6. Externality Firm A and B each produces 80 units of pollution. The federal government wants to reduce pollution levels. The marginal costs associated with pollution reduction are MCA = 50 + 3QA for firm A and MCe = 80 + 3Qe for firm B, where QA and QB are the quantities of pollution reduced by each firm. Firms' marginal benefit of pollution reduction is 0. Society's marginal benefit from pollution reduction, i.e. marginal damage of pollution, is given by MB = 200. a. What is the socially optimal level of each firm's pollution reduction? How much total pollution is there in the social optimum?b. Explain why it is inefficient to give each rm an equal number of pollution permits [if they are not allowed to trade them]. c. Explain how the social optimum can he achieved if rms are given equal numbers of pollution permits but are allowed to trade them. Who sells and who buys permits and what is the price for the last unit of permit being traded? d. Can the social optimum be achieved using a tax on pollution? What tax level should we set? e. Now, aggregate individualsr marginal cost of pollution reduction and derive the social marginal cost [SHE] of pollution reduction (similar to aggregate individual supply curves]. Now suppose the social marginal benefit (SM B] oJrve aEso varies with pollution reduction. Specially SMB=29D Q-r, where Q-r is the total reduction in pollution. Now ignore firm heterogeneity, and calculate the social optimal level of pollution reduction. f. Graph the SMC, 5MB curves, and the social optimal level of pollution reduction, with cost or benet on the vertical axis and pollution reduction on the horizontal axis. Now suppose the government has a wrong estimation of the SMC of pollution reduction. For any given amount of pollution reduction, it overestimates the cost by 15 dollars. What 's the government's conceived social optimal level of pollution reduction? What is the Pigouvian tax based on the conceived information? g. If we set up quantity regulation at this conceived optimal level, what is the dead weight loss? If we set up Pigouvian tax based on this conceived optimal level, what is the deadweight loss? You can simply illustrate the answer using graph, without doing the detailed calculations