[The paper deals with a measure theoretic model of a pure exchange economy. There are two kinds of traders: "big" traders, represented by atoms of the measure space, and "small" traders, represented by the atomless part of the measure space. The restriction of an allocation to the atomless sector is called competitive if there exists a price vector such that the consumption of every "small" trader is a maximal element (in terms of his preference) in the budget set defined by that price vector and by his initial endowment. We consider the set of allocations that are not blocked by any atomless coalition, or by the complement of any atomless coalition, and call it the extlesstex-math extgreater$ extbackslashscr\I\ extasciicircum\2\ extbackslashtext\-core\$ extless/tex-math extgreater. The main results of the paper consist in defining sufficient conditions under which allocations in the extlesstex-math extgreater$ extbackslashscr\I\ extasciicircum\2\ extbackslashtext\-core\$ extless/tex-math extgreater have a competitive restriction to the atomless sector, and vice versa. The economic implications and significance of the results are briefly discussed.]
A summation social choice function is a social choice function whose choice sets are determinable from maximum sums of utilities that preserve individual preference. Assuming the set of alternatives is finite and individual preferences are irreflexive and transitive, a unanimity-type condition is shown to be necessary and sufficient for a social choice function to be a summation social choice function. The effects of conditions of voter independence, anonymity, and neutrality are noted.
[It was suggested in [2] that an appropriate model for an oligopolistic economy is one in which the set of traders consists of some large traders and a continuum of small traders. The cores of such market models are analyzed here. Some of the results are as follows: A duopolistic market in which the duopolists are of the same type is "perfectly competitive," i.e., its core coincides with the set of competitive allocations. At any allocation in the core of any oligopolistic markets, the value of the bundle received by a small trader does not exceed the value of his initial bundle; that is, small traders can never "gain money." Conditions are given under which small traders will not "lose money" either. In addition to the case of duopoly, other conditions are given under which an oligopolistic market will be perfectly competitive.]
[This paper simplifies and extends some previous work on domain restriction. With the help of an easy arithmetical result, two types of necessary and sufficient conditions are established for transitivity and quasi-transitivity under majority rule and transitivity under non-minority rule.]
In most empirical work, the investigator's understanding of the economic process under study is only minimally reflected in the econometric methodology. This paper suggests that in many cases, the construction of a small-scale simulation can prepare the data for regression in a manner which takes cognizance of the theory of the process. Regression is then used to scale the output of the simulation up to observed magnitudes of the variable to be predicted. The simulation has the function of exploring for the nature of the nonlinearities and interactions and thus replaces the usual search for a form which maximizes R2. The simulation may also be helpful where colinear data are a problem. An example is presented in which the effects of wages, unemployment rates, and labor turnover on poverty are studied through a prepared regression. IN THE LAST three decades, regression analysis has become the Procrustean bed into which all economic data are fitted. In the usual empirical paper by an economist, the obligatory theoretical discussion which precedes the description of the regressions generally contributes little more to the empirical methodology than an indication of which variables ought to be included in which equation, what the signs of the coefficients might be expected to be, and whether the regressions should be run in linear or logarithmic form. One reaction to this state of affairs has been the commencement of construction of large systems of microsimulation, notably one at the Urban Institute emphasizing demography and the distribution of income [6], one at the National Bureau of Economic Research on urban problems [4], and one at the University of Maryland featuring money flows [2]. While these big microsimulations are designed to describe the processes of the economy in a more natural way than can be done exclusively by usual regression methods, they tend to take years to build and tend to be unavailable to economists not involved in their building. It is possible, however, to occupy a middle ground between the regression runners and the large-model microsimulators. In many cases, improvement over the usual regression procedures can be gained by a combination of a very simple do-it-yourself simulation model with regression. The simulation model has the function of preparing the data for regression, in the sense of exploring for the nonlinearities and variable interactions inherent in the phenomenon under study. The regression, which uses the output of the simulation as an explanatory variable, has the function of scaling the simulation results up to observed magnitudes of the variable under study.
[The paper proves the asymptotic normality of a generalized least squares estimator utilizing estimated autocovariances of the residual in a regression equation having a residual following a mixed autoregressive, moving-average process. It also proves the asymptotic normality of the best linear unbiased estimator and shows that the two asymptotic distributions are the same.]
