Assume that there are two teams (for simplicity, call them team 1 and team 2) that produce cricket games. Each team is a monopoly in their product market with demand curve:

P(q) = 420 3q

The production function for each team is given by: q(k) = k where k is the quantity of labor hired by the team.

The aggregate supply of labor is: w(K) = 2K

where K = k1 + k2 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) Find each team's best response function?

b) Find the equilibrium wage and amount of labor hired by each team?

c) Find each team's profits?

2. Now, assume that the two teams can collude as a league.

Note that the aggregate product demand curve faced by the league is given by P(Q) = 420 (3/2)Q.

a) Find the equilibrium wage and the amount of labor in the market (K)?

b) If the teams agree to split the profits, how much labor is hired by each team (k)? Find each team's profits?

c) What is the highest level of profits that a team can get if they deviate from this agreement? Is collusion a Nash equilibrium of the one-period game?