Chapter 4

Labor Demand

Copyright © 2008 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

Labor Economics, 4th edition

4 - 3

Introduction

• Firms hire workers because consumers want to purchase a variety of goods and services

• Demand for workers is derived from the wants and desires of consumers

• Central questions: how many workers are hired and what are they paid?

4 - 4

The Firm’s Production Function

• Describes the technology that the firm uses to produce goods and services

• The firm’s output is produced by any combination of capital and labor

• The marginal product of labor is the change in output resulting from hiring an additional worker, holding constant the quantities of other inputs

• The marginal product of capital is the change in output resulting from hiring one additional unit of capital, holding constant the quantities of other inputs

4 - 5

More on the Production Function

• Marginal products of labor and capital are positive, so as more units of each are hired, output increases

• When firms hire more workers, total product rises• The slope of the total product curve is the marginal product of

labor• Law of Diminishing Returns: eventually, the marginal product

of labor declines- Average Product: the amount of output produced by the

typical worker

4 - 6

The Total Product, the Marginal Product, and the Average Product Curves

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

Number of Workers

Ou

tpu

t

Total Product Curve

0

5

10

15

20

25

0 2 4 6 8 10 12

Number of Workers

Ou

tpu

t

Average Product

Marginal Product

The total product curve gives the relationship between output and the number of workers hired by the firm (holding capital fixed). The marginal product curve gives the output produced by each additional worker, and the average product curve gives the output per worker.

4 - 7

Profit Maximization

• Objective of the firm is to maximize profits• The profit function is:

- Profits = pq – wE – rK- Total Revenue = pq- Total Costs = (wE + rk)

• Perfectly competitive firm cannot influence prices of output or inputs

4 - 8

Short Run Hiring Decision

• Value of Marginal Product (VMP) is the marginal product of labor times the dollar value of the output

• This indicates the benefit derived from hiring an additional worker, holding capital constant

• Value of Average Product is the dollar value of output per worker

4 - 9

The Firm's Hiring Decision in the Short-Run

1 4 8

22

38

VMPE

VAPE

Number of Workers

A profit-maximizing firm hires workers up to the point where the wage rate equals the value of marginal product of labor. If the wage is $22, the firm hires eight workers.

4 - 10

Labor Demand Curve

• The demand curve for labor indicates how the firm reacts to wage changes, holding capital constant

• The curve is downward sloping• This reflects the fact that additional workers are costly and alter

average production due to the Law of Diminishing Returns

4 - 11

22

18

8 9 12

The Short-Run Demand Curve for Labor

VMPE

Number of Workers

VMPE

Because marginal product eventually declines, the short-run demand curve for labor is downward sloping. A drop in the wage from $22 to $18 increases the firm’s employment. An increase in the price of the output shifts the value of marginal product curve upward, and increases employment.

4 - 12

Maximizing Profits: a general rule

• The profit maximizing firm should produce up to the point where the cost of producing an additional unit of output (marginal cost) is equal to the revenue obtained from selling that output (marginal revenue)

• Marginal Productivity Condition: this is the hiring rule, hire labor up to the point when the added value of marginal product equals the added cost of hiring the worker (i.e., the wage)

4 - 13

The Mathematics of Marginal Productivity Theory

• The cost of producing an extra unit of output:- MC = w x 1/MPe

• The condition: produce to the point when MC = P (for the competitive firm, P = MR)

- W x 1/MPe = P

4 - 14

Critique of Marginal Productivity Theory

• A common criticism is that the theory bears little relation to the way that employers make hiring decisions

• Another criticism is that the assumptions of the theory are not very realistic

• However, employers act as if they know the implications of marginal productivity theory (hence, they try to make profits and remain in business)

4 - 15

The Short-Run Demand Curvefor the Industry

20

10

3015

Wage

Employment28

20

10

30 60

Wage

Employment

D

D

56

T

T

4 - 16

The Firm's Output Decision

Output

Dollars

p

q*

MC

Output Price

A profit-maximizing firm produces up to the point where the output price equals the marginal cost of production. This profit-maximizing condition is the same as the one requiring firms to hire workers up to the point where the wage equals the value of marginal product.

4 - 17

The Employment Decision in the Long Run

• In the long run, the firm maximizes profits by choosing how many workers to hire AND how much plant and equipment to invest in

• Isoquant: describes the possible combinations of labor and capital that produce the same level of output (the curve “ISOlates the QUANTity of output). Isoquants…

- Must be downward sloping- Cannot intercept- That are higher indicate more output- Are convex to the origin- Have a slope that is the negative of the ratio of the marginal products of

capital and labor

4 - 18

Isocost

• The Isocost line indicates the possible combinations of labor and capital the firm can hire given a specified budget

• Isocost indicates equally costly combinations of inputs• Higher isocost lines indicate higher costs

4 - 19

Isoquant Curves

Capital

Employment

q1

q0

X

K

E

Y

All capital-labor combinations that lie along a single isoquant produce the same level of output. The input combinations at points X and Y produce q0 units of output. Input combinations that lie on higher isoquants produce more output.

