FE431 – Public Finance Practice Exam 1
Prof. Schmitt
Fall 2012
1. In April of 2009, on sold-out flights, United Airlines has decided that "severely
overweight passengers" whose girth infringes on others' space must wait for the next
flight and purchase two tickets, or purchase a business class seat on the same flight,
reported the Chicago Tribune. Explain this practice (no need to tell me if you agree or
not) using public finance terminology.
It is a different way of internalizing the negative consumption externality of flying with
someone who tries to “share your seat”.
2. Jack and Jill (who have never met before) are the only two people who show up at a local
restaurant on Friday night in which their favorite local band is scheduled to play.
Suppose the cost to the band of playing a song is constant and equal to $3. Jack’s demand
for songs is P=8 – 0.25Q, where P is the price he’d pay per song and Q is the number of
songs played. Jill’s demand for songs is P=16 – 0.5Q. The bar owner is considering
having the band play 24, 28, or 32 songs.
a) What “type” of good (private, common property, toll, or public) are band songs?
Public good – if the good is provided (the band plays) it is non-rival (both receive benefits
even if the other is there) and non-excludable (at least because there is no cover charge, that
would make it an excludable public good/toll good).
b) What is the market demand for the band’s songs?
Sum vertically:
P Jakc  P Jill  8  0.25  16  0.5Q  24  0.75Q
c) Which is the economically efficient number of songs for the band to play?
Efficient Q is where sum of MB = MC:
P Jakc  P Jill  24  0.75Q  3
21  0.75Q    21 
Q  21 *
3
Q
4
4
 28
3
d) Why are the other two quantities of songs inefficient?
Need to show at 24 MSB > MC and at 32 MC > MSB and have a good explanation of what
makes something inefficient.
3. Suppose an economy consists of two people, Danny and Natalie. Only two goods exist in
the economy, pizza and soda. Danny’s utility function over the two goods is
U Danny  4 P  2S , where “S” is the number of sodas Danny has and “P” is the slices
of pizza. Natalie’s utility is given by the function U Natalie  S .
a) Use two different indifference curve diagrams to illustrate Danny and Natalie’s
preferences over pizza and soda. Put pizza on the y-axis and soda on the x-axis. For each
person, indicate two different consumption bundles that lie on an indifference curve
representing U=28. Also, be sure to indicate the direction of increasing utility for both
individuals.
Pizza
Pizza
UNatalie=28
7 UDanny=28
14
Soda
28
Soda
b) Now illustrate their preferences using an Edgeworth Box diagram. Make the origin for
Natalie be the lower left corner of the box (again, with pizza on the y-axis and soda on
the x-axis). Assume the total endowment of the two goods is 40 pizzas and 30 sodas, and
suppose Natalie is initially endowed with 0 pizzas and 30 sodas and Danny is endowed
with 40 pizzas and 0 sodas. Indicate both the initial endowment and the area (if possible)
in which Pareto Improvements exist.
30 Soda
Danny
40
USENatalie =30
Pizza
Pizza
40
30
Natalie
No Pareto improvements exist.
Soda
c) Now show the entire contract curve in the Edgeworth Box you drew in part b AND
explain why it has the shape.
30
Soda
40
Danny
USENatalie =30
Pizza
Pizza
40
30
Natalie
Soda
Contract curve;
Natalie would not care about having pizza and would be willing to trade it. That is, if she
starts out will the entire endowment of both goods (top right corner) a PI exists and she can
give Danny all the Pizza. If Danny starts out will the entire endowment of both goods
(bottom left corner) no PI exists.
4. The city of Washington DC had been trying to attract a baseball team. However, not
everyone was willing to use public funding to attract their team (some DC residents are
Oriole fans). Assume 7 Wards preferences are considered, preferences are shown below.
1st
2nd
3rd
4th
5th
6th
7th
Funding
Ward
Ward
Ward
Ward
Ward
Ward
Ward
Level
4
4
1
2
1
4
2
No funding
1
3
3
1
4
3
1
$1 million
2
2
4
3
3
1
3
$3 million
3
1
2
4
2
2
4
$10 million
a) If the city council engages in pair-wise voting, will a winner emerge? If so, who? If
not, explain.
0 vs. 1: 1
0 vs. 3: 0
0 vs. 10: 0
1 vs. 3: 1
1 vs. 10: 10
3 vs. 10: 3
Cycling: 3 is preferred to 10, and 10 is preferred to 1, but 1 is preferred to 3.
This implies someone has multi-peaked preferences.
b) If the city council could only hold three elections on the stadium issue in one
city council meeting, and each proposal (funding level) must be voted on at
least once, is it possible to get the $3million in funding passed? If so, how
does the agenda need to be manipulated to get approval for this funding level?
If not, why not?
So we need to manipulate the agenda so each wins. Easiest way is to have whatever beats
what you want to win eliminated first.
For 0 to win: (0 loses to 1, so we need to have what beats 0 go first)
1 vs. 10  10 then 3 vs. 10  3 and finally 0 vs. 3  0
For 1 to win: (1 loses to 10, so we need to have what beats 1 go first)
3 vs. 10  3 then 3 vs. 1  1 and finally 0 vs. 1  1
For 3 to win: (3 loses to 1 and 0 so we need to have what beats 3 go first)
0 vs. 1  1 then 1 vs. 10  10 and finally 3 vs. 10  3
For 10 to win: (10 loses to 3 and 0, so we need to have what beats 10 go first)
0 vs. 1  1 then 1 vs. 3  1 and finally 1 vs. 10  10
5. It has been shown that many steel plants in Pittsburgh emit toxic pollutants into the air.
The market for steel is described by the following equations:
(Marginal Private Benefit)
MPB:  7  12 Q
(Marginal Private Cost)
MPC:
(Marginal (External) Damage) MD: 
 1.50
1 1
 Q
2 3
Graph the MPB, MSB, and MPC cost curves; be sure to list numbers for all axes. Find the
quantity produced by the market. Find the socially efficient quantity. Calculate the deadweight
loss. (would have only asked you to set it up with numbers with no calculator).
Price
7
MSC = MPC + MD = 2+1/3Q
MPC = 1.5
MPB = 7 – ½ Q
QSE=6
QM=11
14 Quantity
Qmarket  MPC = MPB 7 – ½ Q = 1.5  5.5 = ½ Q  5.5*2 = Q = 11
Qsocially efficient  MSC = MPB 7 – ½ Q = 2 + 1/3Q  5 = 5/6 Q  5*(6/5) = 6
Deadweight loss (area shaded) = ½ b*h; need to calculate height (since it varies with Q)
Height at Q = 11 is 2+ 11/3 = 5 2/3 so DWL = ½ (11 – 6)(5 2/3 – 1.50) =