Labor Supply

1
Chapter 2

• Labor Supply

2
Introduction to Labor Supply

• Labor facts
• Working men decline in labor force participation
  from 90 in 1947 to 75 in 1990
• Working women rise in labor force participation
  from 32 in 1947 to 60 in 1990
• Work hours fell from 40 to 35 per week during the
  same time period

3

• Labor facts continued
• 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 labor force participation
  rates (LFPR) and hours of work than black men

4
Average hours worked/week, 1900-2005
5
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

6
Measuring the Labor Force continued

• Employment Population Ratio (percent of
  population that is employed)
• EPR E/P
• Unemployment Rate
• UR U/LF

7
Measurement Issues

• Labor Force measurement relies on subjectivity
  and likely understates the effects of a recession
• Hidden unemployed persons who have left the
  labor force, giving up in their search for work
• EPR is a better measure of fluctuations in
  economic activity than the UR

8
Overview of the Labor Market
Population of USA

• Dec 2006

Eligible Population/Potential Labor
Force Civilian 15 yrs old (230.108 m)
Not in Labor Force (NLF) Students/Retired/Househol
d workers and Discouraged workers (77.333m)
Labor Force (LF) Working or actively seeking work
(152.775m)
Unemployed (U) Not working but looking for
work (6.849m)
Employed (E) (145.926m)
9
Quick Review of Microeconomics

• Consumers goal maximize their utility given the
  limits imposed by their budget constraints.
• Two goods X and Y
• Prices PX and PY
• Income M
• Utility function U(X,Y)

10

• Review An individual has a series of
  indifference curves representing preferences

1. Indifference curves never cross. 2.
Indifference curves are negatively sloped 3.
Indifference curves are convex to the origin.
4. Slope MRS MUX/MUY (dU/dX)/(dU/dY)
Y
UB
UA
X
11
Review The budget constraint is drawn by using
the following equation

• PXX PYY M
• or
• Y (PX/PY)X M/PY

Y intercept M/PY Slope -(PX/PY)
-MRS
12
Review Combining the budget constraint and the
utility function.

• -MRS-(PX/PY)
• Solve for demand of X and Y.

13
Worker Performance

• Framework used to analyze labor supply behavior
  is the Neo-Classical Model of Labor-Leisure
  Choice
• Utility Function measure of satisfaction that
  individuals receive from consumption of goods and
  leisure (a kind of good)
• U f(C, L)
• Where U is an index

14
Income-Leisure Choice

• Utility increases as you move outward
• The 4 assumptions give us smooth well-behaved
  IDCs
• Do not intersect

C

• Assumptions
• Complete ordering
• More is better
• Transitivity
• DMRS

u1
u0
leisure
15
Marginal Utility

• Marginal utility of leisure (MUL) is the change
  in utility caused by an additional hour of
  leisure, holding constant the amount of good C
  consumed
• Same definition for marginal utility of
  consumption (MUC)
• MULgt 0 and MUCgt0

16
Marginal Rate of Substitution

• Slope of the indifference curve measures the rate
  at which a person is willing to give up leisure
  in return for additional consumption, holding
  utility constant.
• Slope of the indifference curve is given by
• ?C - MUL
• ?L MUC

17
Marginal Rate of SubstitutionContinued

• See graph provided in class
• Consider moving from A to B (small change) Lose
  ?L units of leisure
• ?utility lost ?LMUL
• Gain ?C units of consumption
• ?utility gained ?CMUC
• Since utility must be constant along IDC curve
  ?LMUL ?CMUC 0
• ??C/ ?L -MUL/ MUC

18
Marginal Rate of SubstitutionContinued

• The absolute value of the slope of the
  indifference curve is the marginal rate of
  substitution (MRS) in consumption
• The higher the MRS, the more a person values
  leisure relative to consumption
• MRS is a key determinant of the labor supply
  decision (e.g. taste for work)

19
Potential Income ConstraintIndividuals try to
attain the highest possible IDC. However, they
are constrained by their potential income
constraint.It is a potential income
constraint because it indicates various amounts
of income that can be obtained by giving up
leisure and working at the market wage.The
actual amount of income received depends on the
hours you decide to work at the market wage plus
your non-wage income (income from other sources).
20
What does the Budget Constraint look like?

