Knowledge that Transforms

THE ARROW-PRATT MEASURES of risk aversion for von Neumann-Morgenstern utility functions have become workhorses for analyzing problems in the microeconomics of uncertainty. They have been used to characterize the qualitative properties of demand in insurance and asset markets, to examine the properties of risk taking in taxation models, and to study the interaction between risk and life-cycle savings problems to name just a few applications. Equally importantly, they have generated the linear risk tolerance class of utility functions which has provided canonical examples in such diverse areas as portfolio theory and the theory of teams. Despite these successes, there have been a number of areas for which the results have been weaker than hoped. It is natural to use the risk aversion measures to compare the behavior of individuals in risky choice situations. For example, consider the individual portfolio choice problem in a two asset world with a riskless asset and a risky asset. If individual A has a uniformly higher Arrow-Pratt coefficient of risk aversion than individual B, then B will always choose a portfolio combination with more wealth invested in the risky asset. But, suppose that both assets are risky. Now, there is no obvious sense in which the more risk averse individual can be said to hold a less risky portfolio, but it seems strange that such a simple alteration should destroy the analytics which support the basic intuition. Similarly, consider the basic insurance problem. If one individual, A, is more risk averse than another, B, in the Arrow-Pratt sense, it follows that A will pay a larger premium to insure against a random loss than will B. Typically, though, an individual evaluates partial rather than total insurance, that is, only some gambles can be insured against and others must be retained. In this case, even when the gambles which are retained are independent from those which are insured, it is no longer true that the individual whose Arrow-Pratt measure of risk aversion is higher will pay a larger insurance premium. The situation is no better when we consider comparative statics exercises for a single individual. Decreasing absolute risk aversion in the sense of Arrow and

This paper presents a model of myopic tastes, both in the context of intertemporal decision making and choice under uncertainty. Infinite dimensional consumption plans arise naturally in both contexts, either involving a denumerable number of periods or a countable number of states of the world. The essential feature of our model is that myopic behavior is formalized by defining topologies, on the space of consumption plans, which discount the future or improbable events.

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Two theorems are derived about social choice functions, which are defined on comprehensive convex subsets of utility allocation space. Theorem 1 asserts that a linearity condition, together with Pareto optimality, implies that a social choice function must be utilitarian. Theorem 2 asserts that a concavity condition, together with Pareto optimality and independence of irrelevant alternatives, implies that a social choice function must be either utilitarian or egalitarian. These linearity and concavity conditions have natural interpretations in terms of the timing of social welfare analysis (before or after the resolution of uncertainties) and its impact on social choices.

[Recent advances in optimal mechanism design are used to show that a certain type of auction, similar to the "open English auction," is an optimal mechanism in a certain class of environments.]

[This paper investigates the implications for asset price dispersion of conventional security valuation models. Successively sharper variance bounds on asset prices are derived. Large-sample tests of the bounds are determined and applied to aggregated and disaggregated price and earnings data of U.S. corporations.]

This paper presents the classical theorem on the existence of equilibrium as it was proved in the 1950's with the various improvements that have been made since then.In particular, the elimination of the survival assumption and of the requirement of transitive preferences are carried through with a proof that uses a mapping of social demand.This approach favors intuitive understanding and generalization of the results.Finally, the role of the firm and the introduction of external economies are critically viewed. MYPURPOSE IS TO DISCUSS the present status of the classical theorem on existence of competitive equilibrium that was proved in various guises in the 1950's by Arrow and Debreu [1], Debreu [5, 6], Gale [8], Kuhn [14], McKenzie [17, 18, 19], and Nikaido [22].The earliest papers were those of Arrow and Debreu, and McKenzie, both of which were presented to the Econometric Society at its Chicago meeting in December, 1952.They were written independently.The paper of Nikaido was also written independently of the other papers but delayed in publication.The major predecessors of the papers of the fifties were the papers of Abraham Wald [31, 32] and John von Neumann [30], all of which were delivered to Karl Menger's Colloquium in Vienna during the 1930's.The paper of von Neumann was not concerned with competitive equilibrium in the classical sense but with a program of maximal balanced growth in a closed production model.However, he first used a fixed point theorem for an existence argument in economics and provided the generalization of the Brouwer theorem that was the major mathematical tool in the classical proofs.Wald achieved the first success with the general problem of the existence of a meaningful solution to the Walrasian system of equations.The proofs which were published used an assumption that later became known as the Weak Axiom of Revealed Preference.This axiom virtually reduces the set of consumers to one person, since it is equivalent to consistent choices under budget constraints.In a one consumer economy the existence of the equilibrium becomes a simple maximum problem and advanced methods are not needed.When many consumers with independent preference orders are present, it has been shown (Uzawa [29]) that fixed point methods are necessary.Wald also wrote a third paper whose main theorem was announced in a summary article [33], but which never reached

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