ECON 431 1 October 10, 2021 CAS EC 561 Public Economics Fall XXXXXXXXXXProf. Bahar Erbas Problem Set #1 First and Last Name: _____________Student ID#: _____________ Date: _________ Assignment Date:...

ECON 431
1
October 10, 2021

CAS EC 561 Public Economics
Fall XXXXXXXXXXProf. Bahar E
as

Problem Set #1

First and Last Name: _____________Student ID#: _____________ Date: _________

Assignment Date: October 11th, 2021
Due Date: At the beginning of the class on Thursday, October 21st, 2021. Submit
the printed and stapled copy to me at the end of the class on the submission date.
Scanned and e-mailed copies are not accepted as submissions. Only remote
students can scan and e-mail their submissions to the TA Hannah Zhan
( XXXXXXXXXX). In-person students submission needs to be in-class hard copy
submissions. Please see the syllabus for late submission rule.
Instructions:
1. Please provide your solution, explanation and drawing for every single
question.
2. Please write clearly. If your answers are not readable, then it will have zero
points.
3. Graphs: Please label the axes, lines, curves and areas co
ectly. Graphs with
no labels will not receive any points.

Q XXXXXXXXXXPoints) Let two consumers have preferences described by the following
utility function;
?ℎ(?1
ℎ, ?2
ℎ) = (?1
ℎ)(?2
ℎ), ℎ = 1, 2.

and the following endowments;

Good 1 Good 2
Consumer 1 7 5
Consumer 2 3 15

a. Calculate the consumers’ demand functions by assuming that price of good 1 is
?1 and price of good 2 is ?2.
. For each consumer, write down the excess demand and supply for good 1.
Excess demand of good j for consumer i is ??
?
= (??
?
− ??
?
) where ??
?
is the
demand of consumer i for good j and ??
?
is the endowment of consumer i for
good j. Show that the consumers’ indifference curves are tangential at the
equili
ium.
c. For the market of good 1, write down the aggregate excess demand for good 1.
Aggregate market excess demand is ?1 = ?1
1 + ?2
1 = (?1
1 − ?1
1) + (?2
1 − ?2
1).
mailto: XXXXXXXXXX
2
d. Calculate the price ratio (either
?1
?2
or
?2
?1
) that will clear the market for good 1.
That is to find the price ratio that sets the aggregate excess demand equal to
zero, ?1 = 0. Clearing the market means there is no aggregate excess demand.
e. Show that the aggregate excess demand for good 2 is also zero at the price
atio that is calculated in d.

Q XXXXXXXXXXPoints) In an economy with 2 people, Z and F, has the social welfare
function of ? = ?? + 3?? and the utility possibilities frontier of
??? = ???{2?? + ?? , ?? + 2??}
a. What type of social welfare function does the economy have?
. At what utility levels of Z and F, does this economy achieves social optimum?

Q XXXXXXXXXXPoints) For each of the following policy changes, explain why the change
is not likely to be a Pareto improvement:
a. Building a school, financed by an increase in the local property tax rate.
. Expansion of certain types of cancer facilities, financed out of general revenues.
c. Replacing the system of agricultural price supports with a system on income
supplements for poor farmers.
d. Protecting the domestic aluminum industry from cheap foreign imports by
imposing import taxes on the imported aluminum.

Q XXXXXXXXXXPoints) Let there be ? number of consumers all with the utility function
?ℎ = log(?ℎ) + log(?) and income 1. The private purchase of public good implies
that ? = ?ℎ + ∑ ?ℎ
′
ℎ′≠ℎ . The equili
ium is symmetric.
a. Calculate the private purchase equili
ium level of public good, ??.
. Calculate the social optimal level of public good, ??, for the welfare function
? = ∑ ?ℎ?ℎ=1 .
c. Write the ratio of
?0
??
. Comment on the effect ? getting larger on the contrast
etween the private equili
ium and the social optimum.

Q XXXXXXXXXXPoints) The demands for a public good, ?, of three consumers are given
as ?1 = 10 −
1
2
?, ?2 = 22 −
1
2
?, ??? ?3 = 30 −
1
2
? where G measures
the number of units of the good and pi is the price in dollars. The marginal cost of
the public good is $38.
a. What is the optimal provision of the public good? Illustrate your answer with a
graph.
. Explain (in reference to the details of this problem) why the public good may not
e supplied at all because of the free-rider problem.
c. If the public good is not supplied at all, what is the size of the deadweight loss
arising from this market failure?