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 20 + 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?

Question

Quizplus · Accepted Answer

The revenue for each team is maximized when the derivative of their revenue function with respect to their own ticket price is set to zero. For team A, the revenue is $R_A = P_A \times (10 - 2P_A + P_B)$ and for team B, it's $R_B = P_B \times (20 + P_A - 2P_B)$. Differentiating these with respect to $P_A$ and $P_B$ respectively, setting to zero, and solving the system of equations yields the prices where both teams maximize their revenue, which are $P_A = 4$ and $P_B = 6$.

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