Question 1: Cournot Competition Samarium is a \"rare-earth\" element that is used to produce magnets with permanent magnetization, drugs for chemotherapy, control rods for nuclear reactors and aerospace equipment. It is costly to extract from the ground, creates a lot of pollution when mined and refined. Firms that produce Samarium must plan production in advance and production is relatively slow to adjust. Suppose: e World demand for Samarium is given by the inverse demand curve P =26,000 2Q, where Q 1s in tons. e The marginal cost to extract a ton of Samarium is MC = 2000 (a) Suppose a single firm supplied Samarium. What would be the profit maximizing price set by the monopolist? (b) Suppose two identical firms supplied Samarium. Why might we think Cournot competition would be a reasonable model for this industry? () Write down the profit function for firm A. What is firm A's best response function? (d) In the Cournot equilibrium, how much would each firm produce? What would be the market clearing price? (e) What would be the firms' profits, the consumer surplus and the deadweight loss? (f) What would happen if one of firms (say firm B) faced a capacity constraint and could produce, at most, Q =200. How much would firm A produce? What would be the equilibrium price