8. In the town of Springfield, there are two large firms that emit sulfur dioxide to the environment. The two firms have different abatement cost functions. Their corresponding Marginal Savings functions (which correspond to the marginal savings of not abating each emission unit) are given by: MS_A(S_A) = 30 - S_A and MS_B(S_B) = 30-2S_B, where S_A is the level of emissions produced by firm A and S_A is the level of emissions produced by firm B. The inhabitants of Springfield suffer respiratory illness caused by sulfur dioxide present in the environment. Their aggregate marginal damage function from sulfur dioxide emissions is given by MD(S) = (7/12)S, where S=S_A+S_B. a. What is the efficient level of emissions? b. What is the aggregate surplus implied by the efficient level? c. The local government is considering to institute a tax on emissions. What should the tax per unit of emissions be in order to achieve an efficient level of emissions? d. What is the level of emissions of firm A with the tax you found in (c)? e. What is the aggregate level of emissions with the tax you found in (c)? f. What is the after-tax surplus for each of the two firms? g. What is the total damage with the tax? h. Add both firms' after-tax surplus, the taxes paid to the government and subtract the total damage to find the aggregate surplus with the tax regulation. How does this compare to your answer to (b)?