Coutnot Oligopoly Model

2. (20 points) Consider the following Cournot oligopoly model. There are two firms, 1 and 2 producing a homogeneous product. The market demand is p(Q) = 1-Q, where Q = q1 + 42; q: 2 0 is the output produced by firm i = 1, 2. Firm 1 has a marginal cost MCi(q1) = 0, that is the cost function is ci(q) = 0. Firm 2 has cost function "(92) = =q3. Thus the marginal cost for firm 2 is MOz(q2) = 42. The two firm's simultaneously set their quantities and their objective is to maximize their respective profits. (a) (6 points) Suppose firm 2 decides to produce 92 = ,. Does there exist an output level of of firm 1, q1, such that q2 is a best response to qi ? (b) (6 points) Find the reaction functions for firms 1 and 2 and plot them in a graph (c) (8 points) Solve for the Cournot-Nash equilibrium in this model