• Remember PXX PYY M?
• Lets do some math to get there
• C Hw
• C (24-L)w
• C 24w Lw
• Rewrite to get wL 1C 24w
• Does this look familiar?
• Compare PX ? w, X ? L, PY ? 1, Y ? C

21
More specifically, the slope of the potential
budget constraint depends on the market wage
the higher the market wage the steeper the slope.
Budget Constraint continued
Potential income constraint CwHV
Total time labor leisure or T H L
22
What is the slope of the potential income
constraint?
C
Slope -w
But in this case, income depends on the
leisure/labor choice So, the budget constraint
is
V
leisure
T
C wH V C w(TL) V C (wT V) wL C
Full Income Value of Leisure Consumed
Equation for a line, the budget line
23
Budget continued
Slope -w
Budget line C (wT V) wL
C
E Endowment point, the only feasible point on
the budget line if the person does not work
E
V

leisure
T
24
Combining the IDC and the potential income
constraint gives us the labor-leisure choice.
CwHV
u0
L
Leisure
Labor
25
It is often assumed that non-labor income is zero.
wT
C
u0
L
26
Equilibrium

• Equilibrium occurs at
• point A
• Equilibrium is characterized by the point where
  MRS w

C
A
U (C, L)
T
L
27
Graphical Example

• If w 10 and the consumer has 24 hours to use

C
1024240
A
10770
24
17
L
H
28
Numerical Example 1

• Suppose
• U(C,L) C L
• w 8
• consumer has 24 hours to use
• Max U(C, L) s.t. budget constraint
• Budget constraint

29
Numerical Example, cont.

• Solve for Tangency Condition MRS w
• Two equations and two unknowns
• Answer L , H , C

30
Budget Constraint, Part II

• Suppose V 25
• Shifts budget constraint up by 25.
• If Vgt0, what happens to L, C, and H?

C
B
A
25
L
31
Points to Remember

• Increase in V ? buy more of all normal goods
  including leisure
• ?L gt 0, ? C gt 0, and most importantly, ?H lt 0.
• Pure Income Effect

32
Numerical Example 2

• U(C,L) CL, w 8 and consumer has 24 hours to
  use.
• When V 0
• ? L 12, H 12, and C 96 (from slide 28-29)
• Now let, V 32
• Answer L , H , C

33
Income and Substitution Effects of a Wage Change

• What happens to the equilibrium amount of work
  effort if the wage rises?
• You might work more because the return to work
  effort is higher. In other words, you might
  SUBSTITUTE away from leisure because the
  OPPORTUNITY COST of leisure is higher.

34
Income and Substitution Effects of a Wage Change
Continued

• On the other hand, a higher wage rate also means
  that you have a higher income for each quantity
  of work. Since you hit your target income faster,
  you might want to work less. This is called the
  INCOME effect. The idea is that with more income
  you can afford to buy more leisure (assuming that
  leisure is a normal good).
• So, the income and substitution effects work in
  opposite directions.

35
Income and Substitution Effects
C
u1
u0
C
B
A
V
leisure
IE
SE
TE
36
Income and Substitution Effects
The difference between A and B is purely a matter
of having more potential income from which you
can buy more leisure. If leisure is a normal good
then B lies above and to the right of A.The
difference between B and C is now a pure (or
income compensated) substitution effect, since
you are on the same IDC. The only difference is
that the relative price of leisure is higher. As
a result, you will substitute away from the now
more expensive good leisure towards work.
37
In our example, the SEgtIE, so a wage increase
leads to more work effort and less leisure.
C
u1
u0
C
B
A
V
leisure
IE
SE
TE
38
It is also possible for IEgtSE. In this case, a
wage increase leads to less work effort and more
leisure.
C
u1
u0
C
B
A
V
leisure
IE
SE
TE
39
Key points

• For ?w gt 0, overall, ? C gt 0 unambiguously
• For ? w gt 0, overall, ? L and ? H are ambiguous
  (counteracting effects)
•  
• But we do know
• When IE dominates SE, the individual will work
  less following the wage increase.
• When SE dominates IE, the individual will work
  more following the wage increase.

