Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006
286 INPUT PRICING AND EMPLOYMENT [CHAP. 13rises. If there are 100 identical and perfectly competitive firms purchasing input A, each buys six units of input A at P a ¼ $4(see point E on d 0 a in Fig. 13-2). Fig. 13-313.7 RENT AND QUASI-RENTAny payment for an input over and above the minimum amount needed to bring forth its supply is rent.Rent is a long-run concept; it is the entire payment made to an input whose supply is completely fixed (seeProblem 13.10).Quasi-rent is a payment which need not be made in the short run in order to bring forth the supply of aninput. Thus, quasi-rent equals TR minus TVC (see Problems 13.11 and 13.12).Perfect Competition in the Input Market and Monopoly in the ProductMarket13.8 PROFIT MAXIMIZATION AND LEAST-COST INPUT COMBINATIONSThe firm, which is the monopolistic (or an imperfectly competitive) seller of commodity X but a perfectlycompetitive buyer of inputs A and B, will maximize its total profits when(see Problems 13.13 and 13.14).MP aP a¼ MP bP b¼ 1MC x¼ 1MR x13.9 THE DEMAND CURVE OF THE FIRM FOR ONE VARIABLE INPUTWhen input A is the only variable input for the monopolistic seller of commodity X, the firm’s demandcurve for input A is given by its MRP a curve, which now lies below the VMP a curve because MR x issmaller than P x . The MRP a ¼ MP a. MR x and measures the change in the monopolist’s TR in selling theoutput of commodity X that results from the employment of one additional unit of input A.EXAMPLE 5. The first three columns of Table 13.2 are the same as in Table 13.1. Column (4) gives the declining prices atwhich the monopolist can sell increasing quantities of commodity X. The TR x values of column (5) are obtained by multiplyingQ x by P x . The MRP a values of column (6) are then obtained from the difference between successive TR x values ofcolumn (5). That is, the MRP a measures the change in the monopolist’s TR in selling the output of commodity X that resultsfrom the employment of one additional unit of input A (together with fixed quantities of other inputs). More briefly,MRP a ¼ DTR x /Dq a . The MRP a is also equal to the MP a times the MR x (see Problem 13.15). With monopoly (or imperfectcompetition) in the product market, MR x , P x and so MRP a ¼ MP a. MR x , MP a. P x ¼ VMP a . The MRP a values incolumn (6) fall because both the MP a and the MR x fall. Columns (6) and (1) of Table 2 represent the demand schedule
CHAP. 13] INPUT PRICING AND EMPLOYMENT 287of input A for the monopolist seller of commodity X, when input A is the only variable input. The P a values of $21 in column(7) remain constant because we are assuming here that the monopolist seller of commodity X is a perfectly competitivebuyer of input A. In order to maximize its total profits, this firm will hire more units of input A as long as theMRP a . P a and up to the point where the MRP a ¼ P a . Thus, the firm will hire five units of input A.Table 13.2(1) (2) (3) (4)q a Q x MP a P x ($)(5)TR x ($)(6)MRP a ($)(7)P a ($)3 6 10 60 214 11 5 9 99 39 215 15 4 8 120 21 216 18 3 7 126 6 217 20 2 6 120 26 218 21 1 5 105 215 21EXAMPLE 6. Fig. 13-4 shows the typical shape of a firm’s MRP curve for input A. When input A is its only variable input,and the firm is a monopolist (or an imperfect competitor) in the product market, then the MRP a curve is the firm’s demand curvefor input A. If the firm is a perfectly competitive buyer of input A, it will purchase two units of input A when P a ¼ $8 (point A inFig. 13-4). Thus at point A, P a ¼ $8 ¼ MRP a , VMP a .IfP a falls to $4, the firm will increase the quantity it uses of input Afrom two to three units (point B). Thus at point B, P a ¼ $4 ¼ MRP a , VMP a . The excess of the VMP a over the correspondingMRP a when the firm is in equilibrium is sometimes referred to as monopolistic exploitation (see Problem 13.16).Fig. 13-413.10 THE DEMAND CURVE OF THE FIRM FOR ONE OF SEVERAL VARIABLE INPUTSWhen input A is only one of several variable inputs, then the MRP a curve no longer represents the firm’sdemand curve for input A. We can derive d a by considering the internal effect on the firm that results fromchanges in P a . This internal effect is the same as described in Example 2.13.11 THE MARKET DEMAND CURVE AND INPUT PRICINGIf all the firms demanding input A are monopolists in their respective commodity markets, then the marketdemand curve for input A (D a ) is obtained very simply by the straightforward horizontal summation of eachmonopolist’s demand curve for input A (d a ). On the other hand, if the firms demanding input A are monopolisticcompetitors or oligopolists, in order to go from the firms’ to the market demand curve for input A, we mustconsider the external effect on the firms resulting from changes in P a . (See Section 13.14.)
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CHAP. 13] INPUT PRICING AND EMPLOYMENT 287
of input A for the monopolist seller of commodity X, when input A is the only variable input. The P a values of $21 in column
(7) remain constant because we are assuming here that the monopolist seller of commodity X is a perfectly competitive
buyer of input A. In order to maximize its total profits, this firm will hire more units of input A as long as the
MRP a . P a and up to the point where the MRP a ¼ P a . Thus, the firm will hire five units of input A.
Table 13.2
(1) (2) (3) (4)
q a Q x MP a P x ($)
(5)
TR x ($)
(6)
MRP a ($)
(7)
P a ($)
3 6 10 60 21
4 11 5 9 99 39 21
5 15 4 8 120 21 21
6 18 3 7 126 6 21
7 20 2 6 120 26 21
8 21 1 5 105 215 21
EXAMPLE 6. Fig. 13-4 shows the typical shape of a firm’s MRP curve for input A. When input A is its only variable input,
and the firm is a monopolist (or an imperfect competitor) in the product market, then the MRP a curve is the firm’s demand curve
for input A. If the firm is a perfectly competitive buyer of input A, it will purchase two units of input A when P a ¼ $8 (point A in
Fig. 13-4). Thus at point A, P a ¼ $8 ¼ MRP a , VMP a .IfP a falls to $4, the firm will increase the quantity it uses of input A
from two to three units (point B). Thus at point B, P a ¼ $4 ¼ MRP a , VMP a . The excess of the VMP a over the corresponding
MRP a when the firm is in equilibrium is sometimes referred to as monopolistic exploitation (see Problem 13.16).
Fig. 13-4
13.10 THE DEMAND CURVE OF THE FIRM FOR ONE OF SEVERAL VARIABLE INPUTS
When input A is only one of several variable inputs, then the MRP a curve no longer represents the firm’s
demand curve for input A. We can derive d a by considering the internal effect on the firm that results from
changes in P a . This internal effect is the same as described in Example 2.
13.11 THE MARKET DEMAND CURVE AND INPUT PRICING
If all the firms demanding input A are monopolists in their respective commodity markets, then the market
demand curve for input A (D a ) is obtained very simply by the straightforward horizontal summation of each
monopolist’s demand curve for input A (d a ). On the other hand, if the firms demanding input A are monopolistic
competitors or oligopolists, in order to go from the firms’ to the market demand curve for input A, we must
consider the external effect on the firms resulting from changes in P a . (See Section 13.14.)
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