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 + q2; qi ? 0 is the output produced by firm i = 1, 2. Firm 1 has a marginal cost MC1(q1) = 0, that is the cost function is c1(q1) = 0. Firm 2 has cost function c2(q2) = 1/2q(subscript 2)^2 . Thus the marginal cost for firm 2 is MC2(q2) = q2. The two firm's simultaneously set their quantities and their objective is to maximize their respective profits.

(a) Suppose firm 2 decides to produce ^q2 = 1/2 . Does there exist an output level of of firm 1, q1, such that ?q2 is a best response to q1 ?

(b) Find the reaction functions for firms 1 and 2 and plot them in a graph

(c) Solve for the Cournot-Nash equilibrium in this 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; 4: 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 c(q1) = 0. Firm 2 has cost function ca(92) = =q5. Thus the marginal cost for firm 2 is MC2(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 42 = . Does there exist an output level of of firm 1, q1, such that 92 is a best response to q, ? (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