Question

Suppose coal is only to be extracted over two periods. The inverse demand for coal is estimated to be P = 300 - 2Q, 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 discount rate r = 0.05. Also assume the total initial stock of coal is S0 = 100 for all parts of this question. Please use graphs similar to those 2-period graphs that we used in our class. Also assume there are no externalities in the extraction and consumption of coal.


a. Given the initial stock of coal is S0 = 100. 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 Discounted Value of Social Net Benefits. b. Graph the welfare gain when the manager moves from (i) to (ii) and explain how the gain occurs. i. an allocation that does not take into account MUC, i.e., assuming MUC=0; ii. an allocation with MUC appropriately accounted for. [To answer this question, you need first find out how much will be extracted in period 0 (Q0), if MUC is set to zero, i.e., coal is not considered scarce. With Q0, you can derive Q1. Then you need to explain why (Q0,Q1) thus derived is not optimal and what is the associated welfare difference.]

Answer 1