example: suppose worker utility is given by the more c and l the happier is the worker worker...
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• Example: Suppose worker utility is given by
• The more C and L the happier is the worker
Worker Utility
U C L
C ($)
L (hours)
U(utils)
0 0 0
100 10 31.6
200 20 63.3
300 30 94.9
400 40 126.5
500 50 158.1
• Example: Suppose worker utility is given by
• Holding C constant, the more L goes up the happier the worker is
U C L
C ($)
L (hours)
U(utils)
300 0 0
300 10 54.8
300 20 77.5
300 30 94.9
300 40 109.5
300 50 122.5
Worker Utility
• Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal
10 0 10L
C ($)
L (hours)
U(utils)
300 0 0
300 10 54.8
300 20 77.5
300 30 94.9
300 40 109.5
300 50 122.5
54.85.48
10L
UMU
L
54.8 0 54.8U
Diminishing Marginal Utility
• Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal
20 10 10L
C ($)
L (hours)
U(utils)
300 0 0
300 10 54.8
300 20 77.5
300 30 94.9
300 40 109.5
300 50 122.5
22.72.27
10L
UMU
L
77.5 54.8 22.7U
Diminishing Marginal Utility
• Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal
30 20 10L
C ($)
L (hours)
U(utils)
300 0 0
300 10 54.8
300 20 77.5
300 30 94.9
300 40 109.5
300 50 122.5
17.11.71
10L
UMU
L
94.9 77.8 17.1U
Diminishing Marginal Utility
• Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal
40 30 10L
C ($)
L (hours)
U(utils)
300 0 0
300 10 54.8
300 20 77.5
300 30 94.9
300 40 109.5
300 50 122.5
14.61.46
10L
UMU
L
109.5 94.9 14.6U
Diminishing Marginal Utility
• Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal
50 40 10L
C ($)
L (hours)
U(utils)
300 0 0
300 10 54.8
300 20 77.5
300 30 94.9
300 40 109.5
300 50 122.5
13.01.30
10L
UMU
L
122.5 109.5 13U
Diminishing Marginal Utility
• Example: Suppose worker utility is given by
• If the worker is indifferent between all market baskets located on an indifference curve, then U is being held constant along it while L and C change
U C L
20C
L
U
20C L U
2
02U C L
0U C L
Indifference Curves
• Example: Indifference curve with U0 = 10
210C
L
L C
10 10
40 2.5
100 1
100C
L
U0 = 10
Indifference Curves
400C
L
220C
L
• Example: Indifference curve with U1 = 20
L C
10 40
40 10
100 4
U0 = 10
U1 = 20
Indifference Curves
Budget line
• C = (w)(H) + A
• T = L + H
• T – L = H
• C = (w)(T – L) + A
• C = (wT + A) – w L
• Constraints set boundaries on the worker’s opportunity set of all the consumption baskets the worker can afford
• Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour)
10 80 100 10C L C wT A wL L C
10 800
40 500
80 100800
900 10C L
10 40 80 leisure
500
100
Budget line
1000 10C L
• Example: What happens if A increases to 200 ($ per week)
2010 80 100C L C wT A wL L C
10 900
40 600
80 200
800
10 40 80 leisure
500
100
Budget line
C wT A wL 1060 12C L 100960 12C L
• Example: What happens if w increases to 12 ($ per hour)
L C
10 940
40 580
80 100
800
10 40 80 leisure
500
100
Budget line
The Hours of Work Decision
• Individual will choose consumption and leisure to maximize utility
• Optimal consumption is given by the point where the budget line is tangent to the indifference curve
• At this point the Marginal Rate of Substitution between consumption and leisure (slope of the indifference curve) equals the wage rate (slope of the budget constraint)
• Any other bundle of consumption and leisure given the budget constraint would mean the individual has less utility
• Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour)
10 40 80 leisure
500
100
900 10C L
U2
U1
U0
L* = 41
H* = 80 – 41 = 39
C* = 900 – 10(41) = 490
The Hours of Work Decision
Change in non-earned income
• Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour)
10 40 80 leisure
500
100
900 10C L
U1
L* = 41
H* = 39
C* = 490
1000 10C L 2010 80 100C L C wT A wL
What happens if A increases to 200 ($ per week)?
L* = 38
H* = 42
C* = 1000 – 10(38) = 620
Leisure is an inferior good since hours of leisure falls
• Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour)
10 40 80 leisure
500
100
900 10C L
U1
L* = 41
H* = 39
C* = 490
1000 10C L
What happens if A increases to 200 ($ per week)?
