Consider the Cournot duopoly discussed in lecture. Suppose that the demand curve is now P (q1 +q2) = 1202(q1 +q2). Suppose that firms 1 and 2 simultaneously choose quantity q1 and q2 to supply and that the firms incur a marginal cost of production equal to 20. Assume that the most that each firm can supply is at most 40 because of capacity constraints.

As a result, each firm's utility function is given by:

u1(q1, q2) = (120 2(q1 + q2))q1 20q1

u2(q1, q2) = (120 2(q1 + q2))q2 20q2.

Part a: If firm 2 produces quantity q2, what is the best response for firm 1? Use this to solve for the best response function for firm 1, BR1(q2). Similarly solve for the best response function for firm 2, BR2(q1).

Part b: What are the strictly dominated strategies of each firm in this game? Justify why each of these strategies are strictly dominated. Justify why all other strategies are not strictly dominated.

Part c: What are all of the Nash equilibria of this game?