3. (This question is a variation and continuation of question #4 from Homework #2.} Consider two rms {i.e., rms 1 (EL 2) with heterogeneous marginal abatement cost functions: MAC] = s - 2E1 Balm?2 = 5 E2. Assume the marginal external damages from emissions are: MED = 13.51? A . where EA is the sum of the two rms' emissions. a. What quantity of emissions do rms produce in the absence of government intervention? What are the total external damages? What are the total abatement costs? b. Derive the aggregate marginal abatement cost function (Hint: This will be a kinked function. From the MAC functions you should be able to determine the kink point. Then invert the MAC functions to solve for the emissions functions. Finally, sum up emissions conditional on different MAC levels). c. What is the socially efcient level of emissions? How much do each of the rms emit at the socially efficient level? How much does each of the rms abate relative to their market equilibrium? d. Assume the government uses a tradable permits program to achieve the social optimum. What quantity,r of emissions permits should the government allocate? If the government allocated the permits equally among rms (i.e.. if there are X total emissions permits. lX are given to rm 1 and lX are given to rm 2). which rm will sell some of its permits to the other? How many? How much revenue will it receive in return? e. Assume the government uses an emissions tax to achieve the social optimum. At what level should this tax be set? How much revenue will the tax generate? f. Assume the government uses an abatement subsidy to achieve the social optimum. At what level should the subsidy be set? How much will the subsidy cost the government