FE431 – Public Finance Exam 3
Prof. Schmitt
Fall 2014
Last 4 #’s of Alpha _________________________________________________________
Directions: Be sure to read each question thoroughly and compose your thoughts before
writing your answers. Remember that quality is more important that quantity – so be concise
and direct in your answers. Show all of your work because that is the only way to award
partial credit. Please write your answers in the designated area – if you are using the back,
please indicate that your answer continues on the back.
1. (10 points) What are the reasons the government provides education in the form of public
school (i.e. free education K-12)? Do public schools lead to a change in the amount (or
quality) of education everyone receives? Explain.
Some explanation of externalities (crime reduction, citizenship, social skills, etc.). Depends
on the family – if their consumption was below the quality given by public schools, it
increases it; for some it decreases it because they are willing to forgo some education for a
lot of “all other goods”. For some it doesn’t change at all (they attend private even with
public education). See graph from class A, B, and C.
2. (10 points) Consider an income guarantee program with an income guarantee of $5,000
per year and a benefit reduction rate of 25%. A person can work (or have leisure) of
2,000 hours per year and this person’s current wage rate is $20 per hour. Draw both the
person’s budget constraint with and without the income guarantee (be sure to use
numbers for the intercepts, slope(s) of each budget constraint, and any relevant point on
the line; label the axes and the budget constraints). If this person works 600 hours, how
much welfare do they receive?
income
40,000
Slope= -20
20,000
Slope=-15
5,000
2,000
Leisure
For each hour worked ($20 decrease to $15). For 600 hours, this person will lose
600*5 = $3,000 worth of benefits, so he will earn $2,000 in benefits.
3. (20 points) Baltimore County currently has $100,000 which can be spent on “education”
(E) or “all other goods” (G). The price of education is PE = $4,000 per student, while the
“price” of a unit of “all other goods” is PG=$1,000. (NOTE: for simplicity, you can use
revenues of 100 and prices of PE = $4 and Pg = $1). Assume Baltimore County’s utility
function over E and G is given by U = E*G+3G.
a) (10 points) If Baltimore County qualifies for a federal matching grant in which for
every $1 Baltimore County spends, the federal government will give them $2 more.
How much would the program cost the federal government? How much more
education is purchased?
Need to do two constrained maximization problems
U nogrant  EG  3G
s.t.4 E  G  100
 G  100  4E
Substituting in the budget constraint
U nogrant  E (100  4 E )  3(100  4 E )
100 E  4 E 2  300  12 E
Taking the derivative with respect to E
dU nogrant
 100  8E  12  0
dE
E  88 / 8  11
G  56
Budget constraint changes – now Baltimore County pays 1/3 of total cost (so 1 of every 3 $)
U grant  EG  3G
4
s.t. E  G  100
3
4
 G  100  E
3
Substituting in the budget constraint
U nogrant  E (100 
100 E 
4
4
E )  3(100  E )
3
3
4 2
E  300  4 E
3
Taking the derivative with respect to E
dU nogrant
8
 100  E  4  0
dE
3
3
E  96 * ( )  36
8
G  52
So E increased by 25.
The total spent on E is $144 (4*36), of which 2/3 is covered by the federal government – so it
costs the federal government $96.
b) (10 points) Illustrate your answer using an appropriate graph and provide numerical
values for the intercepts and G and E. Show the income and substitution effects
and discuss why they are positive and/or negative.
100
56
A
52
t
11
B
IC1
25 36
IC2
75
Education
So as the PE falls consume more E (positive substitution effect, takes you from A to t)
Positive income effect (more relative income, takes you from t to B)
4. (30 points) Assume the current phase in rate is 30% up to $9,000, the phase out rate of
10% starts at $12,000, and that the maximum EITC is $2700. Assume two different
people (not a family) Alice earns $5,000 prior to the EITC and Bob earns $10,000 prior
to the EITC.
a) (10 points) At what level of income, will the family not receive any money from the
EITC? How much total income do (again two separate, not married people) Alice and
Bob now have with the EITC?
No family earning over $39,000 will have any EITC. To find this, they receive 2700 in EITC
and any amount above 12,000 they start to lose benefits ($0.10 for each $1.00 earned). Thus,
every $10 earned above 12,000 causes benefits to fall $1  Benefits of $2700 run out in
$27,000 in the phase out range (above $12,000). So 12,000+27,000=39,000
Alice is in the phase-in range. She will earn 30% more than her income. $5,000*0.30 =
$1,500 in benefit and 5000+1500 = 6500 total income.
Bob is at the max range, he’ll earn $2,700 in benefits and 10000+2700=12,700 in total
income.
b) (10 points) Use a graph to illustrate the how an earned income tax credit (EITC)
impacts a family’s budget constraint and number of leisure hours worked. (That is,
with income on the y-axis and leisure on the x-axis show the budget constraint with
and without the EITC).
Income
39,000
12,000
9,000
Leisure
c) (10 points – 5 for each person) Discuss possible changes in leisure hours based on
the EITC for Alice and Bob. (Note: a complete answer will include the directions of
the income and substitution effects).
Bob will consume more leisure. He receives max benefits and only experiences an
income effect (no substitution effect because not in the phase-in or phase-out
regions). As income increases, amount of leisure consumed increases because
Leisure is a normal good.
Alice – it depends on her utility preferences. She will have a positive income effect
(she has more income, so amount of leisure will increase as it is a normal good). But
the substitution effect is negative. This is because the price of leisure increases (she
gets 30% more for each $ worked). She will substitute away from the more
expensive good (leisure). So for her, the impact on leisure depends.
5. (10 points) Discuss why/when in-kind government transfers lead to the same type of
inefficiencies discussed in the article by Joel Waldfogel, "The Deadweight Loss of
Christmas." American Economic Review, December 1993.
There is inefficiency if the person could have been made better off with cash; that is if they
were not going to spend the same amount of money on the in-kind program (housing, food
stamps, etc. and gift). For in-kind programs, often paternalism is an issue because many
believe the government can force people to make better decisions.
6. (10 points) When would a uniform voucher program lead to higher quality/quantity
education than our current public school system? (Note: your response should include
budget constraints and indifference curves).
Vouchers do not crowd out education – they provide everyone an incentive to purchase
more education
G
U2
BC U1
Education
Public school can crowd out education, a person at point A would decrease E (from E2 to E1),
attend the public school in order to get a lot more “all other goods”.
All other goods
A
Budget constraint with public
school
E1 E2
Education
7. (10 points) Explain when a conditional block grant for education leads to a higher level
of spending on education compared to a block grant. (Note: graphs are probably useful,
but are not necessary).
Conditional block grants increases education levels more if you weren’t spending the
amount “conditional” on education. Otherwise, both have just an income effect (increasing
income).