Showing papers on "Ambiguity aversion published in 1977"

Risk aversion and consumer preferences

Abstract: The first part of this article integrates the concept of (relative) risk aversion with respect to income (r) with the static analysis of demand for many commodities Alternative representations of preferences and demand functions, using duality, give rise to many alternative representations and interpretations of r, and to theorems regarding attitudes towards risk in bundles of quantities and in prices In the second part, a previous analysis by Deschamps is corrected and completed by specifying the general form of preferences and demands such that r is a function of the utility level only, independent of relative prices Finally, preferences and demand functions associated with constant r (previously analyzed by Stiglitz and Deschamps) are specified more explicitly and completely A general conclusion emerging is that demand behavior under certainty can hardly throw any light on the nature of attitudes towards risk THE CONCEPT OF THE relative risk aversion function as a unit-free measure of individual aversion to income risk under expected utility maximization, was defined by Arrow [1] and Pratt [15], and has proved useful in various applications Stiglitz [21] studied relations between an individual's aversion to income risk, and his indirect utility and demand functions for many commodities, obtained under certainty in competitive markets In particular, he analyzed the cases of risk indifference and constant relative risk aversion (r) Deschamps [4] extended this analysis to study implications of alternative assumptions: (i) That absolute risk aversion R = rly is independent of prices, nominal or relative, for given income This is equivalent, however, to constant r (which is the case analyzed by Stiglitz) for both cases (ii) That R or r are constant on each indifference surface This is shown to be impossible for R, but meaningful and interesting for r = r(u) Unfortunately, however, Deschamps could not show the utility and demand functions for this case, and conducted an indirect analysis based on the second-order differential equation implied, failing to note that any such r(u) is compatible with homothetic preferences In addition, his analysis contains errors (eg, the case r = 1 constant) and may be subject to misleading interpretations The purpose of this article is twofold: (i) To complete the analysis of risk aversion with many commodities, by using various alternative formulations of the relative risk aversion function to study general relations between income risk aversion and attitudes towards risk with respect to quantities (eg, when both relative prices and income are subject to risk), or with respect to prices (ii) To complete the analysis of Deschamps by showing the general forms of utility and demand functions when r = r(u), and to correct some errors of analysis and interpretation

A Note on Risk Aversion and Indifference Curves

Abstract: In his recent paper in this Journal, Miller [3] proposed, following Adler's results [1], that “the investor exhibits decreasing absolute risk aversion with respect to expected wealth if, as increased holding σ constant, the slope of the indifference loci decreases” [3, p. 301]. He further attempted to have shown that in general the sign of () is the same as the sign of r'(W) (the derivative of the absolute risk aversion measure), but this is not proved.