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PPHA 32400: Principles of Microeconomics and Public Policy II
Sections 1, 2, 3, 4, 5
Winter 2020
March 18, 2020


Final Exam

You have three hours, from 9:00am to 12:00pm, to complete the exam. After completion, you should upload your
Answer Sheet, which is provided on the exam web-site, via the Canvas link. You may upload a file (of photos) of
your calculations, but this is not required.

If the Canvas link does not work, just send your Answer Sheet and work files to Maria Adelaida
(mariaadelaidamc@uchicago.edu). If a question seems vague or unclear, make, write down, and use your own
assumptions.

IMPORTANT: You should start by writing your date of birth in Month- Date format atop of your answer sheet.
These two numbers, M, the month you were born, and D, your birth date, will be used throughout the exam.

Points for each problem are given in the parenthesis, reflecting their relative difficulty (the total is 100).

During the exam, you can use any source material, but cannot communicate with anyone, in- or outside your class.
This is consistent with the University’s academic integrity policy and basic fairness to your fellow students.

Good luck!


Problem 1 (25 points)

In this problem, we use the number D, your birth date.

Consider two firms, AlliedPaper and CleanWater, which operate close to each other. Each of them might
operate at full capacity or not operate at all. AlliedPaper’s operation (producing paper) negatively affects
CleanWater’s profits as CleanWater has to spend more on cleaning the water it uses. At the same time,
CleanWater’s operation hurts AlliedPaper profits as it drives up the local labor costs. The profits of the two
firms (in $ millions) are given in the table below.

CleanWater
Not Operate Full Capacity
AlliedPaper Not operate 0, 0 0, 15
Full capacity D, 0 4, 3

(1) Suppose that the firms choose their strategies simultaneously and independently. Find all Nash
equilibria. What are the equilibrium profits of the firms? Is this equilibrium efficient (maximizes the joint
profits)?

Given that 0 < D ≤ 31, there is only one Nash equilibrium – [Full Capacity, Full Capacity].
The equilibrium pair of payoffs is (4, 3).
This is not efficient since the joint payoff, 7, is lower than that obtained when Allied Paper doesn’t operate
and CleanWater operate at full capacity.
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(2) Now, suppose that the firms choose their strategies sequentially. CleanWater chooses its capacity first,
and AlliedPaper second. Draw the game tree and find, using backward induction, the Stackelberg-Nash
equilibrium. What are firms’ equilibrium profits? Is this equilibrium efficient?
















Given that CleanWater chooses Not Operate, AlliedPaper prefers Full Capacity.
Likewise, given that CleanWater chooses Full Capacity, AlliedPaper prefers Full Capacity.
In anticipation of these best responses, CleanWater prefers Full Capacity.
Then the Stackelberg-Nash equilibrium is [Full Capacity, Full Capacity]. The equilibrium profits are (4, 3).
This equilibrium is not efficient since efficiency arises either when [Not Operate, Full Capacity] is arrived if D < 15 or when [Full Capacity, Not Operate] is arrived if D ≥ 15.

(3) Suppose that there is no laws against pollution – that is, AlliedPaper has all the rights to pollute the
water. If there is an opportunity to negotiate an outcome, is an efficient outcome possible? What could be
firms’ payoffs in this outcome?

Because AlliedPaper is allowed to operate, the outcome without negotiation is [Full Capacity, Full Capacity].
This gives a payoff of 4 to AlliedPaper and 3 to CleanWater. Now, assume that negotiation is possible. By
Coase theorem, we know that the parties will reach the efficient outcome.
• Suppose D < 15. Then, [Not Operate, Full Capacity] is the efficient outcome, which gives 0 to
AlliedPaper and 15 to CleanWater. CleanWater is willing to pay up to 15 - 3 = 12 to reach this
outcome. AlliedPaper accepts only if the payment is at least 4. Therefore, the following agreement
would be obtained: CleanWater pays some x ∈ [4, 12] to AlliedPaper to stop operating.
AlliedPaper's payoff is x, between 4 and 12. CleanWater's payoff is 15 - x, between 3 and 11.
• Suppose D > 15. Then, [Full Capacity, Not Operate] is the efficient outcome, which gives D to
AlliedPaper and 0 to CleanWater. AlliedPaper is willing to pay up to D - 4 to reach this outcome.
CleanWater accepts only if the payment is at least 3. Therefore, the following agreement would be
obtained: AlliedPaper pays some x ∈ [3, D − 4] to CleanWater to stop operating. AlliedPaper's
payoff is D - x, between 4 and D - 3. CleanWater's payoff is x, between 3 and D - 4.
• Suppose D = 15. Either of the agreements above works.

