Question

The mineral unobtainium is a valuable nonrenewable resource with a total estimated supply of 74 million ions. 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.

Answer 1

The hypothetical question involves applying Hotelling's rule to determine optimal production and pricing of a nonrenewable resource over two periods given a certain demand function. Without marginal cost details, an exact solution cannot be provided. Nevertheless, variations in supply and discount rates would generally affect resource pricing and production decisions due to changes in scarcity and time value of money.

Step-by-step explanation:

The Hotelling's rule is a foundational concept in natural resource economics, which gives us insights into the production and pricing strategies for nonrenewable resources like unobtainium. The rule primarily states that the net price of a resource, which is the market price minus the marginal cost of extraction, rises over time at the rate of interest. This conclusion is premised upon the efficient market hypothesis, which assumes perfect competition and intertemporal market equilibrium.

Unfortunately, the scenario provided with unobtainium cannot be answered completely without further information, specifically regarding the marginal cost of extracting unobtainium and the exact structure of the market. However, with the general demand function provided, one could theoretically calculate the optimal allocation of the resource across two periods, assuming our goal is to maximize the present value of the total profits from selling this resource.

In a scenario where additional supply is discovered, the general economic intuition suggests that the increased supply would lead to a decrease in the resource's price and potentially an increase in the quantity consumed in the initial period, as the resource becomes less scarce. Alternatively, when the discount rate falls, the future becomes relatively more valuable compared to the present, which generally encourages extraction companies to save the resource for future sales, leading to potential decreases in present consumption and less of a rapid climb in prices over time.