Q. 1. A baseball team's attendance depends on number of games it wins per season and on price of its tickets. Demand function it faces is Q = N (20 - p), where Q is number of tickets (in hundred thousands) sold per year, p is price per ticket and N is fraction of its games that team wins. Team can increase number of games it wins by hiring better players. If team spends C million dollars on players, it will win .7 - 1/C of its games. Over relevant range, marginal cost of selling an extra ticket is zero.
a. Write an expression for firm's profits as a function of ticket price and expenditure on players.
b. Find ticket price that maximizes revenue.
c. Find profit-maximizing expenditure on players and profit-maximizing fraction of games to win.