IT IS WELL KNOWN that for a finite exchange economy, where preferences are not assumed to be convex, there may be no price or even the core may be empty. For this reason it was proposed to enlarge the set of price and the core by introducing the concepts of equilibrium and core. The existence of approximate for exchange economies, where preferences are not assumed to be convex, has been investigated by R. Starr [6]. He showed that there exists a quasi-equilibrium, provided the number of participants is large enough and there is a bound on the degree of non-convexity [6, p. 30, Assumption D]. In this note we shall show the existence of equilibria (a stronger concept than the one considered by Starr [6, p. 31]) for large economies where the preferences are neither assumed to be convex nor complete. To obtain our result we shall assume that the preferences and the endowments of all participating agents belong to a compact set. In [5] Shapley and Shubik proved that, for a large replica of a given economy with transferable utility, the e-core is nonempty. We shall generalize this result to large economies without transferable utility by using the concept of ?-core as introduced by Kannai [2]. The nonemptiness of the e-core follows easily from the existence of approximate and a relationship between the set of approximate and e-core. The existence of c-core for large economies (with a fixed number of types) can also be deduced from Kannai's Theorem C' [2] in its stronger form (Theorem C in [3]).
We study the properties of the core of large markets. We assume that traders' preferences have certain standard properties, that their preferences belong to a set which is compact with respect to a certain topology, and that there is a bound on their initial endowments. It is then found that if a market contains sufficiently many traders and if there are many traders similar to any one trader, then every core allocation is similar to a price equilibrium in a very strong sense. This fact implies a precise formulation of the following statement: for most large markets, the core decomposes into disjoint clusters of allocations, the allocations in each cluster being very similar. This statement may be interpreted as an explanation of why traders in large markets normally feel that they have little bargaining power.
[The purpose of this paper is to investigate the relationship between the risk aversion function and the demand functions. Two hypotheses about risk aversion are studied: risk aversion independent of prices, and risk aversion constant on each indifference locus. The implications of these hypotheses for the utility and demand functions are then considered; in addition, the derivation of the risk aversion function from the demand functions is examined. The cases of constant (absolute and relative) risk aversion, and the problems raised by the choice of numéraire, are also dealt with.]
It has been conjectured that no system of can preclude strategic voting-the securing by a voter of an outcome he prefers through misrepresentation of his preferences. In this paper, for all significant systems of in which chance plays no role, the conjecture is verified. To prove the conjecture, a more general theorem in game theory is proved: a gameform is a game without utilities attached to outcomes; only a trivial game form, it is shown, can guarantee that whatever the utilities of the players may be, each player will have a dominant pure strategy. I SHALL PROVE in this paper that any non-dictatorial scheme with at least three possible outcomes is subject to individual manipulation. By a voting I mean any scheme which makes a community's choice depend entirely on individuals' professed preferences among the alternatives. An individual manipulates the scheme if, by misrepresenting his preferences, he secures an outcome he prefers to the outcome-the choice the community would make if he expressed his true preferences. The result on schemes follows from a theorem I shall prove which covers schemes of a more general kind. Let a gameform be any scheme which makes an outcome depend on individual actions of some specified sort, which I shall call strategies. A scheme, then, is a game form in which a strategy is a profession of preferences, but many game forms are not schemes. Call a strategy dominant for someone if, whatever anyone else does, it achieves his goals at least as well as would any alternative strategy. Only trivial game forms, I shall show, ensure that each individual, no matter what his preferences are, will have available a dominant strategy. Hence in particular, no non-trivial scheme guarantees that honest expression of preferences is a dominant strategy. These results are spelled out and proved in Section 3. The theorems in this paper should come as no surprise. It is well-known that many schemes in common use are subject to individual manipulation. Consider a rank-order scheme: each voter reports his preferences among the alternatives by ranking them on a ballot; first place on a ballot gives an alternative four votes, second place three, third place two, and fourth place one. The alternative with the greatest total number of votes wins. Here is a case in which an individual can manipulate the scheme. There are three voters and four alternatives; voter a ranks the alternatives in order xyzw on his ballot; voter b in order wxyz; and voter c's true preference ordering is wxyz. If c votes honestly, then, the winner is his second choice, x, with ten points. If c pretends that x is his last choice by giving his preference ordering as wyzx, then x gets only eight points, and c's first choice, w, wins with nine points. Thus c does best to misrepresent his