40
Deriving the labor supply curve - we will do
this in class
41
Labor Supply ElasticityLabor supply elasticity
measures a workers responsiveness to wage
changes. In other words, it measures the change
in hours of work in response to a wage change.
42
Empirical estimates of labor supply elasticity

• Theory predicts a relationship between hours of
  work, wage rate, and non-labor income
• If non-labor income ? then hours worked ?
• If the wage rate ? then the effect on hours of
  work is ambiguous (e.g. H ? or H ?)
• Depends on magnitude of income and substitution
  effects
• We use data to resolve this ambiguity
• Use regression analysis to analyze the
  relationship between H, w, and V

43
Regression Analysis

• Example more educated workers will earn more
  than less-educated workers because they are more
  productive
• Yes, education raises earnings, but several other
  variables also determine earnings
• Some are observable by researchers (e.g.
  occupation, age, state of residence, etc)
• Some are unobservable by researchers, but
  observed by worker and/or employer (e.g.
  ability, preferences, etc)

44
Scatter Diagram Wages and Schooling by
Occupation, 2001
45
The Regression Line
a intercept of line (constant term) ß slope of
line i indexes observations (here workers)
Specify a linear statistical (regression) model
wi a ßsi
ß ?w/?s
a
46
The Scatter Diagram and the Regression Line
47
Multivariate Regression

• We want to isolate the correlation between hours
  of work and w, holding constant other factors,
  such as age, education etc.
• This is easily done using the same regression
  technique shown earlier.
• Hi a ßwi ?agei deduci
• Again, holding constant age and education, if
  ß0.004 then a 1 increase in weekly wages leads
  to a 0.004 increase in hours of work.

48
Empirical estimates of labor supply elasticity

• Hours of work regression Hi a ßwi ?Vi
• Theory predicts ?lt0 (always), ßgt0 if
  substitution effect dominates the income effect,
  ßlt0 otherwise
• Note that ß corresponds to ?H/ ?w, and thus the
  labor supply elasticity is given by s ßw/H
• Typically include other determinants of hours of
  work (age, sex, family structure, education,
  occupation, etc).

49
Empirical estimates of labor supply elasticity
continued

• Empirical estimates for prime-aged males
• s -0.1
• So a 10 increase in wage rate leads to a 1
  decrease in hours worked
• Negative, so income effect dominates substitution
  effect
• Less than 1, so inelastic

50
The Participation Decision
Equilibrium for a Participant
u0
L
Leisure
labor
51
How do you decide whether or not to participate
in the labor market?
This person will not work. The market wage is
below their reservation wage.
u0
52
Equilibrium for a Non-Participant
The reservation wage is the wage at which an
individual is indifferent between participating
and not participating in the labor market.
wr reservation wage
u0
When the MRSgtw at T, you will not participate in
the labor market because the implicit value of
non-market time is high relative to the explicit
market value of non-market time.
53
What happens to a non-participant if the wage
rises?
Case 1
w1
wr
w0
u0
54
What happens to a non-participant if the wage
rises?
Case 2
w1
B
w0
A
u1
u0
55
What happens to a non-participant if V rises?
You stay out of the market
wr
wr
V
u1
u0
If leisure is normal, an increase in non-wage
income never causes anyone to enter the labor
market.
56
What happens to a participant if V rises?
Case 1
Exit the market
B
V
u1
u0
A
57
What happens to a participant if V rises?
Case 2
Stay in the market
u1
u0
B
A
V
58
Given what we have discussed, what types of
people are more likely to work in the labor
market and what types of people are less likely
to work in the labor market?
59
What if there are fixed costs?

• Fixed monetary cost Start-up costs that are
  independent of the number of hours worked.
• What happens to the reservation wage?

C
wr
wr
V
u0
V - M
T
leisure
60
What if there are fixed costs?

• What if you have chosen to work and then a fixed
  monetary cost is imposed?

If you continue to work you work more hours.
C
u0
u1
V
V - M
T
H0
leisure
H1
61
What if there are fixed costs?

• What if you have chosen to work and then a fixed
  monetary cost is imposed?

Could be at U2 and not work or could be at U1 and
work more.
C
u0
u2
V
u1
V - M
T
leisure
62
Fixed Time or Commuting Costs

• How does the reservation wage change when there
  are fixed time costs?

