Simon Fraser University
Fall 2012
Econ 302 Final
Instructor: Songzi Du
Section D200
Thursday Dec. 6, 2012, 3:30 – 6:30 PM
This exam has two parts. Write your name, SFU ID number, and tutorial section number
on each part.
Part II (Questions 6 – 9):
• Name:
• SFU ID number:
• Tutorial section number:
1. This is a closed-book exam.
2. You may use a non-graphing calculator.
3. There is no separate exam booklet. Write your solution in the space following each
question.
4. Show your work! Partial credits are given.
5. We will accept a request for regrade only if the solution is written with a pen.
6. The final has 135 points (45% of the class grade).
7. Stay in your seat if less than 20 minutes remain in the exam. You may leave early if
you finish more than 20 minutes before the exam is over.
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6. (15 points) The market (inverse) demand function for a good is P (Q) = 20 − Q, where
Q is the total quantity of the good on the market. There are two firms, and each of them
has a constant marginal cost of 1 for producing each unit of the good. Firm 1 is the industry
leader, so it sets its quantity of production first. Firm 2 sets its quantity of production after
observing firm 1’s production. Calculate the subgame perfect equilibrium in this game.
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7. (15 points) You have utility over wealth u(w) = w0.3 and start with $10000. Consider a
risky project with probability 0.5 of gaining $5000, and probability 0.5 of losing $3500. Find
the expected value of this project. Find your expected utility, certainty equivalent, and risk
premium for the this project. Would you take the project?
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8.
(15 points) Recall the model of education from class. The worker is either skilled
(s = 1) or unskilled (s = 0), and this is his private information (his type); the probability of
a skilled worker is p. Worker of either type chooses to be educated (e = 1) or not (e = 0),
and education does not change his skill; education has a cost of c to the skilled worker and
k to the unskilled worker. The firm observes the education level (e) of the worker, and offers
him a fair wage which is the probability that he is skilled conditional on his education level:
we = µ(s = 1 | e), and this conditional belief µ is based on the strategy of worker (how
worker of each type chooses education). The utility of a worker from choosing education
level e (e is either 0 or 1) is we − e · c or we − e · k, depending on his type. Assume k > c.
Calculate a semi-separating equilibrium where an unskilled worker gets education with probability q. What is the condition on k and p for this equilibrium to exist?
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9. (15 points) Consider the third price auction with 4 bidders and 2 identical goods: the
top two bidders win the two goods and each pays the third highest bid; everyone else do not
pay. Assume that each bidder wants only one good and has a value vi for it. Suppose that
bidder 1 bids b1 = 7, bidder 3 bids b3 = 9, and bidder 4 bids b4 = 5. If v2 = 6, explain why
in this situation it is optimal for bidder 2 to bid his true value of 6. And explain why it is
optimal for bidder 2 to bid his true value if v2 = 8.
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