Chapter 3

Labor Demand

Note: 본강의자료는 The McGraw Hill Companies에서제공한 Slides와 ‘Personal Economics in Practice (E. Lazear & M. Gibbs)’의일부를활용하여편집되었음.

3-2

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? How many workers should the firm hire? (MRTS=w/r)

3-3

3-1. The Firm’s Production Function• Describes the technology that the firm uses to produce

goods and services.

• The firm’s output can be produced by a variety of capital–labor combinations.

• MPE is the change in output resulting from hiring an additional worker, holding constant the quantities of other inputs.

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

• APE = Q/E, APK = Q/K

3-4

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

Out

put

Total Product Curve

0

5

10

15

20

25

0 2 4 6 8 10 12

Number of Workers

Out

put

Average Product

Marginal Product

TP curve gives the relationship between output and the number of workers hired by the firm (holding capital fixed).

MP curve shows the output produced by each additional worker

AP curve shows output per worker.

3-5

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 firms cannot influence prices of output or inputs. (p and w are given)

3-6

3-2. Hiring (E) Decision in SR

• VMP = MPE * MR ($ value of the output)

: the dollar benefit derived from hiring an additional worker (holding capital constant)

• VAP is the dollar value of output per worker.

3-7

Firm's Hiring Decision in SR

A profit-maximizing firm hires workers up to the point where wage = VMPE. If the wage is $22, the firm hires eight workers.

1 4 8

22

38

VMPE

VAPE

Number of Workers

: How many workers should the firm hire?

3-8

SR Labor Demand Curve

• The demand curve for labor indicates how many workers the firm hires for each possible wage, holding capital constant.

• The labor demand curve is downward sloping. This reflects the fact that additional workers are costly and alter average production due to the Law of Diminishing Returns.

3-9

22

18

8 9 12

SR 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 (to the right), and increases employment.

3-10

Maximizing Profits:Two Rules

• 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: hire labor up to the point where the value of marginal product equals the added cost of hiring the worker (i.e., the wage).

3-11

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 where MC = P (for the competitive firm, P = MR)– W x (1 / MPe) = P

3-12

Critiques 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).

3-13

The Short-Run Demand Curvefor the Industry

20

10

3015

Wage

Employment28

20

10

30 60

Wage

Employment

D

D

56

T

T

Firm Industry

3-14

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.

3-15

3-3. The Employment Decision in LR

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

• Isoquant curves describe the possible combinations of labor and capital that produce the same level of output.

3-16

Isoquant Curves

Capital

Employment

q1

q0

X

K

E

Y

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

3-17

Isocost Lines

• The isocost line indicates all labor–capital bundles that exhaust a specified budget for the firm.

• Isocost lines indicate equally costly combinations of inputs.

• Higher isocost lines indicate higher costs.

3-18

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 on 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).

3-19

The Firm's Optimal Combination of Inputs

Capital

Employment

q0

B

P

A

175

100

C1/r

C0/r

A firm minimizes the cost 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.

3-20

Cost Minimization

• Profit maximization implies cost minimization.

• The firm chooses the 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 ratio of input prices, w / r, at the least-cost choice.

3-21

3-4. LR Demand Curve for Labor

• When the wage drops, two effects arise.– The firm takes advantage of the lower price of

labor by expanding production (the scale effect).

– The firm takes advantage of the wage change by rearranging its mix of inputs even if holding output constant (the substitution effect)

3-22

The Impact of a Wage ↓ Holding Costs Constant

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.

3-23

The Impact of a Wage ↓ on Q & E 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.

3-24

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 (from P to 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.

3-25

Two Special Cases of Isoquants

Capital

Employment

q 0 Isoquant

100

200

5

20

Capital

Employment

q0 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.

3-26

3-5. Elasticity of substitution

• The elasticity of substitution is the percentage change in the capital to labor ratio given a percentage change in the price ratio (wages to real interest).– Formula: %∆(K/L) %∆(w/r).– Interpret a particular elasticity of substitution

number as the percentage change in the capital–labor ratio given a 1% change in the relative price of labor to capital

3-27

Elasticity of Substitution

• Example:If the elasticity of substitution is 5, then a 10% increase in the ratio of wages to the price of capital would result in the firm increasing its capital-to-labor ratio by 50%.

3-28

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.

3-29

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.

3-30

3-6. Application

• Affirmative action and production costs:

– A firm is “color blind” if race does not enter the hiring decision.

– Discrimination shifts the hiring decision away from the cost minimization tangency point on the isoquant.

3-31

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.

3-32

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 will increase this firm’s costs if it must further increase its amount of black labor.

3-33

3-7. Marshall’s Rules

• Labor Demand is more elastic when:– The elasticity of substitution is greater.

– The elasticity of demand for the firm’s output is greater.

– Labor’s share in total costs of production is greater.

– The elasticity of supply of other factors of production such as capital is greater.

3-34

3-8. Factor Demands when thereare Several 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.

3-35

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

D1 D0

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)

3-36

3-9. 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 market-clearing wage is w* at which E* workers are employed.

3-37

3-10. Application: The Employment Effects of Minimum Wages

• The unemployment rate is higher the higher the minimum wage and the more elastic are the labor 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.

3-38

The Impact of the Minimum Wage on Employment

Dollars

S

D

Employment

w*

w

ESE*E

A minimum wage set at w

results in employers cutting employment from E* to E. The higher wage also encourages ES – E*workers to enter the market. Thus, under a minimum wage, ES – E–

workers are unemployed.

3-39

Minimum Wages in the United States, 1938-2007

0

1

2

3

4

5

6

7

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

0

1

2

3

4

5

6

7

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

Nominal Minimum Wage Ratio Min. Wage to Avg. Mfg. Wage

3-40

The Impact of Minimum Wages on the Covered and Uncovered Sectors

SU

Dollars Dollars

SC

EmploymentEU EU EUEC Employment

(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.

3-41

3-11. Asymmetric Variable Adjustment Costs

Change in

C0

+50-25 Employment0

VariableAdjustment 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.

3-42

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.

3-43

Estimating Labor Demand

• One can identify the slope of the labor demand curve, which can be used to calculate the elasticity of labor demand, when the supply curve shifts.

• Problem: Must make sure the labor demand curve is not also changing.

3-44

Problems with Estimating Labor Demand

Dollars

S0

w0

E1E0

D0

Employment

w1

S1

D1

w2

E2

Z

Z

P

Q

R

3-45

The Impact of Wartime Mobilization of Men on Female Labor Supply

-20

0

20

40

60

80

40 45 50 55Mobilization rate

% c

hang

e in

em

ploy

men

t, 19

39-4

9

Regression line has slope +2.62

3-46

The Impact of Wartime Mobilization of Men on Female Wages

20

30

40

50

60

70

80

90

40 45 50 55Mobilization rate

% c

hang

e in

wee

kly

wag

e, 1

939-

49

Regression line has slope -2.58

3-47

End of Chapter 3