Homework 3 1. Consider the problem of a mining firm over two periods (0 and 1). The firm has access to X = 12 units of a nonrenewable resource and must set extraction levels in each period (go and q1, respectively). Price over the two periods is fixed at p = 20. The firm's marginal cost of extraction is MClqr) = 5 + q;. a. What is the firm's total rent maximizing extraction plan assuming it applies a 10% discount rate (r = 0.1). b. Suppose instead X: 35. Redo Problem #1.a. Does your answer change? Provide intuition for your finding using complete sentences. c. Assume once again that X = 12. What are the total resource rents the firm earns under the efficient policy in periods 0 and 1? Total resource rents in this problem are the same as the (total) profit the firm earns from mining. 2. Dysprocorp is a near-monopoly supplier of dysprosium. There is a competitive fringe of dysprosium producers that act as price takers of the price Dysprocorp sets. Market inverse demand for dysprosium is PD(Q) = 400 Q, with P measured in dollars per ton of dysprosium and Q measured in thousands of tons of dysprosium. The fringe marginal cost curve is Mqu;) = 40 + 0.5:}; {with q; and MCF also in thousands of tons of dysprosium and dollars per ton of dysprosium, respectively). Dysprocorp's marginal cost of production is constant at $52 per ton. Dysprocorp needs to plan its strategy for setting the price of dysp rosium. [In this problem, consider a static market equilibrium in one period only and assume that the user cost of dysprosium production for both Dysprocorp and firms in the competitive fringe is zero]. a. Determine the residual demand facing Dysprocorp after accounting for the quantity supplied by the competitive fringe. b. Assume that Dysprocorp's marginal revenue after accounting for the competitive fringe is MRAQr) = 150 (2/3)Q,. How much dysprosium will Dysprocorp supply? c. What is the resulting dysprosium price? d. How much dysprosium is produced by the competitive fringe