A steel factory has the right to discharge waste into a river. The waste reduces the number of fish, causing damage for fisheries. Let X denotes the quantity of waste dumped. The marginal damage, denoted MD, is given by the equation MD = 2 + 5Q. The marginal benefit (MB) of dumping waste is given by the equation MB = 34 - 3Q.
(a) Calculate the efficient quantity of waste.
(b) What is the efficient fee, in dollars per unit of waste, which would cause the firm to dump
only an efficient quantity of waste?
(c) What would be the quantity dumped if the firm did not care about the fishery?
(a) Set MD = MB and solve for Q*. Q* = 4.
(b) Insert 4 units into either MD or MB. Fee = 22.
(c) If the firm did not care about the fisheries, then they will discharge was as long as its
marginal benefit is greater than 0. Therefore, set MB equal to zero and solve for X. X = 34/3.
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