Consider the following two-period model of dynamically efficient extraction of a non-renewable natural resource. Suppose that the constant marginal cost of extraction is 0 in each period and that the total stock available of the resource is=100. Moreover, the marginal benefit is MB(Q_t) = 60 - Q_t, where Q_tis the quantity of resource extracted in period t, for t = 0,1. The discount rate is r =0.25.

1. What is the efficient quantity of resource extracted in each period? What is the marginal user cost of the resource in each period? (Hint: what is the discount factor?)
2. Suppose now that there is a market to trade the resource. What is the equilibrium price corresponding to each period? Using these prices, obtain the rate of return of investing in this natural resource (which is rate of growth of its price). How does it compare with the discount rate? Intuitively justify your answer by relying on the trade off between investing in the natural resource in question and liquidating the stock and putting the proceeds in the bank at an interest rate equal to the discount rate r.
3. How will the answers to questions (a)-(b) change if, because of new discoveries, the known reserves of the natural resource become Q=120? How does this compare with the efficient allocation that would prevail if the resource were fully renewable?
4. How will the answers to questions (a)-(b) change if the discount rate were r = 0? Explain intuitively why it is different to the allocation obtained in (a)-(b)