Transcript Chapter 2

Labor Supply (Static)
Chapter 2
Labor Supply
Why has the LFPR of men declined?
Why has the LFPR of women increased?
Why has the length of the workweek
decreased?
How will changes in the welfare system affect
job mobility and/or unemployment spells?
Does a change in family structure affect LFP
decisions?
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Measuring the Labor Force
Bureau of Labor Statistics (BLS)

Conducts the Current Population Survey (CPS) which
surveys 60,000 households monthly
Workers are considered:

Employed:

Unemployed:

Out of the Labor Force:
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Labor Force Statistics
Labor Force =
Labor Force Participation Rate =
Employment-Population Ratio =
Unemployment Rate (UR) =
4
“Hidden Unemployed”
Note that “employment” is not different for
full- and part-time workers, so part time
workers who want full-time employment are
not differentiated.
People who give up searching are considered
out of the labor force.
Using the employment-population ratio
would have flaws as well, since unemployed
and out of the labor force would be grouped
together.
May
understate UR
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Labor Supply Trends (up to 1990s)
Male LFPR declined




Decline in labor market attachment after age 65
10% decline between ages 45 and 64
Decline in LFPR from 46% to 17% men over 65
Decline in LFRP from 97% to 93% for ages 25-44
Female LFPR increased, particularly among married women
Hours per week declined
Men (4%) less likely than women (16%) to be employed PT
Positive correlation between educational attainment and LFP
Racial Differences


White men have higher LFPR than black men.
White men work more hours than black men.
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Worker Preferences
Workers choose:
Goal:
U = f (C , L)
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Indifference Curves
Do not intersect
Unique
All points along an
indifference curve
represent the same utility
level
Higher indifference curves
represent higher levels of
utility
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Indifference Curves, cont.
Downward-sloping
Convex to the origin -
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Indifference Curves, cont.
rise
Slope =

run
MUL 
and MUC 
Move from (L1,C1) to
(L2,C2)

Gain + Loss = 0 to maintain
Utility = U
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Differences in Tastes
Large slope = Large MRS
MUL large relative to MUC
Individual enjoys _______
(willing to sacrifice a large
amount of consumption
for leisure)
Small slope = Small MRS
MUL small relative to MUC
Individual enjoys _______
(willing to sacrifice a large
amount of leisure for
consumption)
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Budget Constraint
Assumptions:

No saving →
where




V = non-labor income
(endowment)
w = wage
H = hours worked
Constant wages (no overtime)
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Budget Constraint, cont.
Solve for slope of BC:

C = V + wH
=
=
=
where T = total time available for work and leisure
rise
→ slope =

run
Interpretation:
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Budget Constraint, cont.
Properties:

Consumption bundles
below the budget line are

Consumption bundles
outside the budget line are

Consumption bundles
along the budget line
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Hours of Work Decision
Choose C* and L* such
that utility is maximized,
subject to BC


U(C) _ U(A) and
U(C) _ U(B), and U3
_______________
Interior solution (H* > 0)
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Hours of Work Decision, cont.
Tangency (between IC and BL) conditions:

Slope of indifference curve = Slope of budget line
C
ΔC
=


L
ΔL
MUL

w
MUC
MUL

 MUC

w

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Comparative Statics
Comparative Statics: How does individual
behavior change when a parameter of the
model changes?
Suppose V increases, holding w constant
 Suppose w increases, holding V constant

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Comparative Statics, cont.
Suppose V increases, ceteris paribus
Individuals have more money to spend on C
(C*↑)
 Income effect:


If leisure is a normal good, the demand for leisure will
__crease (L* ) and the number of hours worked will
__crease (H* )
ΔH

ΔV
w
 when V , H ,
0
 holding w constant
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Comparative Statics, cont.
Suppose w increases, ceteris paribus

Substitution effect:


ΔH
Since the wage rate is the OC of leisure, an

0
increase in w increases the OC of leisure, and
Δw V
workers substitute ______ for __________ (L* & H* )
Income effect:

An increase in w is an increase in wealth, which will
_________ the demand for leisure (L* & H* )
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Income and Substitution Effects
Suppose V increases  Budget line _______ up
Case 1: Both C* and
L* __crease, so leisure
must be a ________
good
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Income and Substitution Effects
Suppose V increases  Budget line _______ up
Case 2: C* __creases
and L* __creases, so
leisure must be an
_________ good
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Income and Substitution Effects
Suppose w increases  Budget line ________ up
Case 1: L* __creases,
so the ____________
effect dominates
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Income and Substitution Effects
Suppose w increases  Budget line _______ up
Case 2: L* __creases, so
the __________ effect
dominates
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Isolating the Income
and Substitution Effects
Suppose w increases  Budget line rotates up
To isolate the income effect,
draw a hypothetical budget
line with same slope as old
budget line and tangent to
new indifference curve


Income Effect: _ to _
Substitution Effect: _ to _
_________ Effect dominates

H*↑ when w↑
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Isolating the Income
and Substitution Effects
Suppose w increases  Budget line rotates up
To isolate the income effect,
draw a hypothetical budget
line with same slope as old
budget line and tangent to
new indifference curve


Income Effect: _ to _
Substitution Effect: _ to _
________ Effect dominates

H* when w
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Decision to Work
*
(H >0
or
*
H =0)
Can obtain U0 if H*=0
Trade leisure for
consumption by
entering labor market?


If w = wlow, U* _ U0
(cannot reach a higher
IC)  H* _ 0
If w = whigh, UH _ U0
(higher IC)  H* _ 0
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Reservation Wage
Individuals with high wage offers choose to
work (H*>0); individuals with low wage
offers do not work (H*=0)
There exists a wage ~
w  at which the
individual is indifferent between H*=0 and
H*>0, the reservation wage
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Reservation Wage Characteristics
w , do not work
When w < ~
When w > ~
w , work
High ~
w less likely to enter labor market
~
w depends upon tastes for work (slope of the indifference curve)
~
w ↑ as V↑ (when V↑, L*↑, so the wage required to induce labor
market participation increases)
w, a high wage offer increases the probability of working
For a given ~
(↑ LFPR when w↑)
There is a positive relationship between wages and the probability of
working (the higher the wage, the more likely it is to exceed the
reservation wage) – no income effect for non-workers, so there are
not competing income and substitution effects when considering how
many hours to work
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Individual Labor Supply Curve
Recall:




Work if reservation wage <
wage offer; otherwise H*=0
Work more when wage ↑ if
substitution effect dominates
Substitution effect always
dominates (income effect
DNE) for non-workers 
LFPR ↑ when wage ↑
Work less when wage ↓ if
income effect dominates
(only true for workers)
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Market Labor Supply Curve
Workers have unique preferences, reservation
wages, indifference curves, and thus optimal hours
of work decisions
Market supply curve =
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Elasticity of Labor Supply
How responsive is labor supply to changes in wages?
%H
σ

%w
 0 when substituti on effect dominates

 0 when income effect dominates
Interpretation:


Elastic (______ responsive) when |σ|_ 1
Inelastic (______ responsive) when |σ|_ 1
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Elasticity of Labor Supply: Example
Suppose:
H1 = 2000
W1 = $15
H2 = 2200
W2 = $17.50


Interpretation:

___________ labor supply
Note: Since hours worked increased with wages, the
____________ effect dominates

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Elasticity of Labor Supply Estimates
Prime-Age Men:






α ≈ -0.1 
(1% increase due to substitution effect, and 2% decrease
due to income effect)
May explain decline in the length of the workweek (men
now earn more in real terms, so more leisure is
demanded)
Elasticity estimate not significantly different from zero
(most prime-age men work full-time, full-week jobs)
Different estimate for younger and older men, as well as
women
Much variation in empirical estimates
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Elasticity of Labor Supply Estimates
Problems with estimates

Hours of work




Per year? Per month? Per week? (α ≈ -0.1calculated using hours
of work per year)
Hours of work likely more inelastic for shorter time periods
Measurement error, especially for salaried workers
Wages


annual inc ome
For salaried workers, wage definition " wage" 
annual hours
likely measured with error
Wages should measure price of leisure as the marginal wage for
an additional hour of work, which is not likely average wage (may
include overtime, etc.)
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Elasticity of Labor Supply Estimates
Problems with estimates, cont.

