A city has two major league baseball teams, A and B.The number of tickets sold by either team depends on the price of the team's own tickets and the price of the other team's tickets.If team A charges P_a for its tickets and team B charges P_b for its tickets, then ticket sales, measured in hundreds of thousands per season, are 10 - 2P_a + P_b for team A and 5 + P_a - 2P_b for team B.The marginal cost of an extra spectator is zero for both teams.Each team believes the other's price is independent of its own choice of price, and each team sets its own price so as to maximize its revenue.What price do they charge per ticket?

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Quizplus · Accepted Answer

Team A's revenue is (10 - 2P_a + P_b)P_a = 10P_a - 2P_a² + P_aP_b. To maximize this, we take the derivative with respect to P_a and set it equal to zero: 10 - 4P_a + P_b = 0. Solving for P_a, we get P_a = 3. Similarly, for team B, we get P_b = 2.

A City Has Two Major League Baseball Teams, a and B.The