Suppose there are two power plants that release sulfur dioxide (SO2) into air at theircurrent production levels. Each firm currently emits 75 tons per year, thus emitting150 tons total. Local authorities have decided they would like to reduce annual SO2pollution to 100 tons per year (thus a 50 ton reduction).The power plants have different marginal abatement costs given by the following equa-tions: MAC1 =4A1 MAC2 =A2
(a) Derive the total abatement cost functions for each firm. (I. e. find T AC1 and T AC2for any level of A1, A2).
(b) Suppose the local authorities decide to impose a uniform reduction of pollution by both power plants. In order to achieve the 20 unit reduction under this plan, both plants must reduce their emissions (abate pollution) by 10 units each. Find the total cost of abatement under this uniform reduction policy.
(c) Find the efficient abatement amount for each power plant if you wanted to achieve the 20 unit reduction at the most cost-efficient way possible (i. e. find the A1 andA2 that achieves the 20 unit reduction in the cheapest way). What is the total cost of reducing pollution under this plan? How much must each plant pay?
(d) Now suppose the local authorities wanted to achieve this 20 ton reduction in annual SO2 via a pollution tax. This tax is the same for for both power plants and must be paid by each plant for every ton of SO2 emitted annually. Find the optimal tax per ton of SO2. How much does each plant pay in taxes? What is the total cost for each plant from this policy (cost of tax payment and total abatement costs). Which power plant pays more?