The Basic Neoclassical Model of Labor Supply

1
The Basic Neoclassical Model of Labor Supply

• The labor-leisure tradeoff

2
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).

3
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.

4
Change in the wage

• A change in the wage generates
• a substitution effect, and
• an income effect

5
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.

6
Income effect

• as the wage rate rises, an individuals 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.

7
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.

8
Backward-bending labor supply curve
9
Indifference curves

• An indifference curve is a graph of alternative
  combinations of goods that provide a given level
  of satisfaction (utility).

10
Utility function

• It is assumed that the individuals 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
• UU(Y,L)

11
Indifference curve
UUo
12
Indifference curve (contd.)
An indifference curve is downward sloping since
an individual is willing to give up some income
to receive additional leisure (or vice versa).
13
Indifference curves (contd.)
A point that lies above an indifference curve
provides a higher level of utility than a point
on the curve.
14
Indifference curves (contd.)
An indifference curve passes through each point
in the diagram.
(U gt Uo)
15
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.

16
Time constraint

• The time constraint is given by
• H L T
• where
• H hours of work
• L hours of leisure
• T total time available

17
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

18
Budget constraint
Thus, the following two equations must be
satisfied 1. HL T 2. pYwH Rewriting equation
(1) as H T-L and substituting this into
equation (2) results in pYwT-wL
19
Full-income constraint
With a little algebraic manipulation, this
becomes wTpYwL (3)

• This equation is called a full-income constraint.
• full income an individuals 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).

20
Budget constraint
An alternative form of equation (3) is given
by Y -(w/p)L (w/p)T (3) This equation
describes the relationship that exists between
hours of leisure and real income. Equation (3)
is the individuals budget constraint.
21
Budget constraint (contd.)
The intercept of the budget constraint on the
horizontal axis equals T (the maximum amount of
leisure time that an individual can receive).
Notice that H decreases from T to 0 as L rises
from 0 to T.
22
Budget constraint (contd)
The intercept of the budget constraint on the
vertical axis equals wT / p ( real full
income). The slope of the budget constraint
equals -w/p.
23
Optimal work/leisure mix

• Utility is maximized at the point of tangency
  between an indifference curve and the budget
  constraint.

24
Slope of indifference curves

• The absolute value of the slope of an
  indifference curve the opportunity cost of time
  at that point.
• Steep indifference curves indicate a high value
  of time in nonmarket activities

U2
U3
Uo
U1
Y
L
25
Corner solution

• A corner solution occurs when the indifference
  curve is steeper than the budget constraint at
  the point corresponding to zero hours of work.

U2
U3
Uo
U1
Y
wT
p
0 T L T
0 H
26
Corner solution (cont.)

• 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.
  

U2
U3
Uo
U1
Y
wT
p
0 T L T
0 H
27
Corner solution (cont.)

• A corner solution at zero hours of work will
  occur when
• the opportunity cost of time is relatively high,
  and/or
• the market wage rate is low.

U2
U3
Uo
U1
Y
wT
p
0 T L T
0 H
28
Reservation wage

• The absolute value of the slope of the
  indifference curve at the point corresponding to
  zero hours of work is the individuals
  reservation wage (expressed in real terms).

U2
U3
Uo
U1
Y
slope reservation wage
0 T L T
0 H
29
Real wage gt reservation wage

• If the real wage in the labor market exceeds the
  reservation wage, the individual chooses to work.

U2
U3
Uo
U1
Y
Budget constraint slope real wage
slope reservation wage
0 T L T
0 H
30
Real wage lt reservation wage

• If the real wage is less than the reservation
  wage, the individual chooses to remain out of the
  labor force and a corner solution occurs.

U2
U3
Uo
U1
Y
Budget constraint slope real wage
wT
p
slope reservation wage
0 T L T
0 H
31
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.

32
Nonlabor income (cont.)

• Using the definition
• A total amount of nonlabor income
• The time and goods constraints become
• Time constraint H L T (1)
• Goods constraint wH A pY (2)

33
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
(wTA)/p An inspection of this budget constraint
indicates that the slope equals -w/p (as in the
simpler model) and the intercept equals (wTA)/p.
34
Changes in nonlabor income

• As the level of nonlabor income rises, the budget
  constraint shifts vertically upward

Y
A gt A gt 0
wTA
1
o
1
p
wTA
o
A A
p
1
wT
A A
p
o
A 0
0 T L T
0 H
35
Non-labor income (cont.)

• The slope of the budget constraint stays the same
  when nonlabor income changes.
• The budget constraint still terminates at T hours
  of leisure.

Y
A gt A gt 0
wTA
1
p
wTA
o
A A
p
1
1
0
wT
A A
p
o
A 0
0 T L T
0 H
36
Leisure and nonlabor income

• If leisure is a normal good, an increase in
  nonlabor income results in
• An increase in leisure time
• A reduction in work hours

Y
wTA
1
p
wTA
o
p
wT
p
U2
U1
Uo
0 T L T
0 H
37
Leisure and nonlabor income (cont.)

• The change in hours worked that results from a
  change in real income, holding relative prices
  constant, is called a pure income effect.

Y
wTA
1
p
wTA
o
p
wT
p
U2
U1
Uo
0 T L T
0 H
38
Income and substitution effects
Y

• 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

w1 T
p
woT
p
C
A
U1
Uo
0 T L T
0 H
39
Substitution effect
Y

• Substitution effect change in the mix of L and
  Y resulting from a change in relative prices,
  holding utility constant.

w1 T
p
woT
p
C
B
A
U1
Uo
0 T L T
0 H
40
Income effect
Y

• Budget constraint at point B is constructed so
  that it is parallel to the final budget
  constraint.

w1 T
p
woT
p
C
B
A
U1
Uo
0 T L T
0 H
41
Income effect (cont.)
Y

• Movement from point B to C is a pure income
  effect.
• Leisure rises as real income rises in response to
  the higher wage.

w1 T
p
woT
p
C
B
A
U1
Uo
0 T L T
0 H
42
Net effect
Y

• When the income effect is smaller than the
  substitution effect, hours worked increases and
  leisure decreases when the wage rate increases.

w1 T
p
C
woT
p
B
U1
A
Uo
0 T L T
0 H
43
Net effect (cont.)
Y

• 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.

w1 T
p
C
woT
p
B
U1
A
Uo
0 T L T
0 H
44
Income replacement programs

• At a wage rate of w, this individual will work Ho
  hours and consume Lo hours of leisure. Income Yo

45
Unemployment compensation

• If all lost income is replaced when the
  individual becomes unemployed, the individual
  moves from point A to point B if unemployed.

46
Unemployment comp. (cont.)

• utility rises when an individual becomes
  unemployed under complete income replacement.
• unemployment compensation plans do not provide
  full income replacement.

47
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.

48
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).

49
Disability insurance (cont.)

• Disability insurance programs require medical
  examinations by approved physicians to reduce the
  possibility that workers will file fraudulent
  disability claims.

50
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).

51
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.

52
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.)

53
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.

54
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.

55
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.

56
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).

57
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.

58
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.

59
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).

60
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.

61
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.

62
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.

63
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).

64
Disability insurance (cont.)

• Disability insurance programs require medical
  examinations by approved physicians to reduce the
  possibility that workers will file fraudulent
  disability claims.

65
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).

66
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.

67
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.)

68
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.

69
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.

70
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.

71
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).

72
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.

73
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.

74
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).

75
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.

76
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.

77
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.

78
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).

79
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.

80
Earned-income tax credit (cont.)

• The diagram on the left illustrates the effect of
  an earned income tax credit.