1. Part 7
Further Topics
© 2006 Thomson Learning/South-Western

2. Pricing in Input Markets
Chapter 15
Pricing in Input Markets
© 2006 Thomson Learning/South-Western

3. Profit-Maximizing Behavior and the Hiring of Inputs
A profit-maximizing firm will hire additional units of any input up to the point at which the additional revenue from hiring one more unit is exactly equal to the cost of hiring that unit.
Let MEK and MEL denote the marginal expense of hiring capital and labor, respectively.

4. Profit-Maximizing Behavior and the Hiring of Inputs
Let MRK and MRL be the extra revenue that hiring more units of capital and labor allows the firm to bring in.
Profit maximizing behavior requires:

5. Price-Taking Behavior
If the firm is a price taker in the capital and labor market then it can always hire an extra unit of capital at the prevailing rate (v) and an extra unit of labor at the wage rate (w).

6. Marginal Revenue Product
Marginal product is how much output the additional input can produce.
Marginal revenue (MR) is the extra revenue obtained from selling an additional unit of output.
Thus, the profit maximizing rules are:

7. A Special Case--Marginal Value Product
If the firm is also a price taking in the goods market, marginal revenue equals the price (P) at which the output sells.
The profit maximizing conditions become

8. Marginal Value Product
The marginal value product (MVP) of capital and labor, respectively, are special cases of marginal revenue product in which the firm is a price taker for its output.

9. Responses to Changes in Input Prices: Single Variable input Case
Assume the firm has fixed capital and can only vary its labor input in the short run.
Labor will exhibit diminishing marginal physical productivity so labor’s MVP will decline as more labor is hired.
In Figure 15-1, the profit maximizing firm will hire L1 labor hours when the wage rate is w1.

10. FIGURE 15-1: Change in Labor Input When Wage Falls: Single Variable Case
MVP
Wage w1 w2
MVPL
Labor hours L1 L2

11. Responses to Changes in Input Prices: Single Variable input Case
If the wage rate falls to w2 the firm hires increased labor out to L2.
If the firm continued to hire L1 it would not be maximizing profit since labor would be capable of producing more in additional revenue than hiring additional labor would cost.
With one variable input, diminishing marginal productivity results in a downward sloping demand curve.

12. TABLE 15-1: Hamburger Heaven’s Profit-Maximizing Hiring Decision

13. The Substitution Effect
The substitution effect, in the theory of production, is the substitution of one input for another while holding output constant in response to a change in the input’s price.
In Figure 15-2(a), a fall in w will cause the firm to change from input combination A to B to equate RTS to the new w/v.
Diminishing RTS leads to more labor hired.

14. FIGURE 15-2: Substitution and Output Effects of A Decrease in Price of Labor
Capital
per week
Price MC K1 A P K2 q1 L1 L2
Labor hours
per week q1
Output
per week
(a) Input Choice
(b) Output Decision

15. FIGURE 15-2: Substitution and Output Effects of A Decrease in Price of Labor
Capital
per week MC K1 A P K2 B q1 L1 L2
Labor hours
per week q1
Output
per week
(a) Input Choice
(b) Output Decision

16. The Output Effect
The output effect is the effect of an input price change on the amount of the input that the firm hires that results from a change in the firm;s output level.
In Figure 15-2(b), the lower w causes the marginal cost curve to shift to MC’.
The profit maximizing output raises to q2 resulting in more labor hired.

17. FIGURE 15-2: Substitution and Output Effects of A Decrease in Price of Labor
Capital
per week MC
MC’ K1 A P K2 B q1 L1 L2
Labor hours
per week q1 q2
Output
per week
(a) Input Choice
(b) Output Decision

18. FIGURE 15-2: Substitution and Output Effects of A Decrease in Price of Labor
Capital
per week MC
MC’ K1 A C P K2 q2 B q1 L1 L2
Labor hours
per week q1 q2
Output
per week
(a) Input Choice
(b) Output Decision

19. Responsiveness of Input Demand to Price Changes
Ease of Substitution
The size of the substitution effect will depend upon how easy it is to substitute other factors of production for labor.
The size of the substitution effect will also depend upon the length of time as it becomes easier to find substitutes in a longer period of time.

20. Costs and the Output Effect
The size of the output effect will depend upon
How large the increase in marginal costs brought about by the wage rate increase is, and
How much quantity demanded will be reduced by a rising price.
The first depend upon how important labor is in production while the latter depends upon the price elasticity of demand for the final product.

21. Input Supply Resources come from three major sources:
Labor is provided by individuals.
Capital equipment is produced which other firms can buy outright or rent.
Natural resources are extracted from land and can be used outright or sold to other firms.
As shown in earlier chapters, capital and natural resources have upward sloping supply curves.

22. Labor Supply and Wages
Wages represent the opportunity cost of not working at a paying job for individuals.
For purposes of this analysis, wages should be interpreted to include all forms of compensation.
Individuals will balance the monetary rewards from working against the psychic benefits of other, nonpaid activities.

23. Labor Supply and Wages
Labor supply curves will differ based upon individual preferences.
Noneconomic factors such as pleasant working conditions will affect the location of the supply curve.
It is likely that an increase in the wage will result in more labor supplied to the market.
Graphically, the market labor supply curve is likely to be positively sloped.

24. Equilibrium Input Price Determination
In Figure 15-3, the market demand for labor is labeled D, and the market supply of labor is labeled S.
The equilibrium wage and quantity is where quantity demanded equals quantity supplied, [w*, L*].
Other things equal, this equilibrium will tend to persist from period to period.

