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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 I (Questions 1 – 5): • 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. 1 1. (15 points) The market (inverse) demand function for a good is P (Q) = 20 − 2Q. There is a monopolist with a constant marginal cost of 3 for producing each unit of the good. Assume that the government imposes a sales tax of 12%, and the sales tax does not impact the monopolist’s cost. Calculate the monopolist’s price and quantity, and calculate the corresponding consumer’s price. 2 3 2. (15 points) Part i: Find the strategies that survive iterative deletion of strictly dominated strategies (ISD). For each strategy that you delete, write down the (possibly mixed) strategy that dominates it. Hint: two strategies of each player survive. Part ii: Calculate all Nash equilibria (pure and mixed) in this game. W X Y Z A 3, 3 0, 1 3, 0 0, -1 B 0, 1 3, 3 0, -1 3, 0 C 1, -1 1, 0 1, 3 1, 1 D 2, 0 0, -1 2, 1 0, 3 4 5 3. (15 points) Consider the battle of the sexes game, with a twist: player 1 (the girl) has an additional strategy X (say, X = going to ballet with Mom). Specify the payoffs for the strategy X (i.e., complete the third row) so that (B, B) is the unique Nash equilibrium in the game with the strategy X. Hint: ISD. B H B 3, 1 0, 0 H 0, 0 1, 3 X 6 7 4. (15 points) Calculate all Nash equilibria (pure and mixed) in this game. Hint: there are two. D E F A 4, 0 0, 4 3, 0 B 0, 4 4, 0 3, 0 C 0, 3 0, 3 3, 3 8 9 5. (15 points) Find all pure-strategy subgame perfect equilibria of the following game. Hint: there are two. 1 a b 0.5 1 2 c d 0 0 1 e f 2 2 g h i j 1 1 2 0 2 −2 1 −1 10 11