Labor Supply

1
Chapter 6

• Labor Supply

2
Market Demand and Supply
3
There are different dimensions of labor supply

• participation

• hours worked per time period, given participation

• effort level

• level of skill

4
Assumptions

• Individuals choose between work and leisure.
• Work is time spent on a paying job.
• Leisure includes activities where one is not
  paid.
• Education
• Rest
• Work within the household

5
Indifference Curve
Income/day

• The indifference curve shows work and leisure
  combinations that yield the same amount of
  total utility.

• More hours of leisure implies fewer hours of
  work.

0
Leisure Hr
24
24
0
Work Hr
6
Indifference Curve
Wage 10/hour
Income/day

Convex to origin With low hours of leisure,
individuals are willing to give up a large
amount of income to get 1 more leisure
hour. With high hours of leisure, individuals
are willing to give up a small amount of income
to get 1 more leisure hour. (diminishing MRS)
100
40
20
14
0
Leisure Hr
24
24
0
Work Hr
7
Marginal Rate of Substitution
Income/day

• The marginal rate of substitution (MRS) is
  the amount of income one must receive to
  compensate for 1 less hour of leisure.

4

• At 4 hours of leisure (20 hours of work), one
  must receive 4 units of income to compensate
  for 1 less hour of leisure.

1

• At 8 hours of leisure (16 hours of work), one
  receive 1 unit of income to compensate for 1
  less hour of leisure.

• The MRS falls as one moves southeast along an
  indifference curve.

3
4
9
8
0
Leisure
24
24
0
Work
8
Indifference Map
Income/day

• Curves further from the origin indicate higher
  utility.

• A person will maximize utility by getting to
  the highest attainable indifference curve.

Y2
I3
Y1
I2
I1
0
Leisure
24
L2
L1
9
Work-Leisure Preferences
Income/day

• Leisure lovers

I1

• Workaholics

I2
4
3
0
Leisure
24
10
Budget Constraint
Income/day

• The budget constraint shows the combinations
  of income and leisure that a worker could get
  given a wage rate.

360

• At a wage rate of 5, a worker could get a
  maximum income of 120 per day (5/hour 24 ).

240

• At a wage rate of 10, a worker could get a
  maximum income of 240 per day.

120

• At a wage rate of 15, a worker could get a
  maximum income of 360 per day.

Leisure
24
0

• The slope of the budget constraint is wage
  rate.

11
Utility Maximization
Income/day

• The optimal or utility maximizing point is
  where the budget constraint is tangent to the
  highest attainable indifference curve (U).

• At U, the MRS (slope of the indifference
  curve) is the equal to the wage rate (slope of
  the budget constraint)

240
B
U

• At B, the MRS is greater than the wage rate.
  The individual values leisure more than the
  wage rate.

I3
80
I2
I1
A

• At A, the MRS is less than the wage rate. The
  individual values leisure less than the wage
  rate.

Leisure
24
0
16
12
Determinants of the Labor Force Participation
Decision
Income/day

• If a person has a low wage rate and/or steep
  indifference curves he is less likely to
  participate in the labor force.

W

• The reservation wage is the lowest wage
  necessary to induce someone to work.

• College students are less likely to
  participate in the labor force than other
  persons. Why?

H
Leisure
24
0
13
Non-Labor Income
Income/day

• At a wage rate of 10/hour with no other
  income, the optimal hours of leisure is 16 (8
  hours of work) at point U1.

• If the person gets an inheritance that
  generates 60 a day of non- labor income, the
  budget constraint has a parallel shift.

300
240
U2

• The optimal hours of leisure rises to 17 at
  point U2 .

U1
I2
I1
0
Leisure
24
16
17
14
Wage Effect
Income/day

• A change in the wage can have two effects

240

• Income effect and substitution effect.

U
Leisure
24
0
16
15
Income Effect

• Income Effect
• The change in desired hours of work resulting
  from a change in income, holding the wage
  constant.
• Leisure is a normal good, so higher income
  implies a desire for more leisure (fewer hours of
  work).
• For a wage increase, income is raised and so the
  income effect lowers desired work hours.

16
Substitution Effect

• Substitution Effect
• The change in desired hours of work resulting
  from a change in the wage rate, holding income
  constant.
• A higher wage rate raises the relative price of
  leisure.
• For a wage increase, the substitution effect
  lowers desired work hours.

17
Net Effect

• For Wage Increases
• If substitution effect gt income effect, then
  hours of work rise.
• If income effect gt substitution effect, then
  hours of work fall.
• For Wage Decreases
• If substitution effect gt income effect, then
  hours of work fall.
• If income effect gt substitution effect, then
  hours of work rise.

18
Income and Substitution Effects

• At a wage rate of 10/hour, the optimal hours
  of leisure is 16 (8 hours of work) at point U1.

Income/day

• If the wage rate rises to 15/hour, the
  optimal hours of leisure is 15 at point U2.

360

• The income effect (IE) is measured through a
  parallel shift of the old budget constraint.
  The IE is from U1 to U2 (from 16 to 17 hours of
  leisure).

U2
240
U2
I2
U1

• The substitution effect (SE) is measured by
  movement along I2. The SE is from U2 to U2
  (from 17 to 15 hours of leisure).

I1
0
Leisure
24
16
17
15

• The net effect is an increase of hours of work
  by 1 hour.

19
Backward Bending Labor Supply Curve
Wage Rate

• For a given person, hours of work may increase
  as the wage rate rises.

SL

• If the wage rate rises from 10 to 25 per
  hour hours of work rises from 8 to 10 hours per
  day.

25

• Above 25 per hour, hours of work fall.

10

• The backward bending labor supply curve is the
  result of the income and substitution effects of
  a wage change.

0
Hours of Work
24
8
10
20
Backward Bending Labor Supply Rationale

• The substitution effect dominates at low wage
  rates.
• The MRS is low because income is scarce relative
  to leisure.
• The income effect dominates at higher wage rates
• The MRS is high because leisure is scarce
  relative to income.

21
What are the testable predictions of this model?
(LFP Hours worked)
?
1) A higher wage rate
?
2) Higher non-wage income
?
3) A higher value of leisure
22
Empirical Evidence - LFPR
?
1) Men on average have higher wages than women
Real world result
2) For women Higher real wages and lower
fertility and changes in attitudes
regarding child-rearing
?
Real world result
?
3) Married women have higher value of time at
home than single women
Real world result
4) There have been falling wages for the
lowest-skilled older men and increases in
coverage and generosity of pension plans,
social security benefits, retiree health
insurance, and disability insurance.
?
Real world result
23
Empirical Evidence - Hours
5) Overall there has been an increase in wages
Real world result
6) Wage effects on hours worked for men
Real world result

• The labor supply curve is slightly backward
  bending
• for men. The income effect is slightly greater
  than the
• substitution effect.

7) Wage effects on hours worked for women
Real world result

• The substitution effect is greater than the
  income
• effect. Women substitute between work at home
• and market work more than men.

24
Weekly Hours of Work

• Weekly hours of work fell prior to World War
  II due to rising real wages (income effect
  dominated the substitution effect).

• Since World War II, weekly work hours have
  been stable.