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 world demand for samarium is given by the inverse demand curve p -20,000 - 20 q, where q is . in tons. · the marginal cost to extract a ton of samarium is mc = 2000

(a) if samarium were supplied by a monopolist, what price would the monopolist charge?

(b) what would be the monopolist's profit, consumer surplus and deadweight loss?

(c) if two identical firms supplied samarium, what would be the equilibrium? how much would each firm produce? what would be the market clearing price?

(d) what would be the firms' profits, the consumer surplus and the deadweight loss?

(e) briefly explain why your answer in (d) is the same or different than your answer in (b).

(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?

(g) finally, explain what would happen if firms competed in prices (bertrand competition) rather than in quantities?