Extensive research has produced monetary measures of total benefits and total costs of pollution abatement for a pollutant. In particular, if X measures pollution abatement (in thousands of tons), total benefits (in millions of dollars per year) can be approximated by the following relationship: B(X) = 60X - 3X2, while the total abatement costs (in millions of dollars per year) are B(X) = 20X - X2 estimated to be: C(X) = 10X + 2x2 C(X) = 4X+X2 1 (3 points) For pollution abatement X varying from 0 to 10 (thousand tons), in increments of 1, compute total social benefits and total social costs of abatement (suggestion: use a spreadsheet). 2 (2 points) Produce a graph depicting X on the horizontal axis and the benefits and costs of abatement on the vertical axis (you can connect the points you found above by straight line segments). 3 (5 points) Find a level of abatement which maximizes the net social benefit, and justify your answer. What is the maximum net social benefit? 4 (3 points) Given these total abatement benefit and cost relationships, marginal benefit is given by MB(X) = 60 - 6X, and marginal abatement cost is given by MC(X) = 10 + 4X. Use the equimarginal principle to find the optimal level of abatement. 5 (2 points) Graph MB(X) and MC(X) and find the total benefit and total abatement cost using the marginal benefits and marginal costs curves. 6 (3 points) A health watchdog group conducts another study and finds that the total benefits of pollution abatement can be more accurately described by B(X) = 80X - 3X B(X) = 28X _ x2. What is the new optimal level of pollution abatement? Is this result intuitive (why or why not)? 7 (2 points) An industry group reassesses the costs of pollution abatement and finds that abatement costs are in fact higher, and are more accurately described by C(X) = 20X + 2X2 (an independent study confirms this to be accurate). Using the C(X) = 8X + X2 information on benefits from 3.6, what level of pollution abatement should the society choose now? Is the optimal level of pollution abatement greater or smaller than in 3.6? Provide an explanation for the change