Background risk in generalized expected utility theory

Summary. In this paper, it is shown that, for a wide range of risk-averse generalized expected utility preferences, independent risks are complementary, contrary to the results for expected utility preferences satisfying conditions such as proper and standard risk aversion. Received: August 10, 2001; revised version: June 18, 2002 RID="*" ID="*"I thank Simon Grant and an anonymous referee for helpful comments and criticism. This research was supported by an Australian Research Council Senior Fellowship and Australian Research Council Large Grant A79800678.     

Co-monotonicity: Toward a utility function capturing envy

Envy affects economic decisions, and can lead to monotonicity violation. We introduce co-monotonicity—a generalization of monotonicity, expected to hold even in the presence of envy. Experimental results and implications for the form of possible utility functions are discussed.     

A method for constructing an intertemporal utility function from a Friedmanian consumption function

It is shown that the intertemporal utility function can be reconstructed from data on demands if they are restricted to be linear in wealth, or Friedmanian.     

Measuring sustainability performance for China: A sequential generalized directional distance function approach

This paper aims to present certain composite sustainability efficiency indicators for China based on a sequential generalized directional distance function. This approach can measure the sustainability performance of a country with diverse outputs, nature of technologies, and non-radial slacks. First, we propose the concept of a generalized directional distance function under a sequential environmental production technology. Second, we develop several standardized composite indicators related to sustainability performance. We then estimate the sequential generalized directional distance function based on a series of sequential data envelopment analysis models. Finally, we empirically examine regions in China using the proposed model and present some implications based on the empirical results.     

A nested CES-type utility function and its demand and price-index functions

The nested CES-type utility function is introduced in this paper: it consists of an N-level utility tree of slightly modified CES-type functions. Attractive price- and quantity-indices are developed and an elegant system of demand functions, specified in terms of price-indices, results. In addition, some suggestions are made with respect to the estimation of this system.     

Quasi‐geometric discounting: A closed‐form solution under the exponential utility function

This paper studies a discrete‐time utility maximization problem of an infinitely‐lived quasi‐geometric consumer whose labour income is subject to uninsurable idiosyncratic productivity shocks. We restrict attention to a first‐order Markov recursive solution. We show that under the assumption of the exponential utility function, the problem of the quasi‐geometric consumer admits a closed‐form solution.     

A theorem on the identifiability of the von Neumann-Morgenstern utility function from asset demands

If the demand for risky assets is determined by the maximization of an analytical von Neumann-Morgenstern utility function, and if these demands are known as a function of the assets' prices, then this utility function can be constructed without ambiguity.     

Existence of a continuous utility function with path monotonicity: the Wold approach

Summary This paper uses the approach of Wold to prove the existence of a continuous utility function on a subset ofR ⁿ with a path monotonicity assumption. This result is then extended to a Banach space.The research for this paper was begun while visiting the University of Cambridge and the London School of Economics in 1988. I should like to thank Dr. A. Beardon, Professor M. Desai, Professor L. Foldes and Dr. A. Horsley for their hospitality. Also, I am grateful to an anonymous referee for comments that led to an improvement in the exposition.     

Aggregation and the existence of a social utility function

In a well-known paper Gorman (Econometrica21 (1953)) established that the necessary and sufficient condition for the existence of an aggregate, or social, utility function, independent of the distribution of income, is that all individuals' income consumption paths be parallel straight lines. Recently Chipman (J. Econ. Theory8 (1974)), building on the paper of Hurwicz and Uzawa (in “Preference Utility and Demand”) has shown that if the distribution of income is proportional and individual preferences are homothetic, aggregate consumption behavior obeys the necessary integrability conditions. It is shown here that the consistency of aggregate behavior can be derived from more general conditions than the ones used by Chipman and Gorman. Examples of demand systems from which aggregate behavior implies a social utility function are provided. It is then shown that if individual demand functions are linear in income—a form employed by both Gorman and Chipman—it is not necessary that the distribution of income be fixed.     

Inheritance and inequality when wealth enters the utility function

The distribution of wealth and its dynamic development are analyzed within a non-overlapping generations model. All individuals have identical preferences and abilities. Wealth is represented by land, which is available in fixed aggregate supply. Utility depends on a perishable consumption good and—due to a bequest and/or a prestige motive—in addition on land owned. Two configurations can occur as long run equilbrium: equality and two class dichotomy. All Two Class Equilibria are unstable. The Equality Equilibrium is unstable if and only if land is sufficiently productive. In the case of instability there is a process towards maximal concentration of wealth.For helpful discussions I am indebted to G. Clemenz, S. Krasa, and M. Winkler.     

Sealed-bid auctions based on Cobb–Douglas utility function

This paper presents a more general independent private value model based on the assumption that Cobb–Douglas utility function is used to make a tradeoff between the probability of winning the unit and the profit under the first-price and second-price sealed-bid auctions. The equilibrium bidding strategies are given and the seller's expected revenue comparisons are made.     

Expected utility and the siegel paradox: A generalization

It was recently shown by Sinn that, under certain conditions, because of the Siegel paradox, even risk-averse agents can find speculation on forward currency markets attractive. His assumptions are that the spot and forward rates are identically distributed and statistically independent and that the agents' coefficients of relative risk aversion are constant and inferior to unity. We show that both assumptions of statistical independence and constant relative risk aversion can be dramatically relaxed.Thanks are due to H.-W. Sinn, W. T. Epps, and an anonymous referee for useful comments. Thon would like to thank the Department of Economics and The Center for Law and Economics of the University of Miami for research support, and the Prof. W. Keilhau's Memorial Fund for financial support.     

A note on linear utility

This note shows how a spectrum of specific axiomatizations for linear utility for decision-making under risk can be integrated under a generalized axiom scheme in which one of the two binary relations used in the axioms parameterizes specific applications.     

A note on linear utility

Summary We show that any complete, lower-semicontinuous, and translation-invariant preorder defined on a topological vector space admits a linear and continuous utility representation.Thanks are given to an anonymous referee for his/her valuable suggestions and comments.     

A theory of anticipated utility

A new theory of cardinal utility, with an associated set of axioms, is presented. It is a generalization of the von Neumann-Morgenstern expected utility theory, which permits the analysis of phenomena associated with the distortion of subjective probability.     

Regulating oligopolistic industries: A generalized incentive scheme

This paper deals with the design of regulatory mechanisms for oligopolistic industries. The proposed incentive scheme consists of two parts: a subsidy depending upon a firm's contribution to an equilibrium price reduction, and a tax equal to the profit of the previous period. This mechanism is as effective in regulating oligopolies as the well-known incremental surplus subsidy scheme in a monopoly framework. The proposed scheme provides appropriate incentives to enforce competitive behavior in a Cournot oligopoly. The scheme is welfare improving even if firms collude.