Inverse demand in the polluting sector is p = 20 -3q, private average = marginal cost is C = 2 in that sector, and environmental damage per unit of output is 6. In Scenario A the government is able to raise revenue using non-distortionary taxes outside the polluting sector (e.g. by means of a lump-sum tax). In Scenario B, taxes outside the polluting sector are distortionary; every $1 of tax revenue creates an aggregate loss to consumers and producers of $1.10. (a) Given the assumptions in the previous paragraph, and using the concepts developed in this chapter, describe (without math) the social incentives to tax production in the two scenarios, and explain how these differing incentives affect the relative magnitudes of the tax in the polluting sector in the two scenarios. (b) Find the optimal tax for a competitive industry in Scenario A and in Scenario B. Scenario A should be familiar, but Scenario B is a bit different. For this scenario, proceed as follows. (i) Find the level of production, under competition, as a function of an arbitrary tax; denote this function as q (v). (ii) Recall that consumer surplus equals the area below the inverse demand function, above the price. Given the tax r, the price is 6 + v and the quantity sold is q (v) (from part (i)). Use the formula for the area of a triangle to compute consumer surplus. (iii) The tax revenue is v x q, and you are told that the social value of the tax revenue is 1.ly x q. (iv) Find the expression for environmental damage, using part (i). (v) Social surplus, S (v), equals consumer surplus minus environmental damage plus the social value of tax revenue. (For this problem, where marginal cost is constant, producer surplus is always zero.) Using the previous steps, write the expression for social welfare, and maximize it with respect to v. Check that the S (v) is concave, so the first order condition gives a maximum, not a minimum