Elisha A. Pazner

Egalitarian Equivalent Allocations: A New Concept of Economic Equity

Foreword, 671. — I. Introduction, 671. — II. The concept of Pareto-efficient-egalitarian-equivalent-allocations (PEEEA), 674. — III. PEEEA as a fair arbitration scheme for allocations, 676. — IV. Maximin properties of PEEEA, 678. — V. PEEEA in economies with production, 680. — Mathematical appendices, 682.

A Difficulty in the Concept of Fairness

This note raises a new difficulty concerning the possibility of satisfying equity and Pareto efficiency objectives simultaneously. When interpersonal comparisons of utility are ruled out, which is the case considered here, there is no natural way to define the concept of equity. An appropriate criterion for equity discussed in the literature seems to be that of fairness. An allocation is said to be fair (equitable) if no individual in the society prefers the bundle allocated to anyone else over the bundle allocated to him (Dubins and Spanier [2], Foley [3] and Sen [5]). We present here two examples of economies in which no Pareto optimal allocation is fair, even in the absence of externalities, non convexities or other deviations from the classical Arrow-Debreu environment. In the first example there are two consumers, one consumption good and two kinds of labour (one for each consumer). The production possibilities of the economy are characterized by the constant returns to scale technology set {(x, y, z) E R3 I x ul(x,, 0, z1) for x1 >0 and (0, 0, z1 +x1), (0, Y2, z2) is also feasible. Similarly, Y2 0 is incompatible with Pareto optimality because u2(0, Y2+s, Z2-8/10)>U2(0, Y2, Z2) for any 0 u2(0, Y2, 0) as z1 > 1 _ Y2. We are left with the case of Y2 = 1 where any Pareto optimal allocation is of the form (0, 0, z1), (0, 1, z2) and Z +Z2 = 1. Noting that the definition of fairness means that each consumer evaluates the bundles of other consumers from his own point of view, the first individual will look at the bundle (0, 1, Z2) of the second as involving the consumption of one unit of leisure and Z2 units of the consumption good (i.e. as though it were (1, 0, Z2)). Therefore, in order for the allocations under consideration to be fair from the point of view of the first individual, it must be true that 1 Iz1/l0 ? 1 + 1 lz2/10. Similarly, fairness from the point of view of the second individual requires 1+ 2z2 > 2z1. These two inequalities are incompatible (as they imply 1/2+ z2 > z1 ? 10/Il +Z2). This completes our first counterexample. In our second example, in order to illustrate that the result does not depend on permuting commodities when applying the fairness criterion, utility is assumed to depend only on consumption goods. Leisure as such does not yield direct utility but as the consumption (as well as the production) process is time-consuming, leisure time is a necessary input to the welfare of consumers. There are now five commodities: time, two types of labour services and two different consumption goods. Along the lines of the previous example,

Competitive efficiency in an overlapping-generation model with endogenous population

A puzzling result regarding market failure was obtained by Samuelson (1958) in his exact consumption-loan model. He showed that under the conventional assumptions on the economic environment, the fact that ‘each and every today is followed by a tomorrow’ [e.g. Samuelson (1958, p. 482)] may lead competitive markets to fail in achieving the standard Paretoefficiency objective. As the standard sources for market failure (externalities and non-convexities) are absent from Samuelson’s model, it was natural to ‘blame’ the infinity of the time horizon as such for the resulting inefficiency.’ Our purpose in this paper is to show that if certain exogenous features of the Samuelsonian model are treated as being endogenously determined by economic factors, the above-mentioned inefficiency, with its associated puzzles, does not arise. More specifically, in the model presented below, population is an endogenous variable with parental preferences determining the number and ‘quality’ (in a utility sense) of children. Importantly, endowments of children are viewed to be bequeathed to them by parents. Under the assumptions of perfect capital markets and perfect foresight, it is shown that every competitive equilibrium is Pareto-efficient (under any appropriate definition of

Welfare criteria for tax reforms: Efficiency aspects

There are essentially two types of problems to which the normative theory of taxation addresses itself. One of these problems is that of designing de novo (i.e. from scratch) a tax system which is optimal in some appropriate welfare sense. The other major problem is that of finding conditions under which tax reforms, i.e. changes in an existing tax system, are welfareimproving. The efficiency aspects of the latter problem are the subject of this paper. There has been a considerable interest in the theory of tax reform in the last decade. In the earlier part of this decade, most studies of tax reforms concerned themselves primarily with the question of changing price distortions [e.g. Foster and Sonnenschein (1970), Bertrand and Vanek (1971) Kawamata (1974, 1977), Dixit (1975), Hatta (1977) and Rader (1976)]. A common drawback of these studies, however, is that the kind of tax changes analyzed by them rely on an implicit lump-sum tax-transfer mechanism. For instance, some consider the question of whether a reduction in tax rates (such as a radial decrease in distortions) improves welfare. Such a reduction will most likely decrease the tax revenues accruing to the government and hence some lump-sum tax will have to be introduced. Therefore, it is difficult to draw policy-relevant conclusions from these studies. More recently, there have been several studies [e.g. Guesnerie (1977), Diewert (1978), Dixit (1979) Harris (1979) and Weymark (1979)] which deal

Industry equilibrium under random demand

Abstract The paper deals with the characterization of long-run industry equilibrium under random demand, for the two polar cases of perfect competition and pure monopoly. Contrary to the basic theorem of welfare economics for the standard (deterministic) case, it is shown that perfect competition does not in general lead to an optimal (efficient) outcome. Perfect competition is optimal if and only if firms display risk-neutrality with respect to profits. Surprisingly enough, when risk preferences are non-neutral, one could by means of price regulation lead monopoly to behave optimally, whereas this is impossible for competition.

Reviews: Recent Thinking on Economic Justice

The exchange between economics and neighboring disciplines on the subject of distributive justice has been greatly facilitated by Phelps (1973) Economic Justice. To further this dialogue, I present here in a nontechnical manner some recent developments in the pure theory of economic equity. In light of space limitation, I confine this essay to a branch of the equity literature which has developed rapidly since the publication of Phelps’ collection. Thus, rather than surveying interesting developments that are taking place within the traditional approaches, I review in the next few pages what 1 believe to be an interesting new way to confront the problem of economic justice. Distributive justice has many dimensions. In particular, questions of procedural justice are ccrtainly no less relevant than those relating to the quest for an independent criterion for a just distribution. For the importance of this distinction, we are in debt both to RawIs’ A Theory of Jiistice and to Nozick’s treatment of distributive justice in Anarchy, State and Utopia. The present review, though, is confined primarily to recent attempts to define plausible end-state criteria for assessing the justice of a distribution of resources. Except for occasional remarks, procedural justice is ignored. .The reason for this lacuna is that while research efforts are currently addressed to questions of procedural justice as well, concrete results are yet to be obtained. It is to be hoped that in the not too distant future, interesting developments in this area will warrant a careful report. The plan of the article is this: In Section 1 some standard economic terms are briefly recalled. Section 2 reviews the recent economic theory of fairness. In Section 3 some further concepts of economic equity are discussed. Finally, Section 4 presents some clarifying comments of a policyoriented nature. A short Bibliographical Addendum concludes the article.