Question

Suppose major league baseball consists if two types of teams: profit maximizing teams (e.g., Rays) and win maximizing teams (e.g., Red Sox). Before the season, each team decides the number of expected wins they are going to get that season by constructing a roster of players. Fans enjoy wins, but the additional revenue of each win is decreasing and given by the following average revenue (inverse demand) curve ARW) 320-2W It is costly to increase the expected number of wins because the team has to acquire better talent. The cost of an additional win is constant at: MC(W) = 100 You can think of this as being in millions of dollars in order to make it (slightly) more realistic. The total number of games in a season is 162. 1. First, consider market where there are no salary restrictions (a) Solve for the number of expected wins for the profit maximizing teams b) Solve for the number of expected wins for the win maximizing teams c) Compare the consumer surplus, profit and total payroll of profti maximizing teams and win maximizing teams. (d) Is there parity (equal number of expected wins across teams) in this league? Explain. (hint: ignore the fact that the total number of games played across teams has to equal the total number of games in the league)

Answer 1

Given AR(W)= 320-2W

and MC(W)=100

profit maximizing condition: MC=AR

20-2W=100

320-100=2W

220=2W

W=110

probability of win for both the types of teams =1/2

Expected value= Probability of event * No of times the event happens

consumer surplus = 1/2 * Qty demanded at equilibrium * change in price