Problem 2: Cournot Competition (30 points). Consider the problem of the Angels and Dodgers, two teams...

 

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Problem 2: Cournot Competition (30 points). Consider the problem of the Angels and Dodgers, two teams in the MLB. Before the season begins, the Angels and Dodgers simultaneously choose the number of wins WA and Wp they are each going to get this season by constructing a roster of players. Assume that the average revenue (inverse demand) for wins is given by: AR(W) = P(W) = 240 – 2W where W = WA + WD is the sum of the two teams' wins. Baseball fans in Los Angeles will choose one team to support (i.e. buy) which determines the 'price' of a win, and fans don't have preferences for either team before the season begins. It is costly for each team to increase the number of wins because teams must acquire better talent. The cost of an additional win is constant at MC = 180 for each team. a) Suppose that each team chooses their own WA and WD to maximize profits. Find the best response function for each team and then find the Nash equilibrium number of wins for each team. Find the equilibrium price and profits of each team. b) Suppose that each team chooses their own WA and Wp to maximize the number of wins. Find the best response function for each team and characterize the Nash equilibrium number of wins. Find the equilibrium price and profits of each team. c) Suppose that the Angels are maximizing profits while the Dodgers are maximizing the number of wins. At the Nash equilibrium, which team will win more games? Which team gets a higher price? Which team has higher profits? (You can either solve for the new equilibrium values or use your intuition and provide a concise explanation.) Problem 2: Cournot Competition (30 points). Consider the problem of the Angels and Dodgers, two teams in the MLB. Before the season begins, the Angels and Dodgers simultaneously choose the number of wins WA and Wp they are each going to get this season by constructing a roster of players. Assume that the average revenue (inverse demand) for wins is given by: AR(W) = P(W) = 240 – 2W where W = WA + WD is the sum of the two teams' wins. Baseball fans in Los Angeles will choose one team to support (i.e. buy) which determines the 'price' of a win, and fans don't have preferences for either team before the season begins. It is costly for each team to increase the number of wins because teams must acquire better talent. The cost of an additional win is constant at MC = 180 for each team. a) Suppose that each team chooses their own WA and WD to maximize profits. Find the best response function for each team and then find the Nash equilibrium number of wins for each team. Find the equilibrium price and profits of each team. b) Suppose that each team chooses their own WA and Wp to maximize the number of wins. Find the best response function for each team and characterize the Nash equilibrium number of wins. Find the equilibrium price and profits of each team. c) Suppose that the Angels are maximizing profits while the Dodgers are maximizing the number of wins. At the Nash equilibrium, which team will win more games? Which team gets a higher price? Which team has higher profits? (You can either solve for the new equilibrium values or use your intuition and provide a concise explanation.)

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