Suppоse thаt 70 tоns оf а brаnd-new mineral called vibranium is discovered in the country of Wakanda and that Wakanda is the only place on Earth with this mineral. The vibranium industry is perfectly competitive with many small producers that take prices as given. Investors can earn a 15% interest rate elsewhere in the economy. Assume that the inverse demand curve for vibranium is the same in both periods: Pt = 120 - qt, where Pt is the price in period t and qt is the total quantity demanded in period t. For simplicity, assume that there are only two periods, so that all vibranium must be sold either in the first or in the second period. If the objective is to maximize resource rents, a. How much vibranium should be produced in the first period and in the second period? b. Compute the price for vibranium in both periods 1 and 2. HINT: Hotelling’s rule implies that r = (P2 - P1) / P1