Optimal financial investments for non-concave utility functions

We prove a formula for the computation of optimal financial investments in an expected utility framework with arbitrary (not necessarily concave) utility functions. This extends classical results on optimal financial investments for strictly concave utility functions and is of importance particularly for applications of prospect theory where the utility function has a convex-concave shape.     

The electric utility demand for energy in the United States

This paper looks at the use of various fossil fuel inputs in the generation of electrical energy via a two step procedure. First, aggregate energy demand is determined and second, corresponding energy fuel shares are examined. This separation suggests that energy is separable and forms a homogeneous aggregate. Finally the question of the stability of the demand for fuel inputs is addressed.     

Estimating money demand functions for South Asian countries

In this paper, we estimate a money demand function for a panel of five South Asian countries. We find that the money demand and its determinants, namely real income, real exchange rate and short-term domestic and foreign interest rates are cointegrated both for individual countries as well as for the panel, and panel long-run elasticities provide robust evidence of statistically significant relationships between money demand and its determinants. Our test for panel Granger causality suggests short-run causality running from all variables, except foreign interest rate, to money demand, and we find evidence that except for Nepal money demand functions are stable.      

A class of multiattribute utility functions

A function u(z) is a utility function if u′(z) > 0. It is called risk averse if we also have u′′(z) < 0. Some authors, however, require that u ⁽ⁱ⁾(z) > 0 if i is odd and u ⁽ⁱ⁾(z) < 0 if i is even. The notion of a multiattribute utility function can be defined by requiring that it is increasing in each variable and concave as an s-variate function. A stronger condition, similar to the one in case of a univariate utility function, requires that, in addition, all partial derivatives of total order m should be positive if m is odd and negative if m is even. In this paper, we present a class of functions in analytic form such that each of them satisfies this stronger condition. We also give sharp lower and upper bounds for E[u(X ₁,... , X _s )] under moment information with respect to the joint probability distribution of the random variables X ₁,... , X _s assumed to be discrete and representing wealths. Partially supported by OTKA grants F-046309 and T-047340 in Hungary.     

Nominal vs real adjustment in demand for money functions

Recently, Fair (1987) has addressd an interesting question in the areas of demand for money, namely, whether the adjustment of actual to desired demand for money is in nominal or real terms. His conclusion, based on time-seies analysis for twenty-seven countries, including a few developing countries, was that the evidence was overwhelmingly in favour of the nominal hypothesis.

The aim of this paper is to address the same issue for eleven Asian countries. In the process, a reformulation of the test procedure used by Fair is suggested. In addition, the question is also examined within the framework of the error correction model. The models are also tested for structural stability.

The scheme of the paper is as follows. The models and the tests are specified in Section I. The data and the estimation issues are dealt with in Section II. Section III presents the results. The paper is concluded with a brief summary of the major findings.     

The theory of mixed demand functions

The properties of Samuelson's mixed demand functions, which express demand as a function of a mixed set of prