Suppose that the inverse demand curve for a mineral resource is 10(97): 40 24. There are 15 units of the resource to allocate across two periods. The discount rate is 0.08. The industry is perfectly competitive. Extraction costs are C (q) =10q . (a) (b) (C) (d) (e) (3 Write down the maximisation problem that needs to be solved to determine the mining path. ' Write down the Lagrangian for the problem. How much is mined each period? What is the price each period? Calculate the total profits for each period. Explain why in a competitive market firms still make prots