Simon Fraser University Fall 2015
Econ 302 (D200) Quiz
Instructor: Songzi Du
Thursday October 8 2015, 8:30 – 9:20 AM
Write your name, SFU ID number, and tutorial section number both on the exam booklets and on the questionnaire . Hand in both the exam booklets and this questionnaire. But note that only the exam booklets are graded .
• Name:
• SFU ID number:
• Tutorial section number:
General instructions
1. This is a closed-book exam: no books, notes, computer, cellphone, internet, or other aids. A scientific, non-graphing calculator is allowed.
2. If you use decimals in calculation, keep two decimal places.
3. Write clearly. Illegible answers will receive no credit.
4. Show your work! Partial credits are given. Answers without proper explanation/calculation will be penalized.
5. A request for regrade can be accepted only if the exam is written with a pen.
1.
(10 points) The market demand function for a homogeneous good is Q ( P ) = 20 − 4 P .
There are two firms: firm 1 has a constant marginal cost of 1 for producing/selling each unit of the good, and firm 2 has a constant marginal cost of 3.
Suppose that the two firms compete by simultaneously setting their quantities ( q
1 and q
2
), and the price of the good is determined by the market demand function given the total
1

quantity. Calculate the Nash equilibrium ( q
1
, q
2
) in this game, and calculate the price in this equilibrium.
2.
(10 points) Consider the following simultaneous-move game with two players. Each player simultaneously chooses a bid from the set { 1 dollar , 50 dollars, 100 dollars } . (A player must choose a bid and cannot back out of the game.) The player with the higher bid wins a prize of 100 dollars; the other player (the loser) does not receive any prize. If the two bids are the same, neither player receives the prize. Each player must pay his own bid, whether or not he wins the prize. (The loser pays too.) The payoff/utility of each player is simply his net winnings. For example, if player 1 bids 100 and player 2 bids 50, then player
1 gets 100 − 100 = 0 and player 2 gets 0 − 50 = − 50; if player 1 bids 50 and player 2 bids
50, then each gets 0 − 50 = − 50.
(i) Write the normal form (matrix) of this game.
(ii) Calculate a symmetric mixed strategy Nash equilibrium.
3.
(10 points) In Burnaby Mountain there is nothing to do at night but look at the stars or go to the local bar. Let us define the utility of looking at stars as 0, and let the cost of walking to the bar be 1. Suppose that the utility from being at the bar is 2 (so the net utility is 2 − 1 = 1) if there are fewer than 3 people (including oneself) at the bar, and 1/2
(the net utility is 1 / 2 − 1 = − 1 / 2) if there are 3 or more people (including oneself) at the bar. Suppose that there are only 3 people in Burnaby Mountain at night, and they make decisions (looking at stars or going to the bar) simultaneously.
(i) Find the three pure-strategy Nash equilibria.
(ii) Calculate the symmetric mixed-strategy Nash equilibrium. And calculate the utility of each player in this equilibrium.
2