SIMON FRASER UNIVERSITY
Final
Examination
SPRING 2016
ECON 302
D100 (LU)
MICROECONOMIC THEORY II:
STRATEGIC BEHAVIOR
April 18, 2016
INSTRUC TIONS & F ORMAT
DO NOT OPEN THIS EXAM UNTIL INSTRUCTED TO DO SO.
1. On the cover of the answer booklet, write your name, SFU ID number and
tutorial number.
2. Simple (non-graphing, non-programmable) calculators are permitted.
3. Use a pen (not pencil) for regrade eligibility. No other aids are allowed.
4. Label the axes and curves in any graph you draw.
5. Make sure that your solutions are legible and, when asked to show your
work, that the order of your reasoning is clear.
6. Remaining students must stay seated for the last fifteen (15) minutes.
7. At the end of the exam, stay seated and quiet while materi al is being
collected. Hand in BOTH the answer booklet and this questionnaire.
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This exam is out of one hundred and twenty-five (125) points.
There is no choice of questions.
The point value of each question is shown in brackets.
DURATION: 169 minutes
1. (18 points) Consider the following two-player simultaneous-move game:
L
R
T
1,1
0,0
B
0,0
0,0
a) [8] Find every Nash equilibrium (NE) of this game, and explain why there are no others.
Now consider this two-player simultaneous-move game: both players choose an integer from
{0,1,2,3, … , 𝑛}, where 𝑛 ≥ 1, and receive payoff equal to the lower number chosen.
b) [10] Find every NE of this game, and explain why there are no others.
Hint: Try to generalize your reasoning from part a.
2. (32 points) Consider a market with two firms selling a homogeneous good, for which the
demand is Q = 60 – 3P. Neither firm has any fixed cost.
First suppose that both firms choose quantity simultaneously, and that firm 1 has marginal
cost equal to 8, while firm 2 has marginal cost equal to 6.
a) [9] Find the subgame-perfect equilibrium (SPE) of this game. Show your work. How
does it compare to the NE here? Briefly justify your answer.
Suppose instead that firm 1 first builds a capacity 𝑘 at cost 4𝑘. Then, having observed 𝑘,
firm 2 chooses its quantity 𝑞2 (the marginal cost is still 6). Finally, having observed 𝑞2 , firm
1 chooses its quantity 𝑞1 at an additional cost of 4𝑞1, subject to the constraint that 𝑞1 ≤ 𝑘.
(Note that if firm 1 fully uses its capacity, the total cost per unit is 8, just like for part a.)
b) [16] Find firm 2’s strategy in a SPE of this game. (Do not find the whole SPE: it is timeconsuming.) Show your work.
c) [7] Give a coherent qualitative economic intuition for the strategy you found in part b.
3. (14 points) Consider an infinitely repeated game with observed actions where players have
discount factor 𝛿 ∈ (0,1). The stage game is the following symmetric prisoner’s dilemma:
C
D
C
10,10
0,20
D
20,0
3,3
a) [7] Suppose 𝛿 = 0.9. Is the following strategy profile a SPE of the infinitely repeated
game? Give a full justification for your answer.
Both players use the following strategy: Play C in the first stage, and continue playing C
as long as the opponent has played C in all previous stages. If the opponent has played D
in any previous stage, play D.
b) [7] Find all values of 𝛿 ∈ (0,1) for which there exists an SPE where the outcome is that
(C,C) is played at every stage. Show your work, and explain why you found all values.
4. (5 points) In game theory, when we assume that players maximize expected utility, rather the
expected value of some function (e.g. concave, convex) of utility, what are we assuming
about whether players are risk-averse, risk-neutral, or risk-loving toward money? Justify your
answer in five lines or fewer.
5. (45 points) A risk-neutral insurance company is offering Sue an insurance policy for her
upcoming trip. The company is a monopolist, so if Sue refuses the offer, she is uninsured. (In
particular, assume that Sue will not cancel her trip.)
10
Sue’s utility is − 𝑤 − 0.3𝑐, where w denotes her wealth level, in thousands of dollars. Her
initial wealth is $10 thousand. The probability of a loss is 0.25 if c=0, and 0.15 if c=1. A loss
costs $8 thousand.
The company knows all of the above information, but may not know the value of 𝑐.
a) [5] Why is it reasonable to assume that the insurance company is risk-neutral even if one
believes that its shareholders are risk-averse?
b) [16] What is the insurance company’s first-best profit? (That is, what would its maximum
profit be if it can observe 𝑐?) Answer the question in each of the following cases:
i) 𝑐 is a fixed characteristic (type) assigned to Sue before she makes any decision;
ii) 𝑐 is an action that Sue chooses during her trip.
Justify your answers.
Hint: Start by figuring out what form the insurance policy must take in company’s first
best and carefully explaining every step of your reasoning.
Note: Your answer may involve more than one number in one or both of the cases.
For the rest of this problem, suppose that the company is unable to observe 𝑐, so that nothing
in the insurance policy can depend on 𝑐.
For parts c and d, assume that 𝑐 is a fixed characteristic assigned to Sue before she makes
any decision.
c) [5] Can the firm achieve its first-best profit? If so, justify your answer by checking all
relevant conditions. If not, explain why.
d) [5] Suppose the firm charges Sue insurance premium 𝑎𝑥, where 𝑥 ∈ [0,1] is the fraction
of the loss that is insured. The company chooses 𝑎 > 0, and after seeing 𝑎, Sue chooses 𝑥.
What is the word expression describing this type of pricing behaviour by the firm? Can
you tell whether, by selecting the optimal value of 𝑎, the firm achieves its second-best
profit? Why or why not?
For part e, assume instead that 𝑐 is an action that Sue chooses during her trip.
e) [14] Suppose the parameters of the problem (which may be different from those given
above) are such that the firm has two goals: to sell insurance to Sue and to make her
choose 𝑐 = 1. Explain, in words, the key tradeoff faced by the firm in designing the
expected-profit-maximizing contract that achieves these goals. Describe, in words, the
constraints that the contract must satisfy. Are these constraints binding? Why or why not?
6. (6 points) A lecture slide discussing welfare improvements in a market with externalities
through assigning property rights (in a setting with no transaction costs) states:
If there are no income effects, then the outcome does not depend on who is assigned the
property rights.
a) [3] It was mentioned in lecture that the use of the word “outcome” is not entirely
appropriate here. Why? Suggest a word that would be more precise.
b) [3] Why is the condition “If there are no income effects” present in this statement?
7. (5 points) Evaluate the following statement. (Do you agree or disagree? Why?)
The following policies are equally inefficient for reducing carbon emissions, assuming that
both policies lead to the same total quantity of emissions:
- industry-specific regulations
- distributing tradable permits for free.