ECON_481_Exam_2_SPRING_2023_PRACTICE_SOLUTIONS
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Econ 481: Spring 2023 Exam #2_SOLUTIONS
June 3, 2023
Please choose the part that you are more comfortable with.
Part A
Problem #1
Consider a project that is to yield
10
at the end of each period - starting from period
1
- in
perpetuity, but requires investment of
105
at the beginning of period
1
and the beginning of period
2
.
Would you recommend implementing such a project?
a) Yes, as long as the interest rate is higher than
10%
, b) Yes, as long as the interest rate is less
than
5%
, c) Yes, as long as the interest rate is less than
10%
, d) None of the above.
D
Problem #2
Consider two potential public projects. The first one leads to a net benefit of
100
and allows
the two citizens to attain a level of happiness
U
1
= 10
and
U
2
= 12
.
The other project leads to a
net benefit of
120
,
and allows for the two citizens to enjoy utility levels of
U
1
= 9
and
U
2
= 11
.
Which of the two projects is likely to be implemented if traditional cost benefit analysis is applied?
Which of the two should be implemented by if welfare is to be used as a criterion?
a) In both cases the first, b) The first wins in terms of efficiency the second in terms of welfare,
c) The second wins in terms of efficiency and the first in terms of welfare, d) In both cases the
second.
C
Problem #3
Imagine that the US decides to build a wall on the border with Mexico. Construction demands
in total
1
mln hours of labor. The US is considering three options to construct the Wall. Option
one involves hiring only Americans, option two allows for employment of Mexican citizens in the
process of construction, and options three allows for employment of Mexicans, but only if they
happen to be compensated by the government of Mexico. Which of the three options is the worst
from the US perspective?
a) The third, b) The second, c) The first, d) All three are equally good.
C
1
Problem #4
Imagine that there are in total
2
N
+ 1
individuals in the economy. The preferences of a single
individual
i
∈ {
1
,
2
,
3
, ...,
2
N
+ 1
}
are represented with
U
i
=
-
2(
G
-
i
)
2
,
where
G
denotes the level
of provision of a given public good. In a two party system with a simple majority voting rule what
type level of
G
can we expect to be chosen?
a)
1
, b)
N
+1
2
, c)
N
+ 1
, d) None of the above as preferences are not single peaked.
C
Problem #5
Continue with the assumptions of the previous problem, but now assume the government is
interested in maximizing welfare represented with
W
=
U
1
+
U
2
+
U
3
.
What level of
G
do you
expect to see in this case?
a)
1
, b)
N
+ 1
, c)
2
, d) None of the above.
C
Problem #6
There are three families in a given community. Their preferences over the quality of eduction
are given by
H
1
M
1
L
for family
1
M
2
L
2
H
for family
2
and
L
3
M
3
H
for family
3
,
where
H
denotes education of high quality,
M
education of
medium quality, and
L
education of low quality. Which option is going to be chosen if residents
decide on their choice with a simple majority voting rule?
a) L, b) M, c) H, d) The rule does not lead to a conclusion as group preferences induced with
voting are circular.
B
Problem #7
Consider three individuals -
A, B,
and
C
- with private marginal benefits of a given public good
given with
P
A
= 100
-
2
Q, P
B
= 150
-
3
Q,
and
P
C
= 50
-
Q.
It turns out that in this economy it
is optimal to provide
40
units of the good. What is the marginal cost of delivery of the good?
a)
60
, b)
40
, c)
50
, d) None of the above.
A
Problem #8
Continue with the assumptions of the previous problem.
How much should individual
A
be
charged to enjoy the good?
a)
30
, b)
10
,
c)
20
, d) None of the above.
C
Problem #9
Imagine that in a given community,
A,
individuals value education according to
P
A
= 120
-
3
E
A
and in a neighboring community,
B,
the valuation is given with
P
B
= 80
-
2
E
B
.
Imagine that the
marginal cost of education is the same in both places and is equal to
30
.
What is the level of
education chosen in each place?
a)
E
A
= 40
and
E
B
= 40
, b)
E
A
=
E
B
= 30
, c)
E
A
= 30
,
and
E
B
= 25
, d) None of the above.
