Problem 1: Competitive Balance. Demand for wins for Team 1 is: P1(w1) = 100 50w1 where w1 indicates Team 1s winning proportion. Demand for wins for Team 2 is P2(w2) = 150 75w2 where w2 indicates Team 2s winning proportion. They are the only two teams in the league, so w2 = 1 w1. With no league policy, we calculated the equilibrium w1 = 2 5, w2 = 3 5, MC = 60, TC1 = 24, TC2 = 36, 1 = 8, and 2 = 27 1. Now, suppose that the league institutes a revenue sharing agreement where each team pays the other team = 0.3 share of their revenues. a) Draw each teams marginal revenue before revenue sharing. Label any intercepts. b) On the same graph, draw each teams marginal revenue after revenue sharing. Label any intercepts. c) Do any of the equilibrium values (winning percentages, payrolls, profits) change? 2. Suppose instead that the league wants to implement a salary cap. What is the salary cap MCthat achieves perfect balance w1 = w2 = 1 2? 3. Suppose instead that the league implements a very simple form of luxury tax. In particular, the league taxes only Team 2s revenue at a rate of one-third (or = 1 3). For simplicity, assume the tax revenue is wasted by leagues commissioner on expensive cars. a) What is Team 2s marginal revenue MR?2 after being taxed at a rate = 1 3. b) What are the new equilibrium winning percentages, w1 and w2?