• Example: Suppose worker utility is given by

• The more C and L the happier is the worker

Worker Utility

U C L

C ($)

L (hours)

U(utils)

0 0 0

100 10 31.6

200 20 63.3

300 30 94.9

400 40 126.5

500 50 158.1

• Example: Suppose worker utility is given by

• Holding C constant, the more L goes up the happier the worker is

U C L

C ($)

L (hours)

U(utils)

300 0 0

300 10 54.8

300 20 77.5

300 30 94.9

300 40 109.5

300 50 122.5

Worker Utility

• Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal

10 0 10L

C ($)

L (hours)

U(utils)

300 0 0

300 10 54.8

300 20 77.5

300 30 94.9

300 40 109.5

300 50 122.5

54.85.48

10L

UMU

L

54.8 0 54.8U

Diminishing Marginal Utility

• Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal

20 10 10L

C ($)

L (hours)

U(utils)

300 0 0

300 10 54.8

300 20 77.5

300 30 94.9

300 40 109.5

300 50 122.5

22.72.27

10L

UMU

L

77.5 54.8 22.7U

Diminishing Marginal Utility

• Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal

30 20 10L

C ($)

L (hours)

U(utils)

300 0 0

300 10 54.8

300 20 77.5

300 30 94.9

300 40 109.5

300 50 122.5

17.11.71

10L

UMU

L

94.9 77.8 17.1U

Diminishing Marginal Utility

• Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal

40 30 10L

C ($)

L (hours)

U(utils)

300 0 0

300 10 54.8

300 20 77.5

300 30 94.9

300 40 109.5

300 50 122.5

14.61.46

10L

UMU

L

109.5 94.9 14.6U

Diminishing Marginal Utility

• Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal

50 40 10L

C ($)

L (hours)

U(utils)

300 0 0

300 10 54.8

300 20 77.5

300 30 94.9

300 40 109.5

300 50 122.5

13.01.30

10L

UMU

L

122.5 109.5 13U

Diminishing Marginal Utility

• Example: Suppose worker utility is given by

• If the worker is indifferent between all market baskets located on an indifference curve, then U is being held constant along it while L and C change

U C L

20C

L

U

20C L U

2

02U C L

0U C L

Indifference Curves

• Example: Indifference curve with U0 = 10

210C

L

L C

10 10

40 2.5

100 1

100C

L

U0 = 10

Indifference Curves

400C

L

220C

L

• Example: Indifference curve with U1 = 20

L C

10 40

40 10

100 4

U0 = 10

U1 = 20

Indifference Curves

Budget line

• C = (w)(H) + A

• T = L + H

• T – L = H

• C = (w)(T – L) + A

• C = (wT + A) – w L

• Constraints set boundaries on the worker’s opportunity set of all the consumption baskets the worker can afford

• Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour)

10 80 100 10C L C wT A wL L C

10 800

40 500

80 100800

900 10C L

10 40 80 leisure

500

100

Budget line

1000 10C L

• Example: What happens if A increases to 200 ($ per week)

2010 80 100C L C wT A wL L C

10 900

40 600

80 200

800

10 40 80 leisure

500

100

Budget line

C wT A wL 1060 12C L 100960 12C L

• Example: What happens if w increases to 12 ($ per hour)

L C

10 940

40 580

80 100

800

10 40 80 leisure

500

100

Budget line

The Hours of Work Decision

• Individual will 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 between consumption and leisure (slope of the indifference curve) equals the wage rate (slope of the budget constraint)

• Any other bundle of consumption and leisure given the budget constraint would mean the individual has less utility

• Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour)

10 40 80 leisure

500

100

900 10C L

U2

U1

U0

L* = 41

H* = 80 – 41 = 39

C* = 900 – 10(41) = 490

The Hours of Work Decision

Change in non-earned income

• Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour)

10 40 80 leisure

500

100

900 10C L

U1

L* = 41

H* = 39

C* = 490

1000 10C L 2010 80 100C L C wT A wL

What happens if A increases to 200 ($ per week)?

L* = 38

H* = 42

C* = 1000 – 10(38) = 620

Leisure is an inferior good since hours of leisure falls

• Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour)

10 40 80 leisure

500

100

900 10C L

U1

L* = 41

H* = 39

C* = 490

1000 10C L

What happens if A increases to 200 ($ per week)?

