Chapter 2

Labor Supply

Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill/Irwin

2-2

Introduction to Labor Supply

• Labor facts

– Men: labor force participation rates declined from 90% in 1947 to 75% in 1990.

– Women: labor force participation rates rose from 32% in 1947 to 60% in 1990.

– Hours worked fell from 40 to 35 per week during the same time period.

2-3

Measuring the Labor Force

• Current population survey (CPS)

– Labor Force = Employed + Unemployed• LF = E + U• Size of LF does not tell us about “intensity” of

work.

– Labor Force Participation Rate• LFPR = LF/P• P = civilian adult population 16 years or older

not in institutions.

2-4

Measuring the Labor Force

• Current population survey (CPS)

– Employment: Population Ratio (percent of population that is employed).

• EPR = E/P

– Unemployment Rate• UR = U/LF

2-5

Measuring the Labor Force• Labor force measurement relies on

subjectivity and likely understates the effects of a recession.

• Hidden unemployed: persons who have given up in their search for work and have therefore left the labor force.

• The employment rate (E/P) can be a better measure of fluctuations in economic activity than the unemployment rate.

2-6

Labor Force Participation Facts

• Labor force participation (LFP) is greatest for all groups during the ages of 25 to 55.

• LFP increases with education.

• LFP has decreased for men over the age of 65 from 63% in 1900 to under 20% by 2000.

2-7

Labor Force Participation Facts

• More women than men work part-time.

• More men who are high school drop outs work than women who are high school drop outs.

• White men have higher participation rates and hours of work than black men.

2-8

Average hours worked/week 1900-2007

30

35

40

45

50

55

60

1900 1920 1940 1960 1980 2000 2020

Year

Wee

kly

ho

urs

2-9

Neo-Classical Model ofLabor-Leisure Choice

• Utility Function

– Measure of satisfaction that individuals receive from consumption (C) of goods and leisure (L).

– U = f(C, L)• U is an index.• Higher U means happier person.

2-10

Indifference Curves

• Downward sloping, indicating the tradeoff between consumption and leisure.

• Higher curves = higher utility.

• Do not intersect.

• Convex to the origin, indicating that opportunity costs increase.

2-11

Indifference Curves

Consumption ($)

500

450

400

40,000 Utils

25,000 Utils

Hours of Leisure150125100+

2-12

Differences in Preferences

Workers with steeper indifference curves value their leisure relatively more than workers with shallower indifference curves.

U0

U0

U1

U1

Consumption ($) Consumption ($)

Hours of

LeisureHours of

Leisure

2-13

The Budget Constraint• The budget constraint defines the worker’s

opportunity set, indicating all of the consumption – leisure baskets the worker can afford.

• C = wh + V– Consumption equals labor earning (wages ×

hours of work) plus nonlabor income (V).– As h = T – L, can rewrite C = w(T – L) + V.

2-14

Graphing the Budget Constraint

T

EV

wT+V

0

Hours of Leisure

Consumption ($)

Budget Line

2-15

The Hours of Work Decision• Individuals choose consumption and leisure to

maximize utility.

• Optimal consumption is given by the point where the budget line is tangent to the indifference curve.

– At this point the marginal rate of substitution (MRS) between consumption and leisure equals the wage.

– Any other consumption – leisure bundle on the budget constraint would give the individual less utility.

2-16

Optimal Consumption and Leisure

$1100

$1200A Y

$500P

U1

$100U0

U*

E

110

110

40

70

0

0

Hours of Work

Hours of Leisure

2-17

The Effect of a Change in Nonlabor Income on Hours of Work

An increase in nonlabor income leads to a parallel, upward shift in the budget line, moving the worker from point P0 to point P1. If leisure is a normal good, hours of work fall.

F1

P1

$200

U1

U0

E1

E0

P0

70 80 110

F0

$100

Consumption ($)

Hours of Leisure

2-18

The Effect of a Change in NonlaborIncome on Hours of Work

An increase in nonlabor income leads to a parallel, upward shift in the budget line, moving the worker from point P0 to point P1. If leisure is inferior, hours of work increase.

