Collusive Monopsony. Assume that there are two teams that produce hockey games. For simplicity, call them team 1 and team 2. Each team is a monopoly in their product market with demand curve: P (q) = 96 1 2 q The production function for each team is given by: q(`) = 2` where ` is the quantity of labor hired by the team. The aggregate supply of labor is: w(L) = 60 + 2L where L = `1 + `2 is the total amount of labor hired by the two teams. 1. Assume that the two teams compete against one another by simultaneously choosing a quantity of labor to hire. a) Write out the profit function for team 1. b) Find each team's best response function. c) What is the equilibrium amount of labor chosen by each team (`)? d) What is the equilibrium wage (w)? e) What is the profit for each team (n)? 2. Now, assume that the two teams collude as a (monopsony) league. a) Find the aggregate product demand curve for the league. (Aggregate the two teams' identical product demand curves.) b) What is the new equilibrium amount of labor in the market (L)? c) What is the new equilibrium wage (w)? d) How much labor is hired by each team (`)? e) What is the profit for each team (c)?

3. Imagine that team 1 deviates from this agreement while team 2 chooses the collusive amount of labor. a) How much labor should team 1 hire to maximize profits (`1)? b) What is the total amount of labor in the market (L)? c) What is the wage (w)? d) What are team 1's profits from deviating (d)? 4. Now suppose that the teams play this game repeatedly for an infinite number of periods, and teams are deciding whether or not to employ the Grim Trigger strategy. a) If both teams face a discount rate of = 0.7, what is the discounted present value of collusion (collusion)? b) If both teams face a discount rate of = 0.7, what is the discounted present value of deviation (deviation)? c) If both teams face a discount rate of = 0.7, is collusion sustainable? Briefly explain. d) Find the cutoff value of such that collusion is sustainable in equilibrium for all values values of greater than the cutoff. 2