Suppose there are 32 teams in the NFL who all have the same average revenue curve equal to AR(W) = 50 3W and the same marginal cost curve equal to MC = 20, where W represents the number of expected wins. The maximum number of wins a team can get in a season is Wmax = 16.

1. Suppose that half of the teams are profit-maximizers and half of the teams are win-maximizers.

a) How many expected wins will each profit-maximizing team choose?

b) What are the profits of each profit-maximizing team?

c) How many expected wins will each win-maximizing team choose?

d) What are the profits of each win-maximizing team?

Part 2. Suppose that the league implements a policy under which no team can have a total payroll that exceeds 140.

a) What is the maximum number of wins a team can achieve without exceeding the payroll cap of 140?

b) How many expected wins will each profit-maximizing team choose?

c) How many expected wins will each win-maximizing team choose?

d) Did this payroll cap improve competitive balance in the league? Briefly explain.

3. Find a payroll cap that achieves perfect balance in the league.

(Please make sure to answer part 2)