Part VI. The Demand for Pollution We will use setups like the following to illustrate the benefits of market based mechanisms. In this setup, firms have a constant marginal cost of abatement, but there is a limit on their abatement quantity. (For example, a firm has some pollution itself, and it can clean that pollution up, but it can't clean up someone else's pollution.) A cost effective allocation of abatement thus requires that we use up all the capacity for abatement among the lowest cost firms, before moving on to the next tier of cost. In a situation like this, the equimarginal princi- ple won't hold in a literal sense, because we don't have a continuous cost function that can be set equal. Consider a market with 50 firms who act as price takers in all markets. Each firm is producing some good, and its activity produces 10 units of pollution. For the purposes of this problem, assume that the firm cannot change its production activity, but it has a mechanism by which to directly abate its own emissions, at a total cost of C(a,) = Bra, where 8, is a con- stant for each firm. Ten firms have 8, = 1. Ten other firms have A, = 8. Ten other firms have A, = 9. The remaining twenty firms have Be = 20. After abatement, net emissions for each firm are e; = 10-a, where er can- not go below zero (i.e., each firm can abate a maximum of 10 units). 20. Extension questions: Design a table that indicates for ranges of possible tax rates the amount of abatement that would occur, and the amount of pollution. The table should have three rows: the tax rate range (i.e., $0 to $0.99), abatement quantity (total for the market), and pollution quantity (total for the market). (2 points) 5(Hintote: in this setup, if a tax is exactly equal to a firm's marginal cost of abatement, the amount of abatement that they will do is undetermined. Any quantity between 0 and 10 would be consistent with profit maximize- tion, because abatement and the tax cost the firm the same amount. So, in the table, you can just ignore those exact values, but in the graph, you should think about the best way to draw the quantity-price relationship given this reality.) 21. Use this table to draw the demand for pollution, labeling the x- and y-intercept and all relevant values. (3 points) (Hint/ explanation: a pollution tax would put a price on pollution. What we mean by the "demand for pollution" is how much pollution these firms would "buy" from the government (by paying a tax) for any potential price. So, your answer should have price on the y-axis (or tax rate) and quantity on the x-axis, and it should trace out how much pollution the firms would "buy" for each price. To do this, realize that each firm will ei- ther buy none (instead abating all their emissions) or buy all the pollution they need (10 units per firm), except for those exact value cases. Try to think about what each firm will do and then build up the demand curve from there. Conceptually, remember that a demand curve is the marginal benefit curve, and here the marginal benefit of pollution to a firm is the fact that they don't have to pay the cost of abatement.) 22. Extension questions: Suppose the marginal damages from pollution are equal to $9 per unit of pollution. What is the efficient quantity of pollution? What is the efficient quantity of abatement? (2 points)