Knowledge that Transforms

Abstract : Given any problem of decision under risk to which the expected utility hypothesis applies, one may associate to it first a riskless problem in which random disturbances are replaced by their expected values, and second a class of intermediate risky problems with decreasing degrees of uncertainty. In this class the optimal decision depends in principle on the degree of uncertainty but turns out to be independent of it, to the first order of approximation, in the neighborhood of the riskless problem. The first-order certainty equivalence explains why it is so difficult to characterize the situations in which an increase in the degree of uncertainty requires a decrease in the allocation of resources to the risky projects. (Author)

Abstract : It is shown that a market with a continuum of traders possesses a competitive equilibrium even when the preferences are not complete. This generalizes further a result of Aumann, ('Econometrica'; 32: 39-50 (1964); 34: 1-17(1966)) who showed that the convexity assumption may be dispensed within the presence of a continuum of traders. The proof is inspired by the Arrow-Debreu ('Econometrica; 22: 265-290(1954)) proof for the finite case. (Author)

So far we have several conditions for consistency in the simple majority decision rule. These conditions assume that some preference orderings are not in the list of the possible individual orderings and each individual is free to choose any ordering in this list. When the list of the possible individual orderings is too wide, inconsistency may arise. But when the list is selected from a group of narrower ones, inconsistency never arises, no matter how each individual selects his own preference ordering in the list. The purpose of this paper is to give the complete catalogue of such lists. Our catalogue, of course, includes the conditions so far obtained. But it also includes some new conditions.

In this paper we estimate a complete system of demand equations making full use of the restrictions implied by economic theory. Our theoretical model is based on the Klein-Rubin linear expenditure system which was first estimated by Stone. We place primary emphasis on maximum likelihood estimates obtained using annual time series observations of prices and per capita consumption for the U.S. economy in the period 1948-1965. The plan of the paper is as follows: Section 1 begins with a discussion of the problems involved in making systematic use of economic theory to estimate demand functions; this is followed by a brief description of the linear expenditure system and discussion of the specification of its dynamic and stochastic structure. In Section 2 we describe three methods of estimating the linear expenditure system, including the maximum likelihood procedure which we believe is most appropriate. We report our results in Section 3 and our conclusions in Section 4. 1 A. INTRODUCTION The pure theory of consumer behavior is concerned with individual demand functions. An individual's preferences are assumed to be representable by a well behaved utility function, U(x1, .. . , x), where xi denotes the rate of consumption of the ith good. He is supposed to maximize U subject to the budget constraint n (1) E PkXk =I k = 1

This paper discusses recent work on the existence of aggregate production functions in models in which capital goods are specific to firms and cannot be used interchangeably. It is found that this raises problems not only for capital aggregation but also for the existence of labor and output aggregates. Recent work on the question of using aggregate production functions as approximations is also discussed.