25. FIGURE 15-3: Equilibrium in an Input Market
Wage S w* D
Labor hours per week L*

26. Shifts in Demand and Supply
Any factor that shifts the firms’ underlying production function will shift its input demand curve.
Demand for an input is derived from the demand for the output, changes in the prices of the output will shift input demand curves

27. Shifts in Demand and Supply
In Figure 15-3, the demand curve shifts to D’ which reduces equilibrium wages from w* to w’ and equilibrium employment from L* to L’.
The various factors that shift input demand and supply curves are summarized in Table 15-2.

28. FIGURE 15-3: Equilibrium in an Input Market
Wage S w* w’ D D’
Labor hours per week L’ L*

29. TABLE 15-2: Factors That Shift Input Demand and Supply Curves

30. Monopsony
If the firm is not a price taker in the input market, it may have to offer a higher wage to attract more employees.
A monopsony is the condition in which one firm is the only hirer in a particular input market.
If the firm is a monopsony, it faces the entire market supply curve for the input.

31. Marginal Expense
The marginal expense of an input is the cost of hiring one more unit of an input.
The firm has to offer a higher wage to the hired worker and to the workers already employed.
The marginal expense of labor (MEL) will exceed the price of the input if the firm faces an upward-sloping supply curve for the input.

32. A Numerical Illustration
Suppose the Yellowstone Park Company is the only hirer of bear wardens.
The number of people willing to take this job (L) is given by
This relationship is shown in Table 15-3

33. TABLE 15-3: Labor Costs of Hiring Bear Wardens in Yellowstone Park

34. A Numerical Illustration
Total labor costs (w·L) is shown in the third column and the marginal expense of hiring each warden is shown in the fourth column.
Since the new warden and the existing wardens receive the wage increase, the marginal expense exceeds the wage rate.

35. A Numerical Illustration
Figure 15-4 shows the supply curve (S) for wardens.
If Yellowstone wishes to hire three wardens it must pay $6 per hour with total outlays of $18 (point A on the graph).
The wage must be increased to $8 to get a fourth warden (point B) which results in total outlays of $32.

36. FIGURE 15-4: Marginal Expense of Hiring Bear Wardens
Hourly
wage S B $8 A 6
Bear wardens per hour 3 4

37. A Numerical Illustration
The marginal expense of the fourth warden, $14 is reflected in the graph.
The hourly wage ($8) is shown in gray.
The extra outlay to the three previous workers ($8 per hour versus $6 per hour previously) is shown in color.
Total outlays exceed the amount for three wardens by the sum of these two areas.

38. FIGURE 15-4: Marginal Expense of Hiring Bear Wardens
Hourly
wage S B $8 A 6
Bear wardens per hour 3 4

39. Monopsonists and Resource Allocation: A Graphical Demonstration
The demand curve in Figure 15-5 is D.
Since marginal expense (MEL) exceeds the wage, the marginal expense curve is above the supply curve (S).
L1 is the profit maximizing choice while the marginal value product is MVP1 and the wage is w1.

40. FIGURE 15-5: Pricing in a Monopsonistic Labor MarketME
Wage S D
Labor hours
per week

41. FIGURE 15-5: Pricing in a Monopsonistic Labor MarketME
Wage S
MVP1 D
Labor hours
per week L1

42. FIGURE 15-5: Pricing in a Monopsonistic Labor MarketME
Wage S
MVP1 w1 D
Labor hours
per week L1

43. A Graphical Demonstration
L1 is less than L*, the amount hired with perfect competition.
As with a monopoly, the “demand curve” for a monopolist actually consists of the single point given by L1, w1.

44. FIGURE 15-5: Pricing in a Monopsonistic Labor MarketME
Wage S
MVP1 w* w1 D
Labor hours
per week L1 L*

45. Monopsonists and Resource Allocation
Since the monopsonist restrict its input use, it pays an input less than its marginal value product (w1 < MVP1).
Total output could be increased by drawing more labor into the market.
The more inelastic the labor supply, the more the monopsonists can benefit from this profit opportunity.

46. Bilateral Monopoly
A bilateral monopoly is a market in which both suppliers and demanders have monopoly power.
In Figure 15-6, “supply” and “demand” intersect at P*, Q*, but this is not equilibrium since neither player is a price taker.
The monopoly supplier will operate on its marginal revenue curve (MR) and prefer price-quantity combination P1, Q1.

47. FIGURE 15-6: Bilateral Monopoly
Input
price ME S P1 D MR
Quantity per
period Q1

48. Bilateral Monopoly
The monopoly supplier will operate on its marginal revenue curve (MR) and prefer price-quantity combination P1, Q1.
The monopsonistic will operate on its marginal expense curve (ME) and prefer combination P2, Q2.

49. FIGURE 15-6: Bilateral Monopoly
Input
price ME S P* P2 D MR
Quantity per
period Q2

50. Bilateral Monopoly
The monopoly supplier will operate on its marginal revenue curve (MR) and prefer price-quantity combination P1, Q1.
The monopsonistic will operate on its marginal expense curve (ME) and prefer combination P2, Q2.
The final outcome, after bargaining, will lie between these two combinations.

51. FIGURE 15-6: Bilateral Monopoly
Input
price ME S P1 P* P2 D MR
Quantity per
period Q2 Q1 Q*