C
wr
wr
V
u0
T
Tc
leisure
63
Fixed Time or Commuting Costs

• What if you have chosen to work and then a fixed
  time cost is imposed?

You work fewer hours.
C
u0
u1
V
T
Tc
leisure
H0
H1
64
Fixed Time or Commuting Costs

• What if you have chosen to work and then a fixed
  time cost is imposed?

Or you quit working.
C
u0
V
u2
T
Tc
leisure
65
Fixed Work Days

• Fixed work days can lead to underemployment.

C
u0
V
leisure
T
Lf
66
Fixed Work Days

• If you are under employed you might be willing to
  work extra hours for a lower wage (moonlight).

C
moonlighting wage
u1
u0
V
leisure
T
Lf
67
Fixed Work Days

• Fixed work days can also lead to over-employment.

C
u0
V
leisure
T
Lf
68
Overtime wages

• Labor supply increases by construction if the
  overtime wage starts at the equilibrium labor
  supply choice.

overtime wage
C
u1
u0
V
T
leisure
69
Overtime versus the straight-time equivalent

• An overtime wage increases work effort by more
  than an equivalent increase in the wage.

overtime wage
C
straight-time equivalent wage
u1
u0
V
T
leisure
70
Numerical Example I

• U(C, L) CL, T16, w 10 for the first H
  hours and w after that
• Question what is w such that consumer is
  indifferent to working overtime and not working
  overtime?

71
Fixed Work Days with Overtime

• In this case, even an overtime premium might not
  lead to increased work hours.

C
Sometimes an overtime wage will increase hours of
work and sometimes it will not. It does not in
the depicted case.
overtime wage
u0
V
leisure
T
Lf
72
Fixed Work Days with Overtime

• Or, you might work more.

overtime wage
C
u1
V
u0
leisure
T
Lf
73
Work incentive effects of income support schemes

• Income support programs affect behavior by
  altering opportunities (potential income
  constraints).
• To analyze the effect of a specific program ask
  yourself two questions
• What is the impact on non-labor income?
• What is the impact on the wage?
• We will discuss the following income support
  mechanisms demogrants, welfare, negative income
  taxes, and wage subsidies.

74
2005 data on Transfer Programs
from bea.gov
75
Moffitt paper

• We will discuss the major points of the Moffitt
  paper in class at this point.

76
Demogrant

• Examples include family allowance and old age
  pensions in most countries.

C
Since a demogrant is a pure IE, it always reduces
labor supply.
u1
VD
u0
V
leisure
T
l1
l0
77
Aid to Families with Dependent Children (AFDC)

• Origins from the 1935 Social Security Act
• Costs shared by federal and state governments
• Federal government sets baseline standards, but
  state can modify them

78
AFDC (Continued)

• Eligible families must have
• Children under 18, deprived because a of parents
  absence (e.g. single moms) or the unemployment of
  the principal family earner
• States set their own need standard, based on
  family size
• AFDC recipients can also work, but total income
  cannot exceed 185 of the state standard
  (earnings are partially taxed away, up to that
  threshold)
• In 1993, average recipient family received 375
  per month from AFDC

79
TANF (Temporary Aid to Needy Families)

• Grew of out AFDC program in 1996
• Legislation complicated, but basically modified
  AFDC to include
• Stricter eligibility rules
• Lifetime limits (no more than 60 months)
• Work search requirements
• Total expenditures on TANF in 2005 25 Billions,
  so about 14,000 per family (5,600 per recipient)

80
Welfare

• You must have no non-wage income to qualify.

C
VW
leisure
T
81
Welfare

• Case 1 leave work for welfare.

High welfare payments have a big work
disincentive.
C
VW
u1
u0
leisure
T
82
Welfare

• Case 2 keep working.