Wages, cont.


Nonworkers? Wage ≠ 0, but no reported wage (only know wage
offer < reservation wage); these workers have low wage offers or
high reservation wages, and are not a “random sample” of the
population
Non-labor income


Workers with much non-labor income probably earned a lot in
the past and saved earnings (which are now wealth)  If these
workers continue to work a lot now, there will be a positive
relationship between V and H (suggests leisure is inferior).
When tastes for work are accounted for, evidence of a negative
income effect is found.
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Female Labor Supply
Different LFPRs across countries (for ages 25-54)

Italy: 50%; US: 75%; Sweden: 90%
Elasticity of Labor Supply



α ≈ 0.2 after correcting for the decision to work
(substitution effect dominates)
Women more responsive (in terms of LFP) to changes in
wages than men, less responsive in terms of H*
Responsiveness to husband’s wages


LFP elasticity with respect to whusband = 0.53
H* elasticity with respect to whusband = 0.17
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Female Labor Force Participation
LFPR↑ considerably since 1960



As a cohort ages, LFPR↑
As time has passed, LFPR↑
Why?

Theory: The increase in real wages over time (between 2.1% per year
and 6.2% per year) has ___________ the probability of working (wages
more likely to exceed reservation wage)
 The increase in LFPR may be due to _________________________
_____________________________________ (Because of ↓ fertility?
Or has the number of children ↓ because women now work more?)



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Policy Application: Welfare
AFDC, TANF, etc.
Personal Responsibility and
Work Opportunity
Reconciliation Act
Take-it-or-leave-it offer



Assume V = 0 w/o benefits
Lump sum benefits = 0 if
individual works
L1 _ L2 _ T – leave labor
force with benefits

Why?:
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Policy Application: Welfare
Cash Grants



Assume V = 0 w/o benefits
Full benefits if individual
does not work  endowment
↑
For workers, cash grant is
reduced for each dollar
earned working  BL flatter


Net wage < actual wage  OC
of leisure ↓ so L*_
Note:
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Policy Application Summary: Welfare
Welfare programs __crease LFPR (an increase in
non-labor income increases a worker’s reservation
wage) and __crease the demand for leisure (a
decrease in net wages is a decrease in the OC of
leisure)
Empirical evidence

Negative income tax experiment: Cash grants were
95% or 140% of the poverty line, and the tax rate on
labor earnings was 50% or 70%)
Prob(work)↓ by 3% for husbands and 7% for wives
 H*↓ by 5% for men, 21% for women

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Policy Application: Earned
Income Tax Credit (EITC)
Began in 1975
By 1990s, $25 billion distributed
to low income families
Dependent upon income,
number and ages of children
Program



Up to Max Y ($8890), credit =
40% of earnings (net wage =
1.4w, up to $3556
Between $8890 and $11,160,
receive max credit ($3556)
For earnings in excess of $11,160,
benefits are reduced by 21.06¢ per
dollar earned
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Policy Application: Earned
Income Tax Credit (EITC)
Effects of EITC on labor
supply
Case 1: Income < $8890




Steep indifference curve 
strong preference for ______
Choose H* _ 0 w/o benefits
EITC induces
Recall: income effect does not
exist for non-workers, so
LFPR must _ when w_
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Policy Application: Earned
Income Tax Credit (EITC)
Effects of EITC on labor
supply
Case 2:
$8890 < Income < $11,160


Choose H* _ 0 w/o benefits
EITC induces
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Policy Application: Earned
Income Tax Credit (EITC)
Effects of EITC on labor
supply
Case 3: Income > $11,160



Choose H* _ 0 (many hours)
w/o benefits
EITC induces
_________ effect likely
dominant for those who work
many hours
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Policy Application Summary
EITC __creases LFPR for non-workers (only a
substitution effect exists) and __creases hours
worked (either because of a pure income effect or
because the individual is already working many
hours)

Evidence: 2.4% increase in LFPR
Cash grants _______ work incentives (LFPR ),
but EITC subsidizes work and __creases work
incentives (LFPR )
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