Simon Fraser University
Fall 2012
Econ 302 Midterm
Instructor: Songzi Du
Section D200
Tuesday Oct. 30, 2012
Due: end of the class, 10:20 am.
This exam has two parts. Write your name, SFU ID number, and tutorial section number
on each part.
Part II (Questions 5 – 7):
• 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 midterm has 75 points (25% of the class grade).
7. Stay in your seat if less than 20 minutes remain in the class. You may leave early if
you finish more than 20 minutes before the class is over.
1
5. (10 points) The market (inverse) demand function for a good is P (Q) = 10 − Q, where
Q is the total quantity of the good on the market. There are two firms: firm 1 has a constant
marginal cost of 2 for producing each unit of the good, and firm 2 has a constant marginal
cost of 4. 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. Find the subgame perfect
equilibrium in this game.
2
3
6. (10 points) The following stage game is infinitely repeated:
C
D
C
2, 2
20, -10
D
-10, 20
-1, -1
In each period the two players move simultaneously and observe the actions from the previous
periods. Assume that the final payoff of each player is the time-discounted sum of payoffs
from all periods, with a discount factor of δ ∈ (0, 1). Recall the grim-trigger strategy: each
player plays C unless one of them had played D in the past, in which case each player
plays D. Calculate the range of δ such that the grim-trigger strategy is a subgame perfect
equilibrium of this infinitely-repeated game.
4
5
7. (10 points) Two distinct proposals, A and B, are being debated in the capitol. The
Parliament likes proposal A, and the Prime Minister likes proposal B. The two proposals
are not mutually exclusive; either or both or neither may become law. Thus, there are four
possible outcomes, and the utilities of the Parliament and of the Prime Minster are listed in
the following table.
Parliament
4
1
3
2
A becomes law
B becomes law
Both A and B become law
Neither (status quo prevails)
Prime Minister
1
4
3
2
The game moves as follows. First, the Parliament decides whether to pass a bill and whether
it is to contain A or B or both. If the Parliament does not pass a bill then the status quo
prevails. Otherwise, the Prime Minister sees the bill and decides whether to sign or veto
it. If the Prime Minister signs the bill it becomes the law; if he vetoes the bill then the
status quo prevails. Draw the extensive form for this game, and find the subgame perfect
equilibrium.
6
7