The Basic Neoclassical Model
of Labor Supply
The labor-leisure tradeoff
Assumptions:


there are only two possible uses of
time: labor and leisure,
each individual selects the combination
of hours of work and leisure that
maximizes his or her level of
satisfaction (utility).
Opportunity costs


For individuals who are working, the
opportunity cost of an additional hour
of leisure time is the wage rate.
Individuals choose not to work if the
value of leisure time exceeds the
market wage.
Change in the wage
A change in the wage generates:
 a substitution effect, and
 an income effect
Substitution effect



the opportunity cost of leisure time
rises as the wage rate increases.
as leisure time becomes more costly,
individuals consume less leisure time
and spend more time at work.
this is the substitution effect resulting
from a higher wage.
Income effect




as the wage rate rises, an individual’s real
income rises.
this leads to an increase in the consumption
of all normal goods.
if leisure is a normal good, the higher wage
rate will induce the individual to consume a
larger quantity of leisure time (and reduce
hours of work).
This is the income effect resulting from a
wage increase.
Net effect

If leisure is a normal good, an increase
in the wage rate will cause the quantity
of labor supplied to:


increase if the substitution effect is larger
than the income effect, and
decrease if the income effect is larger than
the substitution effect.
Backward-bending labor
supply curve
wage
S
income subs.
effect > effect
wo
income < subs.
effect
effect
Quantity of Labor Supplied
Indifference curves

An indifference curve is a graph of
alternative combinations of goods that
provide a given level of satisfaction
(utility).
Utility function


It is assumed that the individual’s
utility level is a function of two
goods: real income (Y), and leisure
time (L).
In mathematical terms, this utility
function may be expressed as:
U=U(Y,L)
Indifference curve
Y
U=Uo
L
Indifference curve (cont’d.)
Y
An indifference
curve is downward
sloping since an
individual is willing
to give up some
income to receive
additional leisure (or
vice versa).
L
Indifference curves (cont’d.)
Y
A point that lies
above an
indifference curve
provides a higher
level of utility
than a point on
the curve.
A
U=Uo
L
Indifference curves (cont’d.)
Y
An indifference
curve passes
through each point
in the diagram.
(U’ > Uo)
A
U=U'
U=Uo
L
Constrained maximization


Individuals attempt to attain the
highest possible level of utility.
The choice among alternative levels
of Y and L, however, is restricted
due to two constraints:
a time constraint, and
 a goods constraint.

Time constraint:

The time constraint is given by:
H+L=T
where:
H = hours of work
L = hours of leisure
T = total time available
Goods constraint

The goods constraint is given by:
wH = pY
where:
w = wage rate
H = hours of work
p = price index for real income
Y = real income
Budget constraint
Thus, the following two equations must be
satisfied:
1. H+L = T
2. pY=wH
Rewriting equation (1) as: H = T-L
and substituting this into equation (2)
results in:
pY=wT-wL
Full-income constraint
With a little algebraic manipulation, this
becomes:
wT=pY+wL



(3)
This equation is called a full-income constraint.
full income = an individual’s maximum earnings
potential (= wT in this case).
full income equals the total explicit cost of goods
and services (pY) plus the total implicit cost of
leisure time (wL).
Budget constraint
An alternative form of equation (3) is given
by:
(3’)
Y = -(w/p)L + (w/p)T
This equation describes the relationship
that exists between hours of leisure and
real income. Equation (3’) is the individual’s
budget constraint.
Budget constraint (cont’d.)
The intercept of the budget
constraint on the horizontal axis
equals T (the maximum amount
of leisure time that an individual
can receive).
Y
Notice that H decreases from T
to 0 as L rises from 0 to T.
0
T
T
0
L
H
Budget constraint (cont’d)
The intercept of
the budget
constraint on the
vertical axis
equals: wT / p (=
real full income).
Y
wT
p
The slope of the
budget constraint
equals -w/p.
slope = -w /p
0
T
T
0
L
H
Optimal work/leisure mix

Y
wT
p
Y*
U3
U2
U1
Uo
0
T
L*
H*
T
0
L
H
Utility is
maximized
at the point
of tangency
between an
indifference
curve and
the budget
constraint.
Corner solution (cont.)
Uo
Y
U1 U2 U3
wT
p


0
T
T L
0 H
the highest level of
utility in this case
occurs at zero hours
of work.
An individual chooses
to remain out of the
labor force when a
corner solution such
as this occurs.
Corner solution (cont.)
Uo
Y
U1 U2 U3
wT
p

A corner solution at
zero hours of work
will occur when:


0
T
T L
0 H
the opportunity cost
of time is relatively
high, and/or
the market wage
rate is low.
Reservation wage
Uo
Y
U1 U2 U3

|slope| = reservation
wage
0
T
T L
0 H
The absolute value
of the slope of the
indifference curve
at the point
corresponding to
zero hours of work
is the individual’s
“reservation wage”
(expressed in real
terms).
Real wage > reservation wage
Uo
Y
U1 U2 U3

