In the National Basketball Association (NBA), the owners share revenue but not costs. Suppose that one team, the L.A. Clippers, sells only general admission seats to a home game with the visiting Philadelphia 76ers (Sixers). The inverse demand for the Clippers-Sixers tickets is p = 100 - 0.004Q. The Clippers' cost function of selling Q tickets and running the franchise is C(Q) = 10Q.
a. Find the Clippers' profit-maximizing number of tickets sold and the price if the Clippers must give 50% of their revenue to the Sixers. At the maximum, what are the Clippers' profit and the Sixers' share of the revenues?
b. Instead, suppose that the Sixers set the Clippers' ticket price based on the same revenue-sharing rule. What price will the Sixers set, how many tickets are sold, and what revenue payment will the Sixers receive? Explain why your answers to parts a and b differ.
c. Now suppose that the Clippers must share their profit rather than their revenue. The Clippers keep 45% of their profit and share 55% with the Sixers. The Clippers set the price. Find the Clippers' profit-maximizing price and determine how many tickets the team sells and its share of the profit.
d. Compare your answers to parts a and c using marginal revenue and marginal cost in your explanation.