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On Taxation and the Control of Externalities: Reply

American Economic Review 1974
I have no desire to take issue with either of the preceding comments, both of which clearly contribute significant insights on the subject. The Tietenberg comment is entirely apropos, arguing that when the damage caused by emissions varies geographically, a uniform tax rate will not minimize the social costs of achieving a preselected level of environmental quality. I certainly am guilty of some oversimplification on this matter. One of Earl Thompson and Ronald Batchelder's basic points is that where there is a small number of emitters of pollutants in a neighborhood, a case that occurs frequently in practice, the Pigouvian solution may require some modification. For the emitting hirm will then have a motivation to adjust its output of pollutants in a way that makes the tax rate more favorable, just as a monopolist benefits by adjusting his output to secure a more profitable price. I certainly cannot disagree with this conclusion. It is a bit misleading in one respect, however. In Pigou's writings, and in much of the subsequent literature, it seemns quite clear to me that the assumption of pure competition is taken to mean that both prices and tax rates are beyond the influence of the individual firm. Strictly speaking, of course, a firm selling its product in a national market that is perfectly competitive may be the only polluter in its neighborhood. But surely all of us would readily have admitted that competitive solutions, including Pigou's externalities prescription, break down when the firm can influence any of its prices, including the tax it pays on its emissions. I prefer, therefore, to take the ThompsonBatchelder discussion of this point not as a criticism of received doctrine -which is the way they apparently want to view it-but as an illuminating examination of the case in which the firm can influence the tax rate. Their second major point is that the Pigouvian solution may work better than I suggest in cases where there are several local maxima. They argue that the appropriate measure of marginal social damage and thus, of Pigouvian tax at some local maximum point, is not the cost an additional puff of smoke would then impose (ceteris paribus) on nearby laundries, but the opportunity loss as against what it would do if the economy were really at the global optimum.1 For in that case at an inferior local optimum the polluters would still find an inducement in the tax to move toward the global optimum. Perhaps their definition of social damage as opportunity cost will be judged to be stretching the Pigouvian concept. Certainly it is not what emerges from the KuhnTucker conditions whose values are strictly local, and whose shadow prices will lead only to the local maximum. Finally, one protest. Thompson and Batchelder attribute to me a special Pigouvian for the multiple maximum case, but I assure the reader that I do not now nor have I ever advocated any such measure. For I certainly agree with them that there is no known tax rule that survives all forms of nonconvexitv.