Problem 1. Alice and Barbra sell used CDs at music festivals. Each is decidingwhether or not to set up their booth at the last festival of the summer. The festivalis scheduled to take place in Alton, very near where Alice lives. It will cost her only$30 to travel the festival. Barbra is farther away, and it will cost her $100 to travelto Alton. Both Alice and Barbra would prefer to be only CD sellers at the festival,since they would avoid competition. If only one seller is at the festival, she will make$150 during the day (not counting travel costs). If both Barbra and Alice sell CDsat the festival, they will lower their prices and each make $50 during the day. BothAlice and Barbra receive $0 for not attending the festival.1. Draw the Normal Form of the game Alice and Bob are playing, be sure to labelthe game completely.2. Does either player have a dominant strategy? If so, what is it?3. List all pure strategy Nash equilibria for this game. Remember that a Nashequilibrium is a strategy profile.
Econ 444-02 (Corporate Economics), Fall 2015Problem Set #2Due in class Thursday, September 24Problem 1. Alice and Barbra sell used CDs at music festivals. Each is decidingwhether or not to set up their booth at the last festival of the summer. The festivalis scheduled to take place in Alton, very near where Alice lives. It will cost her only$30 to travel the festival. Barbra is farther away, and it will cost her $100 to travelto Alton. Both Alice and Barbra would prefer to be only CD sellers at the festival,since they would avoid competition. If only one seller is at the festival, she will make$150 during the day (not counting travel costs). If both Barbra and Alice sell CDsat the festival, they will lower their prices and each make $50 during the day. BothAlice and Barbra receive $0 for not attending the festival.1. Draw the Normal Form of the game Alice and Bob are playing, be sure to labelthe game completely.2. Does either player have a dominant strategy? If so, what is it?3. List all pure strategy Nash equilibria for this game. Remember that a Nashequilibrium is a strategy profile.Problem 2. Let market demand in the cement industry be given by Q(P ) = 200−P .There are only two firms in the industry and the total cost function for each firm isC(qi ) = 20qi + 400, where i = 1, 2.1. What is the marginal cost for both firms?2. Represent the market price as a function of each firm’s output, q1 and q2 .3. Find the best-response function of each firm.4. Suppose firm 2 produces nothing, that is, q2 = 0. What is firm 1’s optimaloutput level? Compare this quantity with the
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