FE431: PUBLIC FINANCE
Fall 2014
Professor Schmitt
Homework 6 – due December 8th
1. (25 points)Assume that Rebecca and David are married and filing jointly and have one
child. They face the following earned income tax credit (EITC):
EITC
2,917
0.35
-0.20
8550 18,800
34,000
INCOME
a) (15 points) Using a labor supply graph (with “Leisure” on the x-axis and
“Consumption” on the y-axis) show how the EITC impacts Rebecca and David’s
budget constraint.
Income
34,000
18,800
8,550
Leisure
b) (10 points) Prior to the EITC Rebecca and David are currently making $10,000.
Will the EITC increase, decrease, their supply of labor, or is the change
indeterminate? Explain (a complete explanation will include income and/or
substitution effects).
Decrease the supply of labor; all income effects (no substitution because on the slope is the same –
on the parallel portion.
2. (55 points) Currently Bob is earning $1000 in income per month. The price of housing
for Bob is $2 per square foot and the price for all other goods is $1. Bob’s utility for
housing and all other goods is given by U B  200H HG (where H denotes 1 square foot
of housing and G denotes 1 unit of all other goods).
a) (10 points) What is Bob’s optimal consumption of housing and all other goods?
Bob will maximize his utility subject to his budget constraint. This is
U B  200H HG subject to I  PH H  PG G  1000  2H  G
Solving the budget constraint for G and substituting into Bob’s utility
U B  200 H  H (1000  2 H )
G
dU B
 1200  4 H  0
1000
dH
H  300
G  1000  2 H  1000  600  400
400
UB=180,000
BC
300
500
H
b) (15 points) If the government provides a housing subsidy of $400 for each person
earning less than $1500 a month in income, what happens to Bob’s consumption
of housing and all other goods (show graphically).
Since Bob is already buying 300 square foot of housing, he is spending $600 on housing.
Therefore, this can be viewed as an increase in income of $400.
Bob will maximize his utility subject to his budget constraint. This is
U B  200H HG subject to I  PH H  PG G  1400  2H  G
Solving the budget constraint for G and substituting into Bob’s utility
U B  200 H  H (1400  2 H )
dU B
 1600  4 H  0
dH
H  400
G  1400  2 H  1400  800  600
G
1000
600
400
UB2=320,000
BC
UB1=180,000
300 400 500
200
700 H
c) (10 points) If, instead Bob’s utility was given by U B  HG  800H , what would
his optimal consumption of housing and all other goods with and without the
$400 housing subsidy?
Without the subsidy Bob will maximize his utility subject to his budget constraint. This is
U B  HG  800H subject to I  PH H  PG G  1000  2H  G
Solving the budget constraint for G and substituting into Bob’s utility
U B  H (1000  2 H )  800 H
dU B
 200  4 H  0
dH
H  50
G  1000  2 H  1000  100  900
U B  50 * 900  800 * 50  5,000
With the subsidy, he will be “forced” to consume $400 worth of housing (so 200 units) and
he only wanted to consume $100 worth (50 units).
U B  H (1000  2 H )  800 H
H  200
G  1000
U B 2  200 *1000  800 * 200  40,000
d) (10 points) Because both cost the government the same amount ($400), assuming
there are no administrative costs, is the program efficient regardless of Bob’s
preferences? Explain.
Both cost the government $400, but Bob would be on a higher indifference curve with $400
if he had the preferences in part b. So, with no administrative costs, $400 in cash is
preferred when Bob has preferences in part b. With the preferences in part a, he is
indifferent. The housing subsidy might show paternalism.
U B  H (1400  2 H )  800 H
dU B
 600  4 H  0
dH
H  150
G  1400  2 H  1400  300  1100
U B 2  150 * 1100  800 * 150  45,000
3. (30 points) A negative income tax program is a system where benefits decline as a
person increases their income.
a) (5 points) If a person is guaranteed an income of $600 per month and the
marginal tax rate is 30%, what is the break-even income?
Break-even income = guarantee/MTR = 600/.3 = 2000
b) (5 points) If the wage rate is $6.00 per hour, what is the net wage for working
given the negative income tax program above?
$4.20 (lose 30% of $6 to taxes)
c) (10 points) Using a leisure/income graph, illustrate the impact of the negative
income tax program above; be sure to label x-axis, y-axis and your curves (use
actual numbers, assume max leisure hours per month is 2000).
Taxable Income
12,000
2000
600
2000
Leisure
d) (10 points) What is the impact of the negative income tax program above on
labor? Be sure to state the income effect and substitution effects (are they positive
or negative).
At all levels of Income less than the break-even income level (so less than $2000 and anyone
receiving welfare from NIT/TANF) leisure increases. The substitution effect shows that the
price of leisure falls (from 6 to 4.2) so substitute towards cheaper good (leisure). The
income effect shows that income increases so get more of all normal goods (which leisure
is).