In the past few years, several economists, notably Duncan Foley, Hal Varian, E. A. Pazner and David Schmeidler, have produced a novel analytical theory of fairness in the distribution of resources, in contradistinction to the efficiency of their allocation. This work is primarily philosophical in orientation, being concerned primarily with the logical underpinnings of an analysis of fair division, rather than with its application. Here, I offer a nontechnical introduction to the subject, providing a few new results about the construction. But this is only a preliminary to an attempt to show how fairness theory can be used to study policy, employing the issue of rationing of commodities as an illustration. Persons who design public policy are, typically, at least as concerned with issues of equity as with allocative efficiency. The economist's influence is therefore impeded by his inability to deal with issues of fairness in applied problems. Fairness theory, perhaps for the first time, provides an analytic instrument for the purpose. Inevitably, it must, of course, rest upon value judgments as well as observable relationships. But what is remarkable about fairness theory is that both the behavioral relationships and the value judgments on which it is based are, essentially, those used in the standard welfare analysis of resource allocation. In both, the basic data are consumer preferences and production relationships, and in both the basic value judgment is that the desires of the affected individuals, rather than those of some superior arbitrator, must count. Our illustrative policy issue-the rationing of commodities-has reemerged with the fuel problem. Here, I will examine the choice between two points-rationing arrangements, under which consumers are each issued a fixed number of ration points, redeemable at a fixed Pg, per gallon of gasoline, or at another coupon price, P*h per gallon of heating oil, etc. The consumer is thereby subjected to a second budget constraint expressed in ration points rather than money. Economists have suggested that the efficiency of such a rationing system can be improved if it is accompanied by a market, in which consumers with unwanted ration coupons can sell them to others at a market-clearing (money) price. I will show that while there is a valid efficiency argument favoring the white market arrangement over one in which the sale of ration coupons is prohibited, fairness analysis yields a presumption that goes the other way. This may provide some justification for the apparently widespread suspicion of the fairness of white markets among noneconomists.

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.

There is no doubt that Michael Keren is right and that the point is important.1 In the initial discussion of my model, I simply misinterpreted the rising relative cost of the urban public services to nmean that it will beconme harder for society to provide them. As Keren shows, the rising productivity elsewhere in the economy that is the source of the increasing opportunitv cost of the services, also automatically nmeans that the conmmunity will be able mor-e easily, if it wishes, to pay for these services, despite their rising cost. The implications of Keren's point are worth spelling out. The basic argument of the original anal-sis still renmains valid: the financial problem of the cities increases (in part) because the costs of the services rise more rapidly than the general price level. This may well lead to cumulative deteriora

It is gratifying to be the author of a paper has led to comments of the quality printed here. Though I differ with a number of the viewpoints expressed, I think on most of them the reader is best left to judge for himself. There is only one issue on which I want to offer a few remarks. In my paper, I addressed myself to the analytic difficulty posed by the possibility the subjective time discount rate is well below the opportunity cost rate of resources drawn from the corporate sector, and remarked the choice of social discount rate becomes a matter of the theory of the second best. Dan Usher takes up the challenge and tackles the difficult task of an explicit second best analysis, and argues with its help that . . . under certain quite general assumptions, the appropriate interest rate on government projects lies between the rate of time preference and the rate of opportunity cost between present and future consumption in the private sector. David Ramsey, confining himself to the opportunity cost approach, in a world in which the returns to resources differ among sectors of the economy, concludes . . . the social discount rate is a weighted average of observable pre-tax market rates of return. It is, in effect, an average of the opportunity costs associated with each of the sources of funds utilized by a government project, each opportunity cost weighted by the proportion of these funds drawn from the corresponding source. This suggests t . . . public projects which draw resources from low risk, low taxed areas will yield a lower [discount rate] than if the resources were diverted from [other sectors]. Alan Nichols, on the other hand, takes a diametrically opposite view. He argues . . . the correct [social discount] rate . . . is categorically the [highest] of the pertinent opportunity costs. The argument is, apparently, if resources are being employed in two private uses R and S where they yield respective returns of r and s percent, then (if r> s) funds should not flow to a government project unless it too offers at least r percent, even if the funds are derived from S, for in case it would be better to transfer resources from S to R than from S to the government project. Obviously neither of the authors is wrong. Nichols is a perfectionist who will have no truck with second best solutions, while Ramsey will accept any transfers to the public sector provided they constitute improvements. In this imperfect world, my own inclinations lie with Ramsey-I would be unhappy to see opportunities for a better use of resources passed up in an unwillingness to compromise with ideals [1]. Finally, I cannot resist thanking Estelle James for calling to our attention and analyzing an aspect of the problem I had overlooked completely-the case where governmental and private outputs are substitutes. In case the issue, essentially, is not which collection of services should be produced, but who should provide them. And here, clearly, the relevant considerations are not the same as those I discussed.

Статья предназначена для читателей, занимающихся проблемами производства и распределения, но не имеющих значительной математической подготовки. Цель статьи - предоставить как минимум интуитивное понимание того, какое значение и применение в экономике имеют такие методы, как математическое и линейное программирование, анализ затраты-выпуск.