C
2
Problem #10
Would you agree that a policy of subsidizing the provision of education in community
B
and
of taxing the provision of education in community
A
can lead to equalization of consumption of
education, which in turn must be welfare improving?
a) There is no need to intervene in this manner as the levels of education chosen are already
equal, b) It would lead to equalization, but it need not be welfare improving, c) It would further
increases the discrepancy in the level of education in both places, d) Would bring the two levels of
education closer and would definitely lead to a higher welfare in both places.
B
Problem #11
Imagine that individual preferences are represented with
U
(
C
) =
√
C
and that there are two
states of nature
L
and
H
with consumption in the low state
C
L
being equal to
1
and in the high
state
C
H
being equal to
4
.
Furthermore, assume that insurance companies are run efficiently and
operate in a competitive environment. Consider an individual who ends up in the low state with
probability
p
L
.
What is the premium - per dollar of coverage - that this individual will be charged
for complete insurance?
a)
1
-
p
L
, b)
3
, c)
p
L
, d)
0
.
C
Problem #12
Continue with the assumptions of the previous problem, but now assume that the insurance
companies are able to earn profit. What is the highest premium - per dollar of coverage - that the
individual is willing to pay?
a) Same as in the previous problem, b)
p
L
(1+
p
H
3
), c)
4
, d) None of the above.
B
Problem #13
Now imagine that there are two categories of individuals. In the first
p
2
L
=
1
4
and in the second
p
2
L
=
3
4
.
Imagine that the premium is equal to
1
2
per dollar of insurance. Who will be insurance in
this case?
a) Both, b) Only the second, c) Only the first, d) Neither.
C
Problem #14
Consider an unfunded social security system.
Assume that individuals at time
t
contribute
fraction
Ï„
t
= 0
.
15
of their wages to the system, and individuals at time
t
+ 1
are expected to
contribute fraction
Ï„
t
+1
= 0
.
3
of their wages.
Furthermore, assume that wages are expected to
increase at
2%
per period and that labor force expands at
1%
per period.
Finally, assume that
the return on investment in physical capital is equal to
3%
.
What is the rate of return from -
approximately - participating in such a system?
a)
106%
, b)
103%
, c)
102%
, d) None of the above
3
Problem #15
Continue with the assumptions of the previous problem, but now assume that we are dealing
with a fully funded system. What is the return in this case?
a)
6%
, b)
3%
, c)
2%
, d)
1%
.
B
Problem #16
Which of the following goods should be provided locally (city, county level ?)
a) Elementary School, b) Research Hospital, c) Intercontinental airport, d) A welfare program
for families in need.
A
Problem #17
Which of the following goods should be provided at the federal level?
a) Public transportation, b) K-12 education, c) Street lights, d) National Defense.
D
Problem #18
In which of the following self-insurance is most likely to be effective?
a) Social security insurance, b) Automobile insurance, c) Unemployment insurance, d) Disability
insurance.
A
Problem #19
Imagine that the federal government becomes concerned with the the ability to read by elemen-
tary school students and decides to encourage reading by young people.The government has two
options. It can either offer a matching grant (one for one) or a block grant of equal value. Which
of the two options should the government resort to given its stated objective.
a) Block grant as long as it is smaller than the original value of spending on books b) Matching
grant, c) Always a block grant, d) The two must be equally effective as both happen to be of the
same value.
B
Problem #20
Would you recommend provision of complete insurance in the context unemployment insurance?
a) No, as moral hazard issues are likely to become relevant, b) Only for mid-aged individuals,
c) Yes, as self-insurance is unlikely to be relevant in this case, d) Yes, as it must definitely lead to
an improvement in the quality of matches between employees and employers.
A
4
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• The functional form to generate the graph is
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. Q2. On the graph illustrating V(r), determine
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800
. Q1. On the graph illustrating V(1), determine
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O Project B
1: More Info
FOT23
n
0
1
Net Cash Flow
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35,000
35,000
140,000
Project B
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Time
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Cash flow
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€1,000 €2,000
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PI (show the calculation)
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