10. Suppose there are two identical firms in an industry. The output of firm 1 is denoted by q1 and that of firm 2 is denoted by q2. The total cost of production for firm i, i {1, 2}, is

C(qi) = 2 qi

Let Q denote total output, i.e. Q = q1 + q2. The inverse demand curve in the market is given by

P = 14 Q

(a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market price

(b) What would be the quantities produced by each firm and market price under Stackelberg duopoly if firm 1 moves first?

(c) Now suppose the production process in the industry pollutes the environment and generates a marginal social cost given by

MC_E = 3Q

Calculate the deadweight loss arising from the Cournot-Nash equilibrium in this case.

(d) Consider the same scenario as part (c) with marginal social cost from pollution MC_E = 3Q. Suppose the firms can collude, and maximize joint profit. Is the deadweight loss under this scenario higher than or lower than the deadweight loss in part (c)? (It is fine if you guess the answer after calculating output but explain the reason for your guess.)