Suppose that a limited supply of coal is available to be extracted and sold over two time periods by a perfectly
competitive mining industry. Assume that the demand curves for coal in thetwoperiodsaregivenbyP1 =40-2q1 andP2 =40-2q2,whereq1 andq2 denotethe respective amounts of coal produced in periods 1 and 2, while P1 and P2 stand for price of coal in periods 1 and 2 respectively. 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 market equilibrium values of coal production and price in each time period. [10 points]
- (b) Note that market price in part (a) exceeds marginal cost even though the industry is
perfectly competitive. Furthermore, market price goes up over time. Explain these two results in economic terms. [6 points]
(c) Now assume that extraction and consumption of coal are polluting activities, with marginal external cost MECi = 3 + qi in period i (where i = 1, 2). How much coal would be allocated to the first period and how much to the second period in a socially efficient allocation?
(d) Compute the total social welfare loss (in present value terms) if the market fails to account for the externality identified in part (c), and calculate per unit taxes on coal needed in period 1 and period 2 to address this problem.
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