(4) Alternatively, suppose that there is a law that guarantees the CleanWater right to control the water
quality. If there is an opportunity to negotiate an outcome, is an efficient outcome possible? What are the
firms’ payoffs in this outcome?
CleanWater
AlliedPaper AlliedPaper
N.O.
N. O. N.O

F.C.
F.C.
F.C.
(D, 0) (0, 0) (0, 15) (4, 3)
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Because CleanWater owns the rights, without negotiation it prevents AlliedPaper from operating. The
outcome without negotiation is [Not Operate, Full Capacity]. This gives a payoff of 0 to AlliedPaper and 15
to CleanWater.
• Now, assume that negotiation is possible. By Coase theorem, we know that the parties will reach
the efficient outcome. Suppose D < 15. Then, [Not Operate, Full Capacity] is the efficient outcome
anyway, so no side payments are needed to sustain this. AlliedPaper's payoff is 0. CleanWater's
payoff is 15.
• Suppose D > 15. Then, [Full Capacity, Not Operate] is the efficient outcome, which gives D to
AlliedPaper and 0 to CleanWater. AlliedPaper is willing to pay up to D to reach this outcome.
CleanWater accepts only if the payment is at least 15. Therefore, the following agreement would be
obtained: AlliedPaper pays some x ∈ [15, D] to CleanWater to stop operating and allow AlliedPaper
to operate. AlliedPaper's payoff is D - x, between 0 and D - 15. CleanWater's payoff x, is between 15
and D.
• Suppose D = 15. Either of the agreements above works.


Problem 2 (25 points)

In this problem, we again use the number D, your birth date.

There are two types of people in the market for health insurance. The first type does not have any pre-
conditions and their expected cost of medical services is = $10 +D [thousands of dollars]. The second
type does have pre-existing conditions and their expected cost of medical services is $100. People know
their types and their expected cost of medical services is their reservation price – this is the maximum
amount they would agree to pay for insurance. There are 1000 people in total, and is the share of people
without pre-existing conditions.

There is a risk-neutral insurance company. For the insurance company the expected cost of serving a person
with no pre-existing conditions is $10, and for a person who does have preexisting conditions it is $60.

(1) How many people would get medical insurance if information is symmetric, i.e., the insurance company
knows who has pre-existing conditions and who does not?

For simplicity, let us label the type of people without pre-existing conditions as low type and the type of
people with pre-existing conditions as high type.

Note that the maximum willingesses to pay of two types of potential insureds for insurance are respectively
strictly greater than the expected costs of serving these types ( = $10 +D > $10, and $100 > $60). When
insurance companies can observe two types of people separately and offer insurance plans accordingly
(that is, the insurance premium to low type is between and $10 and the premium to high type is between $100 and $60), all the 1000 people should get medical insurance.

(2) When information is asymmetric (that is, the insurance company cannot distinguish people), what is the
threshold ̅ such that for any share < ̅, everyone gets insurance and for any > ̅, the market unravels
and not all people get insurance?

Let P denote the insurance price or premium.

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Suppose first that there’s a pooling equilibrium.
The insurance company prefers offering insurance when the price is weakly larger than the expected costs
of insuring two types of people: P ≥ $10 × + $60 × (1 − ) = $60 − $50⋅
The two types of people want to buy insurance only if the offered price is weakly lower than their expected
costs of medical services: P ≤ v = $10 + P ≤ 100
Notice the only first constraint binds.
Then a pooling equilibrium exists for such that $60 − $50⋅ ≤ P ≤ $10 +
,or more simply $60 − $50⋅ ≤ $10 +
This reduces to
≥ 1 − 50

Now let’s instead suppose
< 1 − 50
In this case, the expected costs of offering insurance is higher than v = $10 + . No high types will be
willing to buy insurance.
Because the company is aware of potential insureds’ reservation prices and P is higher than the reservation
price of low type, they know all the people who want to buy insurance are people of high type. Insurance
contracts are made between the insurance company and people of high type since $100 > $60, as we saw
in part (1).

Therefore, we’ve found the threshold ̅ = 1 −
50
such that

• If θ ≥ 1 −
50
, there is a pooling equilibrium: All the people buy insurance at price P where $60 −$50⋅ ≤ P ≤ $10 +
• If θ < 1 − 50 , there is a separating equilibrium: Only people with pre-existing conditions buy
insurance at price where $60 ≤ ≤ $100.



Problem 3 (25 points)

In this problem, we are going to use M, the numerical value of the month you were born in. Specifically, set
the interest rate =M.

Jen is considering whether to buy a game console, PlayStation 4, in the beginning of 2020. The annual
interest rate is %. Buying the PlayStation 4 costs $325.

There is uncertainty around whether there will be a next generation game console, PlayStation 5. The
uncertainty will be resolved in the beginning of 2021: Sony will announce whether it will produce
PlayStation 5 or not at the last day of 2020. There is a 50% chance that PlayStation 5 will be produced. As
long as PlayStation 5 is not produced, Jen receives a payoff of $50 per year from having a PlayStation 4. If
PlayStation 5 is produced, PlayStation 4 will be worthless after the announcement.
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Therefore, Jen will receive a payoff of $50 per year forever as long as she has a PlayStation 4, and
PlayStation 5 is not produced. If PlayStation 5 is produced, Jen will receive nothing from having a
PlayStation 4.

