02 May Question: Suppose major league baseball consists if two types of teams: profit maximizing teams (e.g., Rays…
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: AR(W) 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.
Now suppose the league institutes a salary cap that restricts the number of expected wins to 80. That is, it makes the marginal cost of an additional win is equal to infinity after the 80th win. (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) Did the salary cap achieve parity? 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) d) Suppose that fans also value parity. Specifically, the salary cap resulted in the following average revenue (inverse demand) curve: AR(W) 420-2W. Did the salary cap achieve
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