IN THIS PAPER we show that application of the traditional theory of the true cost of living index to Lancaster's new approach to consumer theory (cf. [6 and 7]), i.e., to shadow prices of characteristics rather than to ordinary prices of goods, opens a possibility for a convenient treatment of quality changes and of the introduction of new goods. Section 2 is a statement of the relevant properties of Lancaster's model. In Section 3 this model is used to derive a cost of living index, which is not only price compensating but also quality compensating. However, the Laspeyres index which corresponds to this true index and which in principle might be observable, is not always an upper bound on this true index. In this section the relationship to the hedonic price index is also noted. Section 4 contains some concluding remarks.2
[A choice function is defined to exist if there is a "best" (under a binary relation R) element in all non-empty compact subsets of S, the set of all possible alternatives, whereas a demand correspondence exists if there is a "best" element in only the budget sets of S. Some basic restrictions on R are considered. First, if the "at least as good as" sets are closed, then none of the standard restrictions on R are shown to be necessary for the existence of a demand correspondence: the "domination" of finite sets is necessary and sufficient. This is shown to imply that acyclicity of R is necessary and sufficient for the existence of choice functions. Second, if either there is a restriction on convergent P monotone sequences or if R satisfies a regularity condition, then a condition on cyclical sets of alternatives is enough to guarantee the existence of demand correspondences. For the existence of rational choice functions, however, reflexivity, completeness, and transitivity of R, together with the above-mentioned condition on P-monotone sequences, are necessary and sufficient. Finally, if the strictly preferred sets are taken to be convex, then under a restriction weaker than the first, a best element in budget sets exists.]
SAMUELSON MADE THE CONJECTURE stated above in his 1967 paper [7]. He also formalized there the axiom of independence of irrelevant alternatives for cardinal preferences, used here. Preference are cardinal if their representation by a numerical function is invariant under, and only under, positive linear transformations. One may think that the disregard for intensity of preferences, embedded in Arrow's treatment of profiles of ordinal rankings of alternatives, leads to the impossibility result. Samuelson's conjecture points out that this is not the way to refute the conclusions of Arrow's theorem. There is also interest per se in aggregation of cardinal preferences. Such preferences are usually considered as von Neumann-Morgenstern utility, i.e., numerical representation of preferences over lotteries [11]. Since uncertainty is the rule and not the exception whenever decisions are involved, it is of some importance to obtain a social N-M utility over risky outcomes. Given such a utility, the society will be able to choose a best alternative among the several feasible risky actions (i.e., lotteries). However it is not necessary to restrict the interpretation of cardinal preferences to those induced by ordinal ranking over lotteries. One can think of cardinal preferences derived from comparisons between pairs of alternatives (as in an axiomatization of a regret relation). See Alt [1] for an early work of this kind. When working with cardinal preferences a continuity assumption is needed, in addition to unanimity and independence (see the example at the end of the next section). A standard reference for Arrow's theorem is the last chapter of his book [2]. For a general discussion of aggregation of cardinal preferences, see ShapleyShubik [10]. Some other impossibility results involving different notions of cardinal preferences appear in the works of Sen [9], DeMeyer-Plott [4], Schwartz [8], and Fishburn [5]. A model dealing with aggregation of cardinal preferences into social cardinal prefereiLces, as here, is that of Harsanyi [6]. However he is interested in 1 The work of the first author was done at Northwestern University and the work of the second author began at the University of Illinois in Urbana-Champaign and it was completed at the University of Minnesota in Minneapolis. Both authors are on leave from Tel-Aviv University. The authors wish to express their thanks to E. A. Pazner, M. A. Satterthwaite, J. Kelly and the referees for helpful comments. This research was partly supported by NSF Grant # SOC-75-05317.
A wide variety of economic models include as explanatory variables either expectational variables or variables representing the result of some decision-making process. The first category includes both expectations about the future values of variables, e.g., next period's sales, the level of unemployment two quarters ahead, etc. and other subjective variables such as permanent income or the "normal" level of prices and interest rates. Examples of the second type are "desired" capital stock, planned production, or inventory accumulation, and so on.
is misleading if o-2 $ o-2 and n, and n2 are both small, where Y, and Xi are ni x 1 and ni x k observation matrices, ,li is a k x 1 coefficient matrix, and ei is an n, x 1 error matrix for i=1,2. A valid asymptotic test may easily be obtained by regarding (1) and (2) as seemingly unrelated regression equations. In this paper we establish a small sample test which may readily be extended to a test of some of the coefficients in the two regressions.
Recent developments in social theory are critically surveyed in the light of a categorization of interpersonal aggregation problems into four distinct types that seem to require varying treatment but typically do not receive it. Informational inadequacy of the usual social framework is discussed in this context. A fairly thorough exploration of the correspondences between consistency conditions for functions and regularity properties of the binary relation of preference leads to a re-examination of the class of impossibility results in social theory, necessitating reinterpretations of various theorems (including Arrow's). SOCIAL CHOICE THEORY is concerned with relationships between individuals' preferences and social choice (Fishburn (1973, p. 3)). But a great many problems fit this general description and they can be classified into types that are fundamentally different from each other. It can be argued that some of the difficulties in the general theory of social arise from a desire to fit essentially different classes of group aggregation problems into one uniform framework and from seeking excessive generality. An alternative is to classify these problems into a number of categories and to investigate the appropriate structure for each category. In a small way, this is what will be done in this paper, and some of the recent developments in the theory of social will be examined in that light.
[This paper proposes a simple and straightforward method of finding a consistent and efficient set of sectoral capacity growth rates and output and investment levels in a dynamic input-output (IO) model with given production capacities at a certain "base period" of time and given consumption targets for a later "terminal period." The basic problem is that terminal capacities have to be consistent with terminal production requirements as given by the consumption targets, intermediate input requirements, and investment, where both the latter are treated endogenously. The basis for endogenous investment is (a) the assumption that the planning period as a whole is characterized by a set of constant sectoral growth rates and (b) the assumption that investment does not create any excess capacity. These two assumptions form the core of the notions of consistency and efficiency respectively. The method proposed is an integrated iterative procedure with endogenous revision of the division of sectors between those operating at full capacity (bottleneck) and the rest, output and investment levels, and rates of growth. The method is, in fact, a straightforward adaptation of the standard method of solving an IO model by power series expansion. The paper also discusses the method of target revision taken in conjunction with prior bounds on growth rates and certain aspects of the relation between investment and technology in the frame of the model proposed. It ends with a brief review of the literature, criticizing, in particular, the methods and approaches followed in a large number of applied planning models to tackle the set of issues discussed.]
[A kernel of a set of alternative actions over which there is a partial order is defined in terms of optimality properties. It is shown to be the same as the generalized efficient set. A variety of theorems such as uniqueness, existence, and composition in terms of other sets are established. Related sets, such as quasi kernels and weak kernels, are also considered.]
Michael J. Hartley, Parthasaradhi Mallela, The Asymptotic Properties of a Maximum Likelihood Estimator for a Model of Markets in Disequilibrium, Econometrica, Vol. 45, No. 5 (Jul., 1977), pp. 1205-1220