\\-" f""" "" "'-""" -"' 'v J v\" " '- \""""" "' -' """ """ "' "" "'"""' '" ""'"' " """""'r"';'l B.* Consider the same setup as in part B of exercise 21.9. In the previous case where we derived the mar- ket equilibrium, we said that in a model with many rms it was reasonable to model each individual rm as not taking its own impact of pollution into account and to simply model the cost function as c(x) = [312 + 6N} (where the latter entered as a fixed cost). a. Now consider the cost function that benevolent Barney would use for each firm: From the social planner's perspective, the firm's variable costs (captured by 3x2) would still matter, as would the xed cost from pollution (captured by SM? where f is the amount produced by each rm and N is the number of rms in the industry). But Barney also cares about the follow- ing: each unit of x produced by rm i causes an increase in costs of 8 for each of the N rms, which implies that the pollution cost Barney would consider rm i as imposing on society is 6Nx. This implies that Bamey's cost function for each firm is c3(x) = 3x2 + 6N} + 8Nx. Derive from this the marginal and average cost functions that Barney would use for each rm (being sure to not treat the last term as a fixed cost). Repeat parts (c) through (i) from exercise 21.9 using the cost functions Barney would use for each rm to arrive at N*, p*, and X*. Compare your answers to those from exercise 21.9. How do they differ? Suppose, as in part (j) of exercise 21.9, that B = l, 5 = 0.1, and A = 10,580. What are X*, p*, and N*? How much does each individual rm produce? Compare these to your answers in exercise 21.9. Can you give an intuitive explanation for why these answers differ despite the fact that pollution only affects the rms in the industry? What is the Pigouvian tax that is required in order for competitive rms to implement the equi- librium you just calculated in (d)? What price does this imply consumers would pay and what price does it imply producers would receive? Verify that your Pigouvian tax in fact results in prices for consumers and the industry that lead them to demand and supply the output level you calculated in part ((1). (Note: You will need to refer back to your answers to exercise 21.9 to do this part.)