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PPHA 32400: Principles of Microeconomics and Public Policy II
Sections 1-8
Winter 2021
March 18, 2021 - Final Exam

Problem 1 (25 points)

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

Two major game producers, StarGame and PixelS, consider launching their products, which are perfect
substitutes, in the market, in which the demand is described as = 10 × − , where is the price, and is the aggregate output. For both firms, the marginal cost is 0.

(a) Suppose that the firms set their output simultaneously. Calculate the quantity they produce in the Nash-
Cournot equilibrium, determine the market price and profit of each firm.

The StarGame best-response curve is: () = () − ,
and PixelS best-response curve is: () = () −

The residual demand StarGame faces is: () = () − = (10 − ) − () = 10 − −

Solve the first-order condition, we have = 10 − 2 − = = 0 () = 5 − 12

Similarly, we can derive () = 5 − 12 for PixelS.

In equilibrium, we can solve:

= 5 − 12 25 − 12 3 ⇒ = 2.5 + 14 ⇒ =

Plugging it back, we have () = 5 − 12 = 5 − 53 ⇒ =

From the market quantity, we derive the market price: = − = − + =

StarGame’s profit is = × =

PixelS’s profit is = × =

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(b) Suppose that StarGame sets its quantity first. Calculate the quantity they produce in the Stackelberg
equilibrium, determine the market price and profit of each firm.

Since StarGame is the leader, its first-order condition of profit maximization is then = 10 − 2 = ⇒ =

For PixalS, the residual demand is = () − = 10 − − 5 ⇒ = 5 − .

Thus, PixalS’s first-order condition of profit maximization yields the following = 5 − 2 = ⇒ = .

From the market quantity, we derive the market price: = + = 7.5 × = 10 × − ⇒ = .

StarGame’s profit is = × . = .

PixelS’s profit is = . × . = .



(c) Suppose that StarGame has colluded with PixelS so they can operate as a single firm in this market.
Calculate the quantity this firm chooses to maximize its profit, determine the market price and the profit.
= 10 − 2 = ⇒ = = 10 − ⇒ = = (5) × (5) ⇒ =


(d) Calculate and compare consumer surplus, joint profits, and dead-weight losses in (a), (b), and (c).

a)
= 12 2203 × 3 × 2203 × 3 = = .
= I203 × J × I103 × J = = . = 12 I103 × J × I103 × J = = .
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b)

= 12 2152 × 3 × 2152 × 3 = = .
= I152 × J × I52 × J = = .
= 12 I52 × J × I52 × J = = .


c)

= 12 (5 × ) × (5 × ) = .
= (5 × ) × (5 × ) =
= 12 (5 × ) × (5 × ) = .


Thus, the welfare comparisons in ascending orders are:
• Consumer surplus: (c) < (a) < (b)
• Producer surplus: (b) < (a) < (c)
• Deadweight loss: (b) < (a) < (c)



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(e) Suppose that the US government decided to charge a tax of $1 per game sold by PixelS, a foreign
producer. Calculate the quantity these two firms produce in the Nash-Cournot equilibrium, determine the
market price and profit of each firm.

The StarGame best-response curve is: () = () −

And PixelS best-response curve is: () = ( + 1) −


The residual demand StarGame faces is: () = () − = (10 − ) − () = 10 − −

Solve the first-order condition, we have = 10 − 2 − = = 0 () = 5 − 12

Similarly, we can derive the following for PixelS: () = ( + 1) − = (10 − − 1) − () = 10 − 1 − − = 10 − 1 − 2 − = = 0 () = 5 − 12 − 12

In equilibrium, we can solve: = 5 − 12 I5 − 12 − 12 J = 2.5 + 14 + 14
34 = 2.5 + 14 ⇒ = +

Plugging it back: () = 5 − 12 − 12 = 5 − 12 − 53 − 16 ⇒ = −

Market price:
+ = 203 − 13 = 10 − ⇒ = +


StarGame’s profit is = 2 + 3 × 2 + 3

PixelS’s profit is = 2 − 3 × 2 − 3



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Problem 2 (15 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 = $20. 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 $80 + .

(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 and can charge people accordingly?

• D<=20: 1,000 people. Any price between $10 and $20 can work for people without pre-existing
conditions and any price between $80+D and $100 works for people with pre-existing conditions
since it would satisfy both the insurance company and the consumers.
• D>20: 1,000 ∙ . While people without pre-existing conditions still find any price between $10 and
$20 acceptable, the cost of serving people with pre-existing conditions is too high, so they do not
get any 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?

Consider the equilibrium where everybody is buying insurance for the same price of p. The price cannot
exceed the reservation prices of the consumers, so we must have ≤ $20. At the same time, the price
must be at least as large as the expected costs of the company, so ≥ $10 ∙ + ($80 + ) ∙ (1 − ).
Putting these two inequalities together, we find the threshold value of 60+70+. Two cases are possible.

• ≤ 20: the threshold is given by = 60+70+. For above the threshold, a pooling equilibrium is
possible where everybody is buying insurance. For below the threshold, a separating equilibrium
where only people with pre-existing conditions buy insurance is possible.
• > 20: the threshold is the same: = 60+70+. For above the threshold, it is possible that
everybody is buying insurance. However, for below the threshold the company would not be able
to serve the individuals with pre-existing conditions (it is too expensive), so nobody gets served.
Technically, this is still a pooling equilibrium; so, in other words, for > 20 only pooling equilibria
are possible no matter the value of .


Problem 3 (15 points)

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

Consider the following situation. Grace, an employee of a big firm, informs her supervisor that because of
her need to spend more time at home, she wants to be reassigned to another job, which allows for a more
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flexible schedule. The firm has no way to check whether or not Grace has reasonable grounds for this
request, but they want to keep their valuable employee happy. The firm thinks that Grace has high ability
with probability ½ and low ability with probability ½.

The payoffs of Grace and the firm are given by the following table (the first number is the Grace’s payoff;
the second number is the firm’s payoff). Note that this is a table of payoffs, not a 2 × 2 game.

Firm’s Decision
Reassign Keep
Grace’s need to be
reassigned
High D; 700 14.5; 300
Low 15; 200 30; 900

Analyze the following strategic interaction: First, Grace tells the supervisor whether or not she needs the
re-assignment; then, the firm makes the decision.

(a) Given the payoffs, does the following pair of strategies constitute an equilibrium? First, Grace tells the
firm that she does need the reassignment if she really needs it; Grace does not ask for reassignment if the
need is low. Second, the firm reassigns Grace to the new job if she asked to be reassigned and keep her
current assignment if she does not ask for it.

(b) Replace “200” in the payoffs table so that the firm always prefers to reassign Grace even if it does
believe what she says.

(a) First, looking at the firm’s payoffs, if the firm believes Grace’s request, it makes sense to satisfy it
since 700>300 and 900>200. Given the firm’s strategy, for Grace to truthfully report her type it
must be that D>=14.5 and 30>=15. These inequalities are satisfied for D>=15 and they fail
otherwise.
(b) Anything as large as 900 could be used here, making the dominant strategy for the firm.

Problem 4 (15 points)

There are 4 firms that are prepared to bid for an office building being privatized by the government. Each of
the firms and the seller know their own willingness to pay (reservation prices) and do not know the
reservation prices of other firms. Suppose that their reservation prices are (in millions of dollars) 6.5, 15.5,
24.5, and D, respectively.

Answer the multiple-choice questions, choosing one answer in each case.

(1) Suppose that the seller organizes the English (open ascending) auction, in which the price rises
continuously, and participants can drop at any moment. How much the winner of the auction is going to
pay to the seller?

(A) 6.5 million.
(B) 15.5 million.
(C) 24.5 million.
(D) D million.
(E) None of the above.

If 1 <= D <= 15, the answer is (B). If 16 <= D <= 24, the answer is (D). If D >= 25, the answer is (C).
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(2) Suppose that the seller organizes the first-price sealed-bid auction. Which of the following statements is
true?

