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.