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 TC1 = 10 + 2Q1 and marginal cost is MC1 = 2. The second firm's cost function is TC2 = 12 + 8Q2 and marginal cost is MC2 = 8.

i. What is Firm 1's best-response function? What about Firm 2's?

ii. Determine the equilibrium output and selling price of each firm (i.e. Nash-Cournot equilibrium).

b. Assume identical product and production costs. Each firm's cost function is TCi = 2Qi and marginal cost is MCi = 2. Determine the equilibrium output and selling price of each firm (i.e. Nash-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?