Suppose pollution is one-to-one directly related to output so we can treat q as pollution. There are two types of households, H and L, who differ based on how badly they are damaged by overall levels of pollution. Their marginal damage functions are: MDL(q)=(1/4)q MDH(q)=5+(1/4)q There are also two firms, F1 and F2, who differ based on their costs of abatement. Their marginal savings functions are: MS1(q) = 20-2q1 MS2(q) = 15-q2 In this scenario, the socially optimal output is q=10. a. Suppose local municipal codes give homeowners the right to clean air. Is the optimal amount of pollution 0? Discuss the likelihood that this society obtains the optimal level of pollution? Why would they or wouldn't they? Explain relevant issues thoroughly in this context. b. Suppose instead the city council requires each firm to reduce their output to 40 percent of their unregulated baseline output. Is this socially optimal? How much does each firm produce? c. If the city council decides to auction 10 permits total to firms, how many permits are purchased by each firm and what is the market price for permits? d. The revenue from auctioning permits can be used by the city to fund public projects. How does this affect the optimal level of permits issued? Can you tell whether there are too many, too few, or just the right number of permits? What does it depend on? Explain. e. Show the optimal level of pollution (ignoring part d) is 10.