© 2006 Thomson Learning/South-Western

Part 7 Further Topics

© 2006 Thomson Learning/South-Western

Chapter 15 Pricing in Input Markets

Profit-Maximizing Behavior and the Hiring of Inputs

3  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 ME K and ME L denote the marginal expense of hiring capital and labor, respectively.

4

Profit-Maximizing Behavior and the Hiring of Inputs

 Let MR K and MR L be the extra revenue that hiring more units of capital and labor allows the firm to bring in.

 Profit maximizing behavior requires:

ME K ME L



MR K



MR L

.

 15 .

1 

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).

v



ME K w



ME L



MR K



MR L

.

 15 .

2 

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:

v



ME K w



ME L

 

MR K MR L

 

MP K MP L



MR



MR

.

 15 .

3 

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

v w

 

MP K MP L

 

P P

 15 .

3 

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.

v



MVP K w



MVP L

 15 .

5 

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 L is w 1 . 1 labor hours when the wage rate

FIGURE 15-1: Change in Labor Input When Wage Falls: Single Variable Case

MVP Wage w 1 w 2

10

0 L 1 L 2 MVP L Labor hours

Responses to Changes in Input Prices: Single Variable input Case

11  If the wage rate falls to w 2 increased labor out to L 2 .

 the firm hires If the firm continued to hire L 1 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.

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

Labor Input per Hour

1 2 3 4 5 6 7 8 9 10

Hamburgers Produced per Hour

20.0 28.3 34.6 40.0 44.7 49.0 52.9 56.6 60.0 63.2

Marginal Product (Hamburger)

20.0 8.3 6.3 5.4 4.7 4.3 3.9 3.7 3.4 3.2

Marginal Value Product ($1.00 per Hamburger)

$20.00 8.30 6.30 5.40 4.70 4.30 3.90 3.70 3.40 3.20

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.

FIGURE 15-2: Substitution and Output Effects of A Decrease in Price of Labor

Capital per week Price MC K 1 K 2 A 0 L 1 q 1 L 2 Labor hours per week (a) Input Choice P 0 q 1 Output per week (b) Output Decision

14

15 FIGURE 15-2: Substitution and Output Effects of A Decrease in Price of Labor

Capital per week Price K 1 K 2 A 0 L 1 B q 1 L 2 Labor hours per week (a) Input Choice P 0 MC q 1 Output per week (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 q 2 resulting in more labor hired.

17 FIGURE 15-2: Substitution and Output Effects of A Decrease in Price of Labor

Capital per week Price K 1 K 2 A 0 L 1 B q 1 L 2 Labor hours per week (a) Input Choice P 0 MC MC’ q 1 q 2 Output per week (b) Output Decision

18 FIGURE 15-2: Substitution and Output Effects of A Decrease in Price of Labor

Capital per week Price K 1 K 2 A 0 L 1 B C q 2 q 1 L 2 Labor hours per week P 0 (a) Input Choice MC MC’ q 1 q 2 Output per week (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 0 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 0 L’ L*

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

Demand

Demand Shifts Outward

Rise in output price Increase in marginal productivity

Demand Shifts Inward

Fall in output price Decrease in marginal productivity

Labor Supply Capital Supply

Supply Shifts Outward

Decreased preference for Leisure Increased desirability of job Fall in input costs of equipment makers Technical progress in making equipment

Supply Shifts Inward

Increased preference for Leisure Decreased desirability of job Rise in input costs of equipment makers

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 (ME L ) 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

L

 1 2

w

 15 .

6   This relationship is shown in Table 15-3

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

Hourly Wage

$2 4 6 8 10 12 14

Workers Supplied per Hour

1 2 3 4 5 6 7

Total Labor Cost per Hour

$2 8 18 32 50 72 98

Marginal Expense

$2 6 10 14 18 22 26

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 6 A 0 3 4 Bear wardens per hour

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 6 A 0 3 4 Bear wardens per hour

39 Monopsonists and Resource Allocation: A Graphical Demonstration  The demand curve in Figure 15-5 is D.

 Since marginal expense (ME L ) exceeds the wage, the marginal expense curve is above the supply curve (S).

 L 1 is the profit maximizing choice while the marginal value product is MVP 1 and the wage is w 1 .

40 FIGURE 15-5: Pricing in a Monopsonistic Labor Market

ME Wage S D 0 Labor hours per week

41 FIGURE 15-5: Pricing in a Monopsonistic Labor Market

ME Wage S MVP 1 D 0 L 1 Labor hours per week

42 FIGURE 15-5: Pricing in a Monopsonistic Labor Market

ME Wage S MVP 1 w 1 D 0 L 1 Labor hours per week

43

A Graphical Demonstration

 L 1 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 L 1 , w 1 .

44 FIGURE 15-5: Pricing in a Monopsonistic Labor Market

ME Wage S MVP 1 w* w 1 D 0 L 1 L* Labor hours per week

45

Monopsonists and Resource Allocation

  Since the monopsonist restrict its input use, it pays an input less than its marginal value product (w 1 < MVP 1 ).

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 P 1 , Q 1 .

47 FIGURE 15-6: Bilateral Monopoly

ME Input price S P 1 D 0 Q 1 MR Quantity per period

48

Bilateral Monopoly

 The monopoly supplier will operate on its marginal revenue curve (MR) and prefer price-quantity combination P 1 , Q 1 .

 The monopsonistic will operate on its marginal expense curve (ME) and prefer combination P 2 , Q 2 .

49 FIGURE 15-6: Bilateral Monopoly

ME Input price S P* P 2 D MR 0 Quantity per period Q 2

50

Bilateral Monopoly

   The monopoly supplier will operate on its marginal revenue curve (MR) and prefer price-quantity combination P 1 , Q 1 .

The monopsonistic will operate on its marginal expense curve (ME) and prefer combination P 2 , Q 2 .

The final outcome, after bargaining, will lie between these two combinations.

51 FIGURE 15-6: Bilateral Monopoly

ME Input price S P 1 P* P 2 D 0 Q 2 Q 1 MR Q* Quantity per period