F1

P1

$200

U1

U0

E1

E0

P0

7060 110

F0

$100

Consumption ($)

2-19

More Leisure at a Higher WageWhen the income effect dominates the substitutioneffect, the worker increases hours of leisure inresponse to an increase in the wage.

G

U1

QD

D

R

P

U0

V

F

E

8575 1100 70 Hours of Leisure

Consumption ($)

2-20

More Work at a Higher WageWhen the substitution effect dominates the incomeeffect, the worker decreases hours of leisure inresponse to an increase in the wage.

G

D

D

F

E

U1

Q

R

P

U0

V

8070 1100 65

Consumption ($)

Hours of Leisure

2-21

To Work or Not to Work?• Are the “terms of trade” sufficiently attractive

to “bribe” a worker to enter the labor market?

• Reservation wage: the lowest wage rate that would make the person indifferent between working and not working.

– Rule 1: if the market wage is less than the reservation wage, then the person will not work.

– Rule 2: the reservation wage increases as nonlabor income increases

2-22

The Reservation Wage

H

Y

GX

UH

E

U0

Hours of LeisureT0

Has Slope -whigh

Has Slope -w

Consumption ($)

2-23

Labor Supply Curve• Relationship between hours worked and

the wage rate.

– At wages slightly above the reservation wage, the labor supply curve is positively sloped (the substitution effect dominates the income effect).

– If the income effect begins to dominate the substitution, hours of work decline as the wage rate increases (a negatively sloped labor supply curve).

2-24

The Backward Bending Labor Supply Curve

Hours of Work0

Wage Rate ($)

4020 30

10

20

25

2-25

Labor Supply Elasticity• The labor supply elasticity (σ) measures

responsiveness in hours worked to changes in the wage rate.– σ = Percent change in hours worked divided by

the percent change in wage rate.– Labor supply elasticity less than 1 is inelastic as

hours of work respond proportionally less than the change in wages.

– Labor supply elasticity greater than 1 is elastic as hours of work respond proportionally more than the change in wages.

2-26

Labor Supply of Women

• Substantial cross-country differences in women’s labor force participation rates.

• Over time, women’s participation rates have increased.

• In most studies on women, substitution effects dominate income effects (upward sloped labor supply curve).

2-27

Growth in Female Labor Force Participation Rates and the Wage, Cross Countries 1960-80

• Source: Jacob Mincer, “Intercountry Comparisons of Labor Force Trends and of Related Developments: An Overview,” Journal of Labor Economics 3 (January 1985, Part 2): S2, S6.

1 2 3 4 5 6 7 8 9

Percentage Change in Wage

0

1

2

3

4

5

6

7F

em

ale

Pa

rtic

ipa

tion

Gro

wth

Rat

e of

USSR

United States

Israel Britain

France

Sweden

Germany

Italy

Australia

Spain

Japan

Netherlands

2-28

Derivation of the Market Labor Supply

Curve from Individual Supply Curves

0 0 0

w ~

B

w ~

A

w ~

B

w ~

A h

A

h A + h

B

(a) Alice (b) Brenda (c) Market

Wage Rate ($) Wage Rate ($) Wage Rate ($)

Hours of Work

h A

h B

2-29

Policy Application: Welfare Programs and Work Incentives

• Cash grants reduce wage incentives.

• Welfare programs create work disincentives.

• Welfare reduces supply of labor by increasing nonlabor income, which raises the reservation wage.

2-30

Effect of a Cash Grant onWork Incentives

• A take-it-or-leave-it cash grant of $500 per week moves the worker from point P to point G, and encourages the worker to leave the labor force.

F

Consumption ($)

500

Hours of Leisure

0 11070

GU1

U0

P

2-31

Effect of a Welfare Program on Hours of Work

Hours of Work

$500

U0 U1

G

E

P

F

R

Q

H

D

D

0 11010070

slope = -$5

slope = -$10

Consumption ($)

2-32

Policy Application:The Earned-Income Tax Credit

• The EITC should increase labor force participation of nonworkers of targeted groups.– The EITC encourages some non-workers to

start working and never encourages a worker to quit working.

• The EITC produces an income effect.– Hours worked should change.