L* = 50
H* = 30
C* = 1000 – 10(50) = 500
Leisure is a normal good since hours of leisure increases
Change in non-earned income
• Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour)
800
10 40 80 leisure
500
100
L* = 41
H* = 39
C* = 490
Since w is the price of Leisure, the law of demand holds
C wT A wL 1060 12C L 100960 12C L
L* = 40
H* = 40
C* = 1060 – 12(40) = 580
• What happens if w increases to 12 ($ per hour)
An increase in w increases Hbecause SE > IE
Change in the wage rate
• Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour)
800
10 40 80 leisure
500
100
L* = 41
H* = 39
C* = 490
C wT A wL 1060 12C L 100960 12C L
L* = 46
H* = 34
C* = 1060 – 12(46) = 508
• What happens if w increases to 12 ($ per hour)
An increase in w decreases Hbecause IE > SE
Change in the wage rate
• When the Income Effect dominates:
U1
U0
A
6040 800 44
TE
Consumption ($)
SE
IE
Leisure
An increase in w decreases Hbecause IE > SE
Change in the wage rate
• When the Substitution Effect dominates:
U1
U0
A
5040 800 35
TE
Consumption ($)
An increase in w increases Hbecause SE > IE
SE
IE
Leisure
Change in the wage rate
The reservation wage
• Are the “terms of trade” sufficiently attractive to bribe a worker to enter the labor market?
• Reservation wage: the minimum increase in income that would make the person indifferent between working and not working
– Rule 1: if the market wage is less than the reservation wage, then the person will not work
– Rule 2: the reservation wage increases as nonlabor income increases
• Initially the individual does not work because w is too low
U2
U0
A
7040 800
Consumption ($)
Leisure
U1
L* = 80
H* = 0
If w increases a little,H* = 0
If w increases a lot,L* = 70H* = 10
The reservation wage
Labor Supply
• Relationship between hours worked and the wage rate
– At wages slightly above the reservation wage, the labor supply curve is positively sloped (the substitution effect dominates)
– If the income effect begins to dominate, hours of work decline as wage rates increase (a negatively sloped labor supply curve)
– Labor supply elasticity
• (% change in hours worked) / (% change in wage rate)
• Labor supply elasticity less than 1 means “inelastic” (insensitive)• Labor supply elasticity greater than 1 means “elastic”
• Example of backward bending labor supply:
% (30 40) / 40 .25.71
% (27 20) / 20 .35
H
w
Hours of Work
0
Wage Rate ($)
4024 30
10
20
27
SE > IE
IE > SE
% (40 24) / 240.667
% (20 10) /10
H
w
Labor Supply
Female Labor Supply (1960-1980)
• Source: Jacob Mincer, “Intercountry Comparisons of Labor Force Trends and of Related Developments: An Overview,” Journal of Labor Economics 3 (January 1985, Part 2): S2, S6.
1 2 3 4 5 6 7 8 9
Percentage Change in Wage
0
1
2
3
4
5
6
7
Fe
ma
le P
art
icip
atio
n
Gro
wth
Rat
e of
USSR
United States
Israel Britain
France
Sweden
Germany
Italy
Australia
Spain
Japan
Netherlands5 1.5 3.5ˆ 0.5838 2 6
Let A = $500 per month, w = $5 per hour, and BRR = –0.5
Welfare Programs and Work Incentives
H wH ABenefit
ReductionActual
TransferTotal
Income
0 0 500 0 500 500
1 5 500 -2.5 497.5 502.5
2 10 500 -5 495 505
3 15 500 -7.5 492.5 507.5
176 880 500 -440 60 940
199 995 500 -497.5 2.5 997.5
200 1000 500 -500 0 1000
201 1005 500 -500 0 1005
202 1010 500 -500 0 1010
• In some states the cash grant is reduced at the “benefit reduction rate”. The BRR acts as a tax on earnings.
Consumption ($)
500
Hours of Leisure0 8040
U1
L* = 40
H* = 40
L* = 55
H* = 25
55
BRR = tax = 50%U0
Welfare Programs and Work Incentives
• If states choose a BRR equal to 100%, workers will not work because earnings are taxed at a rate of 100%.
Consumption ($)
Hours of Leisure0 8040
U0
L* = 40
H* = 40
BRR = tax = 100%
U1
500
L* = 80
H* = 0
Welfare Programs and Work Incentives
• Choosing a BRR equal to 0%, means the worker will work more than she did when the BRR was equal to 50%.
Consumption ($)
500
Hours of Leisure0 8040
L* = 40
H* = 40
L* = 55
H* = 35
45
BRR = tax = 0%U1U0
Welfare Programs and Work Incentives
• The EITC phase in a cash grant at 40% for low-income workers is a wage subsidy (negative tax) of 40%.
Consumption ($)
500
Hours of Leisure0 8040
L* = 40
H* = 40
L* = 35
H* = 45
35
EITC = -tax = -40%U1U0
Welfare Programs and Work Incentives
Leisure
Consumption ($)
110
10,350
13,520
14,490
17,660
33,178
Net wage is 40% above the actual wage
Net wage equals the actual wage
Net wage is 21.06% below the actual wage
0
Welfare Programs and Work Incentives