Suppose that a limited supply of coal is available to be extracted and allocated as fuel over two time periods by a social planner. Assume that the marginal benefits from coal are given by MB1 = 40 2q1 and MB2 = 40 2q2, where q1 and q2 denote the respective amounts utilized in periods 1 and 2. The marginal cost of extracting coal is MC = 4 in both time periods. The total amount of coal available, X , is 10 units and the rate of discount is 40% (i.e., r = 0.4).

(a) Compute the socially desirable values of coal use and associated marginal benefits in each time period. [10 points]

(b) Explain the concept of marginal user cost (MUC) of coal and compute its value in each time period. [10 points]

(c) In which directions would you expect the socially desirable values of utilization and MUC of coal in each time period to change if the discount rate, r, increased? Also provide intuitive explanations for your answers.