Budget constraint
|slope| = real wage
|slope| = reservation
wage
0
T
T L
0 H
If the real
wage in the
labor market
exceeds the
reservation
wage, the
individual
chooses to
work.
Real wage < reservation wage
Uo
Y
wT
p
0
T
If the real
wage is less
than the
reservation
Budget constraint
wage, the
|slope| = real wage
individual
chooses to
|slope| = reservation remain out of
wage
the labor force
and a corner
solution occurs.
T L
0 H
U1 U2 U3

Nonlabor income




Initially, it was assumed that all income was
received in the form of labor income.
Individuals, however, also receive income
from nonlabor income.
income from nonlabor sources is referred to
as “unearned income.”
nonlabor income may be received in the form
of interest payments, rent, dividends, profits,
alimony payments, transfer payments, lottery
winnings, lawsuit settlements, or any other
income that does not vary with hours worked.
Nonlabor income (cont.)

Using the definition:


A = total amount of nonlabor income
The time and goods constraints
become:


Time constraint:
H+L=T
Goods constraint: wH + A = pY
(1)
(2)
Nonlabor income (contd.)
Solving equation (1) for H:
H=T-L
Substituting this into equation (2) results in:
w(T - L) + A = pY
Solving this for Y results in the following budget constraint:
Y = -(w/p)L + (wT+A)/p
An inspection of this budget constraint indicates that the
slope equals -w/p (as in the simpler model) and the
intercept equals: (wT+A)/p.
Changes in nonlabor income
Y
wT+A1
p
wT+Ao
p
wT
p

A >A >0
1
o
A = A1
A = Ao
A=0
0
T
T L
0 H
As the level of
nonlabor
income rises,
the budget
constraint
shifts
vertically
upward
Non-labor income (cont.)
Y
wT+A1
p
wT+Ao
p
wT
p

A >A >0
A = A1
A = Ao

A=0
0
T
T L
0 H
The slope of the
budget constraint
stays the same
1
0 nonlabor
when
income changes.
The budget
constraint still
terminates at T
hours of leisure.
Leisure and nonlabor income
Y
wT+A1
p
wT+Ao
p
wT
p

U2
U1
Uo
If leisure is a
normal good,
an increase in
nonlabor
income results
in:


0
T
T L
0 H
An increase in
leisure time
A reduction in
work hours
Leisure and nonlabor income (cont.)
Y
wT+A1
p
wT+Ao
p
wT
p

U2
U1
Uo
0
T
T L
0 H
The change in
hours worked
that results
from a change
in real income,
holding relative
prices constant,
is called a “pure
income effect.”
Income and substitution effects
Y

w1 T
p
woT
p
C

A
U1
Uo
0
T
T L
0 H
A wage increase
from wo to w1
results in a
movement from
point A to C.
In this case, leisure
rises, so the
income effect
exceeds the
substitution effect
Substitution effect
Y

w1 T
p
woT
p
C
B
A
Uo
0
T
U1
T L
0 H
Substitution
effect =
change in the
mix of L and Y
resulting from
a change in
relative prices,
holding utility
constant.
Income effect
Y

w1 T
p
woT
p
C
B
A
Uo
0
T
U1
T L
0 H
Budget
constraint at
point B is
constructed
so that it is
parallel to the
final budget
constraint.
Income effect (cont.)
Y

w1 T
p
woT
p

C
B
A
Uo
0
T
U1
T L
0 H
Movement
from point B to
C is a pure
income effect.
Leisure rises as
real income
rises in
response to
the higher
wage.
Net effect
Y

w1 T
p
C
woT
p
B
A
U1
Uo
0
T
T L
0 H
When the income
effect is smaller than
the substitution
effect, hours worked
increases and leisure
decreases when the
wage rate increases.
Net effect (cont.)
Y

w1 T
p
C
woT
p

B
U1
A
Uo
0
T
T L
0 H
When the wage
changes, individual
substitution and
income effects are
not observed.
A backward-bending
labor supply curve
may be explained
using income and
substitution effects.
Income replacement programs

At a wage rate
of w, this
individual will
work Ho hours
and consume Lo
hours of leisure.
Income = Yo
Unemployment compensation

If all lost
income is
replaced when
the individual
becomes
unemployed,
the individual
moves from
point A to
point B if
unemployed.
Unemployment comp. (cont.)


utility rises when
an individual
becomes
unemployed
under complete
income
replacement.
unemployment
compensation
plans do not
provide full
income
replacement.
Unemployment comp. (cont.)