L* = 50

H* = 30

C* = 1000 – 10(50) = 500

Leisure is a normal good since hours of leisure increases

Change in non-earned income

• Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour)

800

10 40 80 leisure

500

100

L* = 41

H* = 39

C* = 490

Since w is the price of Leisure, the law of demand holds

C wT A wL 1060 12C L 100960 12C L

L* = 40

H* = 40

C* = 1060 – 12(40) = 580

• What happens if w increases to 12 ($ per hour)

An increase in w increases Hbecause SE > IE

Change in the wage rate

• Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour)

800

10 40 80 leisure

500

100

L* = 41

H* = 39

C* = 490

C wT A wL 1060 12C L 100960 12C L

L* = 46

H* = 34

C* = 1060 – 12(46) = 508

• What happens if w increases to 12 ($ per hour)

An increase in w decreases Hbecause IE > SE

Change in the wage rate

• When the Income Effect dominates:

U1

U0

A

6040 800 44

TE

Consumption ($)

SE

IE

Leisure

An increase in w decreases Hbecause IE > SE

Change in the wage rate

• When the Substitution Effect dominates:

U1

U0

A

5040 800 35

TE

Consumption ($)

An increase in w increases Hbecause SE > IE

SE

IE

Leisure

Change in the wage rate

The reservation wage

• Are the “terms of trade” sufficiently attractive to bribe a worker to enter the labor market?

• Reservation wage: the minimum increase in income 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

• Initially the individual does not work because w is too low

U2

U0

A

7040 800

Consumption ($)

Leisure

U1

L* = 80

H* = 0

If w increases a little,H* = 0

If w increases a lot,L* = 70H* = 10

The reservation wage

Labor Supply

• 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)

– If the income effect begins to dominate, hours of work decline as wage rates increase (a negatively sloped labor supply curve)

– Labor supply elasticity

• (% change in hours worked) / (% change in wage rate)

• Labor supply elasticity less than 1 means “inelastic” (insensitive)• Labor supply elasticity greater than 1 means “elastic”

• Example of backward bending labor supply:

% (30 40) / 40 .25.71

% (27 20) / 20 .35

H

w

Hours of Work

0

Wage Rate ($)

4024 30

10

20

27

SE > IE

IE > SE

% (40 24) / 240.667

% (20 10) /10

H

w

Labor Supply

Female Labor Supply (1960-1980)

• 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

7

Fe

ma

le P

art

icip

atio

n

Gro

wth

Rat

e of

USSR

United States

Israel Britain

France

Sweden

Germany

Italy

Australia

Spain

Japan

Netherlands5 1.5 3.5ˆ 0.5838 2 6

Let A = $500 per month, w = $5 per hour, and BRR = –0.5

Welfare Programs and Work Incentives

H wH ABenefit

ReductionActual

TransferTotal

Income

0 0 500 0 500 500

1 5 500 -2.5 497.5 502.5

2 10 500 -5 495 505

3 15 500 -7.5 492.5 507.5

176 880 500 -440 60 940

199 995 500 -497.5 2.5 997.5

200 1000 500 -500 0 1000

201 1005 500 -500 0 1005

202 1010 500 -500 0 1010

• In some states the cash grant is reduced at the “benefit reduction rate”. The BRR acts as a tax on earnings.

Consumption ($)

500

Hours of Leisure0 8040

U1

L* = 40

H* = 40

L* = 55

H* = 25

55

BRR = tax = 50%U0

Welfare Programs and Work Incentives

• If states choose a BRR equal to 100%, workers will not work because earnings are taxed at a rate of 100%.

Consumption ($)

Hours of Leisure0 8040

U0

L* = 40

H* = 40

BRR = tax = 100%

U1

500

L* = 80

H* = 0

Welfare Programs and Work Incentives

• Choosing a BRR equal to 0%, means the worker will work more than she did when the BRR was equal to 50%.

Consumption ($)

500

Hours of Leisure0 8040

L* = 40

H* = 40

L* = 55

H* = 35

45

BRR = tax = 0%U1U0

Welfare Programs and Work Incentives

• The EITC phase in a cash grant at 40% for low-income workers is a wage subsidy (negative tax) of 40%.

Consumption ($)

500

Hours of Leisure0 8040

L* = 40

H* = 40

L* = 35

H* = 45

35

EITC = -tax = -40%U1U0

Welfare Programs and Work Incentives

Leisure

Consumption ($)

110

10,350

13,520

14,490

17,660

33,178

Net wage is 40% above the actual wage

Net wage equals the actual wage

Net wage is 21.06% below the actual wage

0

Welfare Programs and Work Incentives