(1) What is the Net Present Value of buying the PlayStation 4 in the beginning of 2020?

Let R be such that R =
100
=
100
.
The Net Present Value of out interest is
2020 = −325 + 50 + 12 � 501 + + 50(1 + )2 + ⋯� = −275 + 12 50 = −275 + 12 �100 ∙ 50�
Note that −325 + 50 = −275 is the net flow of payoff of buying PlayStation 4 generated in 2020.
And 1
2
�
50
1+
+ 50(1+)2 + ⋯� is the discounted sum of expected payoffs that arise after 2020. This is
simplified as follows: 12 � 501 + + 50(1 + )2 + ⋯� = 12 50 = 12 �100 ∙ 50� = 12 5000

Therefore, it follows
2020 = −275 + 12 5000 = −275 + 2500

(2) Would Jen buy the PlayStation 4?

Jen would buy the PlayStation 4 if the Net Present Value of buying the PlayStation 4 in the
beginning of 2020 is positive. This implies
−275 + 2500

> 0
or
< 2500275 = 9.0909⋯
That is, for ≤ 9, Jen would buy the PlayStation 4.


Now suppose Jen has the option of waiting until the beginning of 2021, when the uncertainty around
PlayStation 5 will be resolved. This way, Jen can wait for the announcement and decide whether to buy the
PlayStation 4. The price of PlayStation 4 will still be $325 in the beginning of 2021.

(3) What is the Net Present Value of waiting until the beginning of 2021, from the perspective of the
beginning of 2020?

= 0 + 12� 11 + (−325) + 11 + �50 + 501 + + 50(1 + )2 + ⋯��= 12� 11 + (−325) + 11 + �1 + 50�� = 12 11 + (−325) + 12 50 = 12 100100 + (−325) + 12 100 ∙ 50

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This simplifies to
= − 16250100 + + 2500


(4) Calculate the option value of waiting until the beginning of 2021.

The option value of waiting until the beginning of 2021 is simply the difference between the Net
Present Value of waiting until the beginning of 2021 (as derived in part (3)) and the Net Present
Value of buying the PlayStation 4 in the beginning of 2020 (part (1)):
− 2020 = − 16250100 + + 2500 − �−275 + 2500 � = − 16250100 + + 275



Problem 4 (20 points)

In this problem, we again use M, the numerical value of the month you were born in.

Consider the following situation, which we will model as a cheap talk game. There is a lobbyist who knows
whether a subsidizing green energy would help the economy or hurt the economy. There is a politician who
doesn’t know about the economic consequences of subsidizing green energy. The politician can ask the
lobbyist, but the lobbyist has her own personal preferences about green energy subsidies.

The payoffs of the lobbyist and the politician are given by the following table (the first number is the
lobbyist’s payoff; the second number is the politician’s payoff).

(Please note that this table is not a 2x2 game!)

Politician’s decision
Subsidize Not Subsidize
Subsidizing
green energy
Helps 100; 100 55; 50
Hurts 10 × ; 0 55; 50

Analyze the following strategic interaction (a sequential game):

First, the lobbyist tells the politician whether green energy subsidies help or hurt the economy. Then, the
politician decides whether to subsidize green energy or not.

(1) Given the payoffs, can the following pair of strategies be an equilibrium?

• The lobbyist tells the truth.
• The politician follows the lobbyist’s advice: if the lobbyist tells that subsidies help the economy, the
politician subsidizes green energy. If the lobbyist tells that subsidies hurt the economy, the
politician does not subsidize.

The lobbyist tells the truth only if his or her payoff when the politician subsidizes is weakly lower than that
when the politician does not subsidize given that he or she tells “Hurts”. This is when
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Subsidize Subsidize Not Not
55 ≥ 10 ∗ M
, or M ≤ 5.5
Then the above pair of strategies is indeed an equilibrium if M ≤ 5, but it’s not an equilibrium if M ≥ 6
since the lobbyist in this case should lie by telling “Helps” when subsidizing green energy actually hurts.

















(2) Suppose that the politician cannot talk to the lobbyist, so the politician has to decide on her own. The
politician assumes that the probability that green energy subsidies help the economy is 0.6. What is the
expected value of subsidizing green energy for the politician? What is the politician’s optimal decision?

The expected value of subsidizing green energy for the politician in this setup is 0.6(100) + 0.4(0) = 60

We also need to know the expected value of not subsidizing. It is 0.6(50) + 0.4(50) = 50

Since subsidizing green energy generates strictly higher expected values, under the belief that the
probability that green energy subsidies help the economy is 0.6, the politician’s optimal decision is to
subsidize.
Lobbyist
Politician Politician
Helps

Hurts
(55, 50) (100, 100) (10*M, 0) (55, 50)