The mineral unobtainium is a valuable nonrenewable resource with a total estimated supply of 74 million tons. Suppose that the inverse demand curve for the unobtainium in each of the two periods is P_t = 200 − 2Q_t, where Q_t is quantity in time period t measured in millions of tons and P is the price in time period t. The discount rate is 10%.

a. Use Hotelling’s rule to solve for the amount of unobtainium produced in period 1 and in period 2, and the price for unobtainium in periods 1 and 2.

b. Suppose that a new discovery of a large unobtainium ore deposit adds to the supply so that now there are 95 million tons rather than 74 million tons. Use Hotelling’s rule to solve for the amount of unobtainium produced in period 1 and in period 2, and the price for unobtainium in periods 1 and 2. How does your answer for production and price compare to that in (a)? Explain the economic intuition for these changes.

c. Now suppose that the interest rate falls from 10 to 5% and that supply is 95 million tons. Use Hotelling’s rule to solve for the amount of unobtainium produced in period 1 and in period 2, and the price for unobtainium in periods 1 and 2. How does your answer for production and price compare to that in (b)? Explain the economic intuition for these changes.