C
u0
VW
leisure
T
83
Numerical Example IV

• Suppose a consumer has 20 hours to use, and can
  receive a welfare benefit of 20, and
• U(C, L) CL
• Case 1 No work
• C , L , U
•  
• Case 2 Work
• C , L , U
•  
• If indifferent between working and not, w

84
How can we get people off welfare?

• Reduce the welfare payment
• Increase wages
• Reduce the 100 implicit tax of welfare

85
Negative Income Tax

• Income after taxes and transfers is C G (1-t)E

G the basic guarantee E labor market
earnings t implicit tax rate
C
G
leisure
T
86
Negative Income Tax

• Case 1 Keep working, but work less

Assuming that leisure is normal, the new
equilibrium will lie to the right of the old
equilibrium because the IE and the SE work in the
same direction.
C
G
u1
u0
leisure
T
87
Negative Income Tax

• Case 2 Quit working

C
G
u1
u0
leisure
T
88
Negative Income Tax Graph Example 2

• Budget constraint is
• C G if H 0 (or L T)
• C G (1 t )(wH) if H gt 0 but lt G/wt
• C wH if H gt G / wt
• Example G 500, t 0.50 and w 10
• Breakeven income level G/t 1000
• Hours of work at breakeven G / wt 100
• Note that everyone gets at least 500

89
Negative Income Tax Graph Example 2
C
W10
W5
1000
R
u1
P
500
u0
leisure
T
90
Negative Income Tax Graph Example 2
Income Effect P?Q Substitution Effect Q ?R
Both reduce hours worked!
C
Q
R
P
u1
G
u0
leisure
T
91
Numerical Example V

• Suppose a consumer has 20 hours to use, and can
  receive a welfare benefit of 20 with 50
  tax-back rate, and U(C, L) CL
• w

92
Wage Subsidy

• Since one of the problems with negative income
  tax and welfare is that they discourage work
  effort, some have suggested using a wage subsidy
  instead.

C
u0
leisure
T
93
Wage Subsidy

• However, the disincentive effect of a wage
  subsidy is lower than for an EQUIVALENT (same
  utility) negative income tax.

C
ws
wage subsidy equilibrium
negative income tax equilibrium
w
G
u1
u0
leisure
T
94
Wage Subsidy

• This is not to say that a wage subsidy is
  necessarily better.
• A wage subsidy does nothing to help
  unemployables.
• A negative income tax targets the poor better
  (given limited funds for income support payments)
  because payments depend on income level.

95
Earned Income Tax Credit

• The earned income tax credit (EITC) is another
  way to help low-income individuals.
• By 2003, EITC was the largest cash benefit
  program in the U.S. granting almost 34 billion
  per year back to low-income earners.
• The average credit per family was 1,784

96
EITC Eligibility

• Must have earned income from employment or from
  self-employment
• The taxpayers earned income must be less than
• 34,458 if the taxpayer has more than one
  qualifying child
• 30,338 if the taxpayer has one qualifying
  child
• 11,490 if the taxpayer has no qualifying
  child

97
Earned Income Tax Credit Example

• In 2003, a single woman with 2 kids could claim a
  credit of up to 40 of her earnings as long as
  she earned less than 10,750 per year.
• The resulting maximum credit is 4300 for a total
  income of 15,050
• The maximum credit is available as long as she
  earns between 10,750-14,040 for a total income
  between 15,050-18,340.
• Beyond 14,040 the credit begins to be phased
  out.
• Each additional 1 earned reduces the credit by
  0.2106 until the credit is credit is gone.

98
EITC graph example

EITC credit
4300
Earned Income
10,750
14,040
34,458
99
EITC

Assuming a wage10 per hour and 16 hours per day
available for work in a year with 365 days.
C
leisure
T163655840
2042
329
1075
At 10 per hour it takes L4300/2.106 2042
hours for the subsidy to hit 0.
1404
3446
100
EITC and Labor Supply
In general, one would expect employment to
increase for this person, but as the IE and SE go
in opposite directions, it is also possible that
they work less.
C
u1
u0
leisure
T
101
EITC and Labor Supply
Employment decreases means a pure IE
C
u1
u0
leisure
T
102
EITC and Labor Supply
Employment decreases IE and SE move together.
But it doesnt have to hit at the kink point,
could also be above.
C
u1
u0
leisure
T
103
EITC and Labor Supply
If you are above the last subsidy cutoff but have
really flat IDCs it is possible that you work
less, but more likely EITC has no impact (see
next slide).
C
u1
u0
leisure
T
104
EITC and Labor Supply
EITC has no effect.
C
u0
leisure
T
In general, EITC has no impact on high wage
people.
105
Retirement

• Between 1950 and 2000 the labor force
  participation rate of men aged 55-64 fell from
  87 to 67.
• What caused this?

