About 45 million tons of NOz, a pollutant, are emitted annually in the US by automobiles and electric power plants. The marginal costs of abatement are 0.5Qe for powerplants, where Qe is the amount of NOz in millions of tons abated by powerplants; and 4.5 + 0.1Qa , where Qa is the amount of NOz in millions of tons abated by automobiles.
(a) What are the formulas for the total cost of abatement by powerplants and by automobiles? (Hint: see the formulas given on page 37 of the lecture on Cost Minimization and Conditional Input Demand Functions)
(b) Congress passes legislation requiring that annual emissions of NOz from power plants and automobiles be reduced by a total of 15 million tons. If the goal is to minimize the cost of meeting this target, how much abatement should be undertaken by power plants and how much by automobiles? Explain the rule that generates this answer.
(c) What is the annual total cost of the emission abatement in part (b)?
(d) Following lobbying by the automobile companies, Congress instead decides only to regulate NOz from power plants, and not from automobiles. It requires power plants to reduce their emissions NOz by 15 million tons annually. What is the total cost of emission abatement in this case? How does it differ from the total cost computed in (c), and why?
(e) Following a report by the President's Council of Economic Advisers, Congress is persuaded to introduce an emissions tax intended to reduce NOz from power plants and automobiles by a total of 15 million tons annually. What is the amount of the tax per ton of NOz emissions that it should set? Explain your answer.