Suppose coal is only to be extracted over two periods. The inverse demand for coal is estimated to be P = 300 - Q, where P is the price of coal and Q is the quantity demanded. The marginal cost of extraction is given by MC = 2Q. These relations do not change from period to period. Assume an interest rate of r = 0.05.
a. What level of extraction would appear to be efficient from a STATIC perspective?
b. Suppose the initial stock of coal is S0 = 300. Would the dynamically efficient extraction levels be the same or different than in your answer to part a? Why?
c. Under the assumptions of part b, would coal be scarce from an economic perspective? Why or why not?
d. Suppose the initial stock of coal is S0 = 150. What is the efficient level of coal extraction in each period? Graph this result on a two-period graph, and label the areas corresponding to the Present Value of Social Net Benefits (PVSNB).
e. Graph the welfare loss of an extraction plan in which the manager fails to account for the marginal user cost (MUC) (that is, the MUC is assumed to = 0, so that the outcome from part a above is chosen). Explain why the loss occurs.
f. What do you think will happen to the efficient extraction plan if the discount rate increased to r = 0.1, and why? (you don’t have to re-calculate the results; just explain how you think extraction will be re-allocated across periods)