(A) The price that the winner pays cannot exceed 24.5 million.
(B) The bidder with highest reservation price can never win.
(C) It is optimal for every bidder to bid her own reservation price.
(D) The price that winner pays cannot exceed D million.
(E) None of the above.

If D <= 24, the answer is (A). If D >= 25, the answer is (D).

(3) Suppose that the seller organizes the second-price sealed-bid auction. What is the reservation price
(maximum willingness to pay) of the winner?

(A) 6.5 million.
(B) 15.5 million.
(C) 24.5 million.
(D) D million.
(E) None of the above.

If D <= 24, the answer is (C). If D >= 25, the answer is (D).




Problem 5 (30 points)

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

Answer the multiple-choice questions; no explanation is needed. There is always a unique correct answer.

(1) Suppose that you estimated the outcome of the project using the internal rate of return approach, and
the calculated value is M-7.5.

(A) The project is worth implementing.
(B) The project is not worth implementing.
(C) The internal rate of return approach is not equivalent to the net present value approach.
(D) None of the above.
If M=>8, then (A). If M<=7, then (B).

(2) Choose the correct statement.

(A) The Cournot competition with 2 firms results in as much social welfare as the competition with M firms.
(B) The Cournot competition with 2 firms results in less social welfare as the competition with M firms.
(C) The Cournot competition with 2 firms results in more social welfare as the competition with M firms.
(D) None of the above.
If M<2, then (C). If M=2, then (A). If M>2, then (B).


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(3) Alex owns a bond (an obligation from someone to pay the nominal value at a specified date) with the
nominal value of $100 with the due date a year from now. The interest rate is M%.

(A) It makes sense to sell the bond today for $55.
(B) It makes sense to sell the bond today for $75.
(C) It makes sense to sell the bond today for $95.
(D) None of the above.

If M <= 5, the answer is (D). If M >= 6, the answer is (C).


(4) In a market with negative externalities such as pollution,

(A) the socially efficient level of production is less than what competition will obtain.
(B) the socially efficient level of production is equal to what competition will obtain.
(C) the socially efficient level of production is more than what competition will obtain.
(D) the socially efficient level of production cannot to be compared to what competition will obtain.

(5) Mergers of two big firms are often scrutinized by the government because

(A) it can harm the shareholders of the firms involved.
(B) this might create dead-weight losses.
(C) a merger might result in a higher consumer surplus.
(D) it can bring higher profits to both firms.

(6) Suppose that the customer considers making an investment that will bring $100 with probability ½ and
$M× 10 with probability ½.

(A) The expected value of the investment is below $66.
(B) The variance of the investment is below 700.
(C) Insurance that costs $10 and pays $60 when the outcome is low makes the agent fully insured.
(D) None of the above.

If M<4, then the correct answer is (A). If M = 4, the answer is (C). If M >4, the answer is (B).


(7) If a college does not require that an applicant reports her test score, reporting the score is

(A) a signal that there is no moral hazard.
(B) a signal that the college faces adverse selection.
(C) a signal to the college that the applicant’s score is high.
(D) providing the college with no new information.

(8) At age 40, Joe is considering quitting his job and going back to a college to complete his degree. He
needs two more years full-time. Tuition is $8,500 per year. He earns $40,000 per year. A college degree
would raise his annual income by $ × 1,000 per year. He will retire at age 70. His benefit of a degree
would be

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(A) 8,500 × .
(B) $ × 1,000 × .

(C) $ × 1,000 × .

(D) $ × 1,000 /r.

(9) The auction platform eBay has a seller reputation system to

(A) reassure sellers about the reliability of the buyers.
(B) reduce the moral hazard problem among the sellers.
(C) reduce the adverse selection problem among the buyers.
(D) increase the competition between sellers.

(10) If a car insurance company requires the policyholders’ driving records, it is most likely that the
company

(A) charges some customers higher premiums than others.
(B) charges all customers the same premiums.
(C) charges no premiums at all.
(D) has only customers that drive safely.