106
Definition of Retirement

• The individual is out of the labor force with the
  intention of remaining out permanently
• The individual has reduced his hours
  substantially from some lifetime average and
  intends to maintain hours at or below the current
  level
• The individual receives some of his income as
  pension benefits
• The individual appears on some company's
  retirement roll
• The individual receives primary social security
  payments (not derivable from another's
  employment)

107
Retirement
C
Imagine that you are 50 and trying to decide when
to retire. Assume that you expect to live until
80.
u0
Years of retirement
30
108
Retirement Case 1 Retire sooner
C
How does a wage increase effect your retirement
decision?
u1
u0
Years of retirement
30
IEgtSE -- retire sooner
109
Retirement Case 2 Retire later
C
u1
u0
Years of retirement
30
IEltSE -- retire later
110
How does a pension benefit increase effect the
retirement decision?
u1
u0
Slope changes because you only get the higher
pension during the years you are retired.
C
VNP
VN
Years of retirement
30
SE leads to less work IE leads to less work So
you retire sooner
111
Social Security

• Most workers are entitled to Social Security
  monetary benefits upon their retirement
• Social Security income is the most important
  source of income of retirees in the U.S.
• The monthly benefit to which the worker is
  entitled depends upon that earnings record (work
  history) and upon the age at which the retiree
  chooses to begin receiving benefits
• Earliest age to claim benefits is 62 (but
  benefits are reduced)

112
Social Security

• So far we have assumed that a retired person
  withdraws completely from the labor market.
• But many retired people work at least part time.
• As of 2000, the Social Security system allows
  people 65-69 to earn 17,000 with no penalty, but
  after that they face a 33 tax back rate.
• The earnings test does not apply after age 70

113
Financing of Social Security

• Workers contribute to Social Security through
  payroll taxes or self-employment taxes (FICA and
  SECA), as required by the Federal Insurance
  Contributions Act
• The FICA tax rate is 6.2, and earnings are
  taxable up to a maximum taxable amount (97,500
  so the maximum tax paid is 6,045)
• 159 million workers contributed to the Social
  Security fund in 2005

114
Suppose Social Security is 10,000 and the going
wage rate is 20 per hour. Assuming no other
non-wage income.
C
116,480
47,303
27,000
10,000
T173656205
leisure
With a tax back rate of 33, subsidy is zero
L10,000/6.61515.15 hours
1515.15
850
2365.15
115
How does Social Security impact labor supply?
C
Case 1 There is a pure IE, so labor supply
decreases.
116,480
u1
u0
10,000
leisure
T
116
How does Social Security impact labor supply?
C
Case 2 Employment decreases IE and SE move
together. But it doesnt have to hit at the kink
point, could also be above.
u1
u0
116,480
10,000
T
leisure
117
How does Social Security impact labor supply?
C
Case 3 If you are above the last subsidy cutoff
but have really flat IDCs. It is possible that
you work less, but more likely that Social
Security has no impact (see next slide).
u0
u1
116,480
10,000
leisure
T
118
How does Social Security impact labor supply?
C
Case 4 Social Security has no impact.
116,480
u0
10,000
leisure
T
119
Fertility

• Essays on the Principle of Population Malthus
  (1798)
• As incomes rise above subsistence people marry
  younger and have more children leading to an
  increase in population and a return to
  subsistence.

120
The Household Decision

• Households derive utility from the number of
  children (N) and the quantity of goods consumed
  (X)
• The household has an exogenous income (I)
• Let pN and pX denote the price of a child and the
  price of the consumption good
• Households must choose N and X to solve the
  following problem
• Max U(N,X) such that pNN pXX I

121
The Household Decision

• .

Equilibrium tangency between I.C. and budget
line. That is, (MUX/ pX) (MUN/ pN)
X
I/Px
Slope x I/PX (PN/PX)N
u0
N
I/PN
122
If non-wage income rises

• Assuming both goods are normal.

X
u1
u0
I/PX
N
I/PN
123
If the price of children rises

• .

A?B Income effect, consume less of all normal
goods B ?C substitution effect, consume less of
the relatively pricier good (here children) and
more of the relatively cheaper good (here X)
X
A
C
u0
B
u1
N
IE
SE
124
End chapter 2