2-33

The EITC and the Budget Line

Hours of Leisure

Consumption ($)

110

10,350

13,520

14,490

17,660

33,178

E

J

H

G

F

Net wage is 40% above the actual wage

Net wage equals the actual wage

Net wage is 21.06% below the actual wage

2-34

Labor Supply over the Life Cycle

• Wage rates change over the worker’s life (over the life cycle).– Wages are low when young.– Wages rise with time and peak around age 50.– Wages decline or remain stable after age 50.

• The changes in wages over the life cycle are “evolutionary” wage changes that alter the price of leisure.

2-35

Theoretical Issues ofEvolutionary Wages

• A person will work more hours when wages are higher (i.e., the substitution effect tends to dominate the income effect).

• The profile of hours of work over the life cycle will have the same shape as the age-earnings profile.

• Intertemporal substitution hypothesis: people substitute their time over the life cycle to take advantages of changes in the price of leisure.

2-36

The Life Cycle Path of Wages and Hours for a Typical Worker

Age

Wage Rate

50 Age

Hours of work

50

2-37

Hours of Work over the Life Cycle for Two Workers with Different Wage Paths

Age

Jack

t * Age t *

Joe

Wage Rate Hours of

Work

Jack

Joe (if substitution effect dominates)

Joe (if income effect dominates)

Joe’s wage exceeds Jack’s at every age. Although both Joe and Jack work more hours when the wage is high, Joe works more hours than Jack if the substitution effect dominates. If the income effect dominates, Joe works fewer hours than Jack.

2-38

Labor Force Participation Rates over the Life Cycle in 2005

30

40

50

60

70

80

90

100

15 25 35 45 55 65

Age

La

bo

r fo

rce

pa

rtic

ipa

tio

n r

ate

Male

Female

2-39

Hours of Work over the Life Cycle in 2005

500

1,000

1,500

2,000

2,500

15 25 35 45 55 65

Age

An

nu

al

ho

urs

of

wo

rk

Male

Female

2-40

Labor Supply Over theBusiness Cycle

• Added-worker effect.– So-called “secondary” workers currently out of

the labor market are affected by a recession because the main breadwinner becomes unemployed or faces a wage cut.

– A secondary worker may choose to enter the labor force during these bad times

– The labor force participation rate of secondary workers (i.e., the added worker effect) is counter-cyclical.

2-41

Labor Supply Over theBusiness Cycle

• Discouraged worker effect.

– Unemployed workers find it very difficult to find jobs during a recession, so they give up searching.

– Discouraged workers exit the labor force during bad times.

– The labor force participation rate of discouraged workers is pro-cyclical.

2-42

Labor Supply Over theBusiness Cycle

• The discouraged worker effect dominates the added-worker effect, especially during recessions.

2-43

Retirement• Lifetime income is higher the longer a worker

puts off retirement.

• If pension benefits are constant, wage increases have a substitution and income effect, so lifetime income might not be altered.

• An increase in pension benefits reduces the price of retirement, increasing the demand for leisure and encouraging the worker to retire earlier.

2-44

The Impact of the Social Security Earnings Test on Hours of Work

• The Social Security earnings test (which taxes retirees when they earn more than $17,000 per year) generates the budget “line” that affects behavior in varying ways.

• The repeal of the earnings test moves retirees to another budget line, as a result:– One retiree would not change his hours of work.– A second retiree would reduce his hours.– A third retiree might increase or decrease his hours,

depending on whether substitution or income effects dominate.

2-45

Fertility

• Malthus Theory of Fertility: as incomes rise, families want more children (children are normal goods so the income effect is large).

• An increase in the price of a person’s time (i.e., an increase in the wage) increases the opportunity cost of exiting the labor market to rear children.

2-46

The Fertility Decision

Goods

I/pX

Number of Children

P

Indifference Curve

3 I/pN

The household’s utility depends on the number of children and on the consumption of goods. A utility-maximizing household chooses point P and has three children.

2-47

The Impact of Income and Prices on the Household’s Fertility

U0

U0

U1

U1P

P

R

43 Number of Children

Goods

Goods

D

R

21 3 Number of Children

Q

I/PX

(a) Increase in Income

(b) Increase in the price of children

2-48

End of Chapter 2