Name:
Section:
Midterm
Analytical Politics I
2020
Due by Wednesday, Nov 4, at 5 PM (Central Time)
• You can start working on the midterm now, and there is not limit on how much time
you spend on it as long as you submit it via Canvas before 5pm Chicago time on
Wednesday, Nov 4.
• As long as your submission is legible, and it is clearly labeled which answers correspond
to which questions, we do not have any particular preference about how to submit
your answers (i.e., you can print the midterm, write the answers and scan it or you
can use a separate file for your answers).
• This is an open-book and open-notes exam. You are not allowed, however, to consult
any materials related to this class that were not distributed this year by us, nor
are you allowed to communicate with anyone about the midterm before Wednesday
(even as to whether the exam was “easy” or “hard”).
• You should answer all of the questions.
• You must justify all answers by showing your work/argument. No credit
will be given for undefended answers.
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1. Consider a society with 25 low-income individuals, 70 middle-income individuals, and
5 high-income individuals. Currently, the society has a private health care system.
Members of the low-income group do not have access to health care, members of the
middle income group have access to basic health care, while members of the high-
income group have access to excellent health care. The society is considering moving
to a universal health care system in which everyone would have access to basic health
care. The utility that an individual gets from the different health care systems is
summarized below.
Private Health Care Universal Health Care
Low Income
(25 Individuals)
0 20
Middle Income
(70 Individuals)
20 20
High Income
(5 Individuals)
50 20
(a) What health care system would a Rawlsian prefer?
(b) What health care system would a utilitarian prefer?
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(c) Suppose monetary transfers are not possible. Is it a Pareto improvement to move
from private to universal health care?
(d) Suppose monetary transfers are not possible. What health care systems are
Pareto efficient?
(e) Suppose monetary transfers are possible, and everyone values a dollar at one util.
What are the Pareto efficient health care systems?
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(f) Suppose monetary transfers are possible, and everyone values a dollar at one util.
Is it possible to make a Pareto improvement by moving from private to universal
health care? Explain.
(g) Suppose monetary transfers are possible, and low- and middle-income groups
value a dollar at one util. The value of a dollar for the high-income group is 1
3
of a util.
• How much money would a member of the low-income group be willing to
pay for a move to universal health care?
• How much would a member of the high-income have to be compensated to
be willing to move to universal health care?
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• Is it possible to make a Pareto improvement by moving from private to
universal health care?
2. Congyi and Dahlia are building a bridge over a river together. Congyi starts from the
left-bank of the river and Dahlia starts from the right-bank of the river. Each chooses
how much effort to put in. Effort can be any real number between 0 and 1. Each
individual bears costs of effort ei
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.
The quality of the bridge is only as good as the “weakest link”. In particular, quality
is given by a function G(eC , eD) as follows:
G(e1, e2) =
{
eC if eC < eD
eD if eC ≥ eD.
This means for instance that G
(
1
4
, 1
2
)
= 1
4
or G (0, 1) = 0. It also means that the
quality of the bridge is the same under the strategy profile
(
1
4
, 1
2
)
and the strategy
profile
(
1
4
, 3
4
)
. In both cases it is 1
4
. In words, it means that if one of them works hard
and the other slacks off, the bridge will reflect the effort of the slacker.
(a) Let’s figure out Congyi’s best-response correspondence. [Hint: You do not need
calculus for this problem.]
First, suppose Dahlia contributes 1
4
.
i. What is Congyi’s payoff if he contributes eC <
1
4
?
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Section:
ii. What is Congyi’s payoff if he contributes eC >
1
4
?
iii. What is Congyi’s payoff if he contributes eC =
1
4
?
iv. Comparing these payoffs, what is Congyi’s best response to eD =
1
4
?
v. Extending this logic, what is Congyi’s best-response to any eD?
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(b) Describe two pure-strategy Nash equilibria of this game.
(c) Compare these two equilibria and explain whether one of them Pareto dominates
the other.
(d) What social dilemma does this comparison illustrate?
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(e) Give an example of that social dilemma not discussed in class or the book.
3. There are two parties competing for the seats in the U.S. Congress. Before the election,
each party must decide how much money to raise and spend on political advertising.
For any given level of spending by one party, the other party can increase the number
of seats it wins and decrease the number of seats the other party wins by increasing
the amount of money it spends on advertising.
The amount of money spent on political advertising in the U.S. is very large. As
a result, many politicians complain that they spend most of their time fundraising
instead of policy making and that they wish all sides would scale down campaign
advertising.
(a) What social dilemma do you think best explains this situation? Explain.
(b) Would a Pareto improvement, in this situation, involve more or less advertising
by each of the parties?
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(c) Suppose that the supporters of one party propose that their party unilaterally
commits to advertise at the level they wish both sides would scale down to. Does
it seem likely that their party will be better off for having done so?
(d) Suppose the leaders of the two parties meet and both say they’ll scale down their
advertising. Are they likely to honor that deal? Why or why not?
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4. Consider a model of a society made up of N = 100 people. Each individual must
decide whether to be tolerant (T ) or intolerant (I). All else equal, everyone likes
being tolerant better than being intolerant. In particular, an individual who behaves
tolerantly gets a utility gain of 20 and an individual who behaves intolerantly gets a
utility gain of 0.
In addition, people like to fit in. As a result, they gain benefits the more people
behave like them. If n other people behave in the same way as person i, then she gets
an extra payoff of n. (Note 0 ≤ n ≤ 99.)
Suppose, then, that person i believes nT other people will behave tolerantly, with
0 ≤ nT ≤ 99 and nI other people will behave intolerantly. (Notice, this implies
nI = 99 − nT .) Person i’s payoff from behaving tolerantly is
ui(T, nT , nI) = 20 + nT .
Person i’s payoff from behaving intolerantly is
ui(I, nT , nI) = nI = 99 − nT .
(a) For what values of nT is it a best response for person i to behave tolerantly? For
what values of nT is it a best response for person i to behave intolerantly? (Note
that nT must be a whole number.)
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(b) Is there a Nash equilibrium where everyone behaves tolerantly? Is there a Nash
equilibrium where everyone behaves intolerantly?
(c) Write down the utilitarian payoff for society for all equilibria identified in (b).
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(d) In what sense does this model illustrate one of our social dilemmas? Give an
example of a real world phenomenon not discussed in class that this model might
be a good analogy for.
(e) Is this a setting in which an effective policy response is likely to require ongoing
or short-run intervention by the government?
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