The original level
of utility is
attained at an
income level of Y’
when
unemployed.
In the U.S.,
unemployment
compensation is
roughly equal to
½ of full-time
earnings.
Disability insurance

If disabled workers
receive the same level
of income after an
injury as before and
receive more leisure
time, their level of
utility would increase
(assuming that “pain
and suffering” and
medical expenses are
fully compensated).
Disability insurance (cont.)

Disability
insurance
programs require
medical
examinations by
approved
physicians to
reduce the
possibility that
workers will file
fraudulent
disability claims.
Partial disability



A work-related injury that results in a partial disability
reduces the wage that the affected worker will
receive.
This reduction in the wage generates both
substitution and income effects on the quantity of
labor supplied.
If the goal is to adequately compensate the worker,
however, an appropriate income replacement scheme
would be to provide a payment that is just large
enough to offset the income effect resulting from the
reduction in the wage (since it is only the income
effect that involves a loss in utility).
U.S. welfare system


The first major national attempt at providing
aid to low-income households in the U.S.
occurred during the Great Depression. Most
of the relief programs developed during this
period, however, were temporary programs
designed to deal with the problems resulting
from the depression.
The modern U.S. welfare system was
introduced in the early 1960s as part of the
War on Poverty during the Johnson
administration.
Poverty level


A poverty level was established based upon
studies that attempted to determine the
amount of income required to provide
households with an adequate level of
nutrition and basic necessities.
It is assumed that a household of a given size
in a particular geographical area must receive
a particular level of income (Yt) to ensure
that these basic needs could be satisfied.
(This level of income is higher for larger
households and for residents in geographical
regions where the cost of living is higher.)
Benefits under basic welfare system



The government provides welfare benefits to
those households in which the level of income
falls below the target level (Yt).
Welfare benefits may take the form of either
monetary payments or subsidies for food,
housing, medical care, or other basic
commodities.
The goal is to provide a level of welfare
benefits that brings the level of household
income up to the target level.
Basic welfare system – budget constraint


If the individual does not
work at all, the level of
welfare benefits equals
Yt.
If the individual is
working, but receives a
level of income that falls
below Yt, the
government provides
enough welfare benefits
to provide a total income
of Yt.
Budget constraint (cont.)


The budget constraint is
horizontal at an income
level of Yt. In this portion
of the budget constraint,
the marginal wage (the
additional income resulting
from an additional hour of
work) equals zero.
If a welfare recipient
works an additional hour
and receives a wage of $6,
welfare benefits are
reduced by $6, leaving
total income unchanged.
Welfare and labor supply

an individual who, in the
absence of a welfare
system, has a level of
income that lies below
the target level of
income would always
prefer to leave the labor
force when such a
welfare system is
available (since the level
of income and leisure
both increase in this
case).
Welfare and labor supply (cont.)

Some individuals who,
in the absence of this
welfare system, would
have received a level
of income that
exceeds Yt, would
also choose to leave
the labor force.
Welfare and labor supply (cont.)

Note that the
substitution effect
of lowering the
marginal wage to
zero reduces the
quantity of labor
supply, as does the
income effect
resulting from the
provision of welfare
benefits.
Revised welfare system – 1967-1981

To reduce the labor supply disincentive
effects resulting from this type of welfare
system, this system was replaced in 1967
with a welfare system in which individuals
were able to keep a small amount of monthly
earned income without giving up any welfare
benefits. Beyond this point, welfare benefits
were reduced by $2 for every $3 earned (as
compared to a $1 reduction for every $1
earned under the earlier system).
Welfare revision: 1981


During the Reagan administration, the welfare
system was restored to a form that was essentially
equivalent to that of the early 1960s. The reason for
the change was a desire to reduce welfare benefits
for higher income welfare recipients while preserving
benefits for the “truly needy.”
With the restoration of a system that provides a
marginal wage of zero, the number of “working poor”
declined and a larger share of welfare recipients
remained out of the labor force.
Workfare



Beginning in 1997, a “workfare” system has been
adopted.
Welfare recipients are required to work a minimum
number of hours to qualify for welfare benefits.
(welfare benefits are zero unless welfare recipients
work the required minimum number of hours or are
engaged in approved job training or educational
programs).
Individuals are restricted to receiving welfare benefits
for a maximum of five years under this system.
Workfare budget constraint


Individuals receive no
benefits if they work
fewer than the minimum
number of hours (Hm, in
this example).
If they work Hm or more
hours, they receive the
same level of benefits as
under the earlier system.
Workfare and labor supply


it is expected that
welfare recipients
would choose to
work Hm hours.
If they work more
than this, the
marginal wage is
zero (until they
work enough
hours so that all
benefits are
eliminated).
Earned-income tax credit


The earned-income tax credit provides
additional income to low-income
households with a smaller labor supply
disincentive effect than the current
welfare system.
Under this system, a tax credit is
provided that rises with income up to a
point and then gradually declines.
Earned-income tax credit (cont.)

The diagram on
the left illustrates
the effect of an
earned income
tax credit.