Demand for a product is given by the following inverse demand function: P = 50 − 2Q. Only two firms supply the market, acting independently and making output decisions simultaneously.

a. Assume identical product but different production costs. Firm 1’s cost function is C(Q1 ) = 10 + 2Q1 and the second firm’s cost function is C(Q2 ) = 12 + 8Q2.

i. What is Firm 1’s best-response/reaction function? What about Firm 2’s? Graph these response functions.

ii. Determine the equilibrium output and selling price of each firm (i.e. Cournot equilibrium). Label on the graph.

b. Assume identical product and production costs. Each firm’s cost function is C(Qi ) = 2Qi . Determine the equilibrium output and selling price of each firm (i.e. Cournot equilibrium). Calculate the profits of each firm.

c. Suppose now that the firms in part (b) collude, act as a monopolist seeking to maximize the total industry profits. Determine the output and selling price. What is each firm’s profit?