a.Consider the Cournot duopoly model where the inverse demand function and the cost functions are given by

P = 120 - Q; c1 = 10 + 3q1; c2 = 12 + 6q2;

where Q = q1 + q2 is the total production quantity and qi is the production quantity of firm i, for i = 1; 2. Give the profit functions of the firms and compute the Nash equilibrium defined by the quantity each firm chooses to produce. Compute the profit of each firm, the consumer surplus, and the total surplus at equilibrium.

b. Consider the leader-follower duopoly model with the inverse demand function and the cost functions as defined in Part a. Let the reaction function of firm 2 be

r2(q1) = 57 - q1/2

Give the profit function of firm 1 and find the equilibrium strategies (production quantities) of the firms.