary inputs at their given prices. In addition, the MP
curve (and thus the MRP curve) of variable inputs which are substitutes for input A will shift to the left, so the firm will
purchase fewer of these inputs at their given prices. Both of these effects will cause this firm’s MP a and MRP a curves to
shift to the right, as the firm attempts to maximize profits and reestablish a least-cost combination of inputs. This shift in
the firm’s MRP a curve as P a changes is referred to as the internal effect (i.e., the effect internal to the firm) resulting
from the change in P a .
Fig. 13-1