4 - 20

Isocost Lines

Capital

C1/r

Isocost with Cost Outlay C1C0/r

Isocost with Cost Outlay C0

EmploymentC0/w C1/w

All capital-labor combinations that lie along a single isocost curve are equally costly. Capital-labor combinations that lie on a higher isocost curve are more costly. The slope of an isoquant equals the ratio of input prices (-w/r).

4 - 21

The Firm's Optimal Combination of Inputs

Capital

Employment

q0

B

P

A

175

100

C1/r

C0/r

A firm minimizes the costs of producing q0 units of output by using the capital-labor combination at point P, where the isoquant is tangent to the isocost. All other capital-labor combinations (such as those given by points A and B) lie on a higher isocost curve.

4 - 22

Cost Minimization

• Profit maximization implies cost minimization• The firm chooses a least cost combination of capital and labor• This least cost choice is where the isocost line is tangent to the

isoquant• Marginal rate of substitution equals the price ratio of capital to

labor

4 - 23

Long Run Demand for Labor

• If the wage rate drops, two effects take place- Firm takes advantage of the lower price of labor by

expanding production (scale effect)- Firm takes advantage of the wage change by rearranging its

mix of inputs (while holding output constant; substitution effect)

4 - 24

The Impact of A Wage Reduction, Holding Constant

Initial Cost Outlay at C0

Capital

4025

75

q0

RP

C0/r

Wage is w1Wage is w0

q0

A wage reduction flattens the isocost curve. If the firm were to hold the initial cost outlay constant at C0 dollars, the isocost would rotate around C0 and the firm would move from point P to point R. A profit-maximizing firm, however, will not generally want to hold the cost outlay constant when the wage changes.

4 - 25

The Impact of a Wage Reduction on the Output and

Employment of a Profit-Maximizing Firm

150100

MC1MC0

p

Dollars

Output

100

150

5025

RP

Capital

Employment

•A wage cut reduces the marginal cost of production and encourages the firm to expand (from producing 100 to 150 units).

•The firm moves from point P to point R, increasing the number of workers hired from 25 to 50.

4 - 26

Long Run Demand Curve for Labor

w1

w0

5025

Dollars

Employment

DLR

The long-run demand curve for labor gives the firm’s employment at a given wage and is downward sloping.

4 - 27

Substitution and Scale Effects

100

200

D

R

P

Q

D

5025 40

Capital

Employment

Wage is w1

Wage is w0

C0/r

C1/r

A wage cut generates substitution and scale effects. The scale effect (the move from point P to point Q) encourages the firm to expand, increasing the firm’s employment. The substitution effect (from Q to R) encourages the firm to use a more labor-intensive method of production, further increasing

employment.

4 - 28

Elasticity of Substitution

• When two inputs can be substituted at a constant rate, the two inputs are called perfect substitutes

• When an isoquant is right-angled, the inputs are perfect complements

• The substitution effect is large when the two inputs are perfect substitutes

• There is no substitution effect when the inputs are perfect complements (since both inputs are required for production)

• The curvature of the isoquant measures elasticity of substitution

4 - 29

Isoquants

Capital

Employment

q 0 Isoquant

100

200

5

20

Capital

Employment

q 0 Isoquant

Capital and labor are perfect substitutes if the isoquant is linear (so that two workers can always be substituted for one machine). The two inputs are perfect complements if the isoquant is right-angled. The firm then gets the same output when it hires 5 machines and 20 workers as when it hires 5 machines and 25 workers.

4 - 30

Elasticity Measurement

• Intuitively, elasticity of substitution is the percentage change in capital to labor (a ratio) given a percentage change in the price ratio (wages to real interest)

• %∆K/L%∆w/r• This is the percentage change in the capital:labor ratio given a

1% change in the relative price of the inputs

4 - 31

The Short- and Long-Run DemandCurves for Labor

Dollars

Short-Run Demand Curve

Long-Run Demand Curve

Employment

In the long run, the firm can take full advantage of the economic opportunities introduced by a change in the wage. As a result, the long-run demand curve is more elastic than the short-run demand curve.

4 - 32

Isoquants when Inputs are either Perfect Substitutes or Perfect Complements

Capital

Employment

q 0 Isoquant

100

200

5

20

Capital

Employment

q 0 Isoquant

4 - 33

Application

• Affirmative action and production costs- A firm is “color blind” if race does not enter the hiring decision

at all- Discrimination shifts the hiring decision away from the cost

minimization tangency point on the isoquant

4 - 34

Affirmative Action

q*

P

Q

Black Labor

White Labor

The discriminatory firm chooses the input mix at point P, ignoring the cost-minimizing rule that the isoquant be tangent to the isocost. An affirmative action program can force the firm to move to point Q, resulting in more efficient production and lower costs.

4 - 35

Affirmative Action

q*

Q

P

Black Labor

White Labor

A color-blind firm is at point P, hiring relatively more whites because of the shape of the isoquants. An affirmative action program increases this firm’s costs.

4 - 36

Marshall’s Rules

• Labor Demand is more elastic when:- Elasticity of substitution is greater- Elasticity of demand for the firm’s output is greater- The greater labor’s share in total costs of production- The greater the supply elasticity of other factors of production

(such as capital)

4 - 37

Factor Demand with Many Inputs

• There are many different inputs- Skilled and unskilled labor- Old and young- Old and new machines

• Cross-elasticity of factor demand- %∆Di%∆wj

- If cross-elasticity is positive, the two inputs are said to be substitutes in production

4 - 38

The Demand Curve for a Factor of Production is Affected by the Prices of Other Inputs

Price of input i

Employment of input i

D0

Price of input i

Employment of input i

D1D0

D1

The labor demand curve for input i shifts when the price of another input changes. (a) If the price of a substitutable input rises, the demand curve for input i shifts up. (b) If the price of a complement rises, the demand curve for input i shifts down.

(a)(b)

4 - 39

Labor Market Equilibrium

Dollars

Supply

whigh

w*

ESED E*

wlow

Demand

Employment

In a competitive labor market, equilibrium is attained at the point where supply equals demand. The “going wage” is w* and E* workers are employed.

4 - 40

Application: The Employment Effects of Minimum Wages

• The unemployment rate is higher the higher the minimum wage and the more elasticity the supply and demand curves

• The benefits of the minimum wage accrue mostly to workers who are not at the bottom of the distribution of permanent income

4 - 41

Minimum Wages in the United States, 1938-2005

Source: U.S. Bureau of the Census, Statistical Abstract of the United States. Washington, DC, Government Printing Office, various issues; U.S. Bureau of the Census, Historical Statistics of the United States, Colonial Times to 1970, Washington, DC, 1975; and U.S. Bureau of Labor Statistics, Employment and Earnings, Washington, DC, Government Printing Office, January 2006.

0

1

2

3

4

5

6

1938 1944 1950 1956 1962 1968 1974 1980 1986 1992 1998 2004 2010

Year

0.2

0.3

0.4

0.5

0.6

Ratio

Nominal Wage

4 - 42

The Impact of the Minimum Wage on Employment

Dollars

S

D

Employment

w*

w

ESE*E

A minimum wage set at w forces employers to cut employment (from E* to E). The higher wage also encourages (ES - E*) additional workers to enter the market. The minimum wage, therefore, creates unemployment.

4 - 43

The Impact of Minimum Wages on the Covered and Uncovered Sectors

SU

Dollars Dollars

SC

EmploymentEU EU EUECEmployment

(b) Uncovered Sector

E

SU

SU

w

w*w*

DUDC

(If workers migrate to covered sector)

(If workers migrate to uncovered sector)

(a) Covered Sector

If the minimum wage applies only to jobs in the covered sector, the displaced workers might move to the uncovered sector, shifting the supply curve to the right and reducing the uncovered sector’s wage. If it is easy to get a minimum wage job, workers in the uncovered sector might quit their jobs and wait in the covered sector until a job opens up, shifting the supply curve in the uncovered sector to the left and raising the uncovered sector’s wage.

4 - 44

Adjustment Costs and Labor Demand

• The expenditures that firms incur as they adjust the size of their workforce are called adjustment costs

- Variable adjustment costs are associated with the number of workers the firm will hire and fire

- Fixed adjustment costs do not depend on how many workers the firm is going to hire and fire

4 - 45

Asymmetric Variable Adjustment Costs

Change in

C 0

+50 -25 Employment

0

Variable Adjustment Costs

Changing employment quickly is costly, and these costs increase at an increasing rate. If government policies prevent firms from firing workers, the costs of trimming the workforce will rise even faster than the costs of expanding the firm.

4 - 46

Slow Transition to a New Labor Equilibrium

Employment

B150

A100

C50

Time

Variable adjustment costs encourage the firm to adjust the employment level slowly. The expansion from 100 to 150 workers might occur more rapidly than the contraction from 100 to 50 workers if government policies “tax” firms that cut employment.

4 - 47

Shifts in Labor Supply and Labor Demand Curves Generate the Observed Data on Wages and Employment

Dollars

S0

w0

E1E0

D0

Employment

w1

S1

D1

w2

E2

Z

Z

P

Q

R

4 - 48

The Impact of Wartime Mobilization of Men on Female Labor Supply

-20

0

20

40

60

80

40 45 50 55

Mobilization rate

% c

han

ge

in e

mp

loym

ent,

193

9-49

Regression line has slope +2.62

4 - 49

The Impact of Wartime Mobilization of Men on Female Wages

20

30

40

50

60

70

80

90

40 45 50 55

Mobilization rate

% c

han

ge

in w

eekl

y w

age,

193

9-49

Regression line has slope -2.58

4 - 50

End of Chapter 4