Suppose that Penn Products and Teller Industries are both emitting 30 metric tons of perfluorocarbons (PFCs) into the atmosphere. Regulators wish to reduce emissions to 40 metric tons overall, and plan to achieve this with a system of tradable permits. Penn's marginal abatement costs are given by MAC P= 5e P, where e Pis the number of metric tons of emissions that Penn is cutting. Thus, the cost of cleaning up the first metric ton is $5, the second ton costs $10 to clean up, and so on. Teller's marginal abatement costs are given by MAC T= 7.5e T, where e Tis the number of metric tons of emissions that Teller cuts.a. The lowest-cost way to reduce emissions is found when both firms' marginal abatement costs are equal-ized. Equate Penn's and Teller's marginal abatement costs, and solve for e Pin terms of eT.For each metric ton that Teller cuts, how many tons should Penn cut?

b. Because 20 metric tons are to be cut, we know that e P+ e T= 20. Use your answer for (a) to solve for e T. How many metric tons will Teller be responsible for cleaning up if the cleanup is done efficiently? How about Penn?

c. Calculate the cost of Teller's share of the cleanup. Do the same for Penn, and then compute the total cost of reducing PFC emissions by 20 metric tons.

d. Suppose that Teller cleans up one metric ton less, and Penn cleans up one more ton. Recompute the total cost of the cleanup to determine if the outcome you found in (c) was efficient. Then, double check your work by reversing the situation: Let Teller clean up one additional metric ton, and Penn one fewer ton.

e. If government regulators give Penn and Teller each their own twenty 1-ton pollution permits and allow them to trade, how many permits will end up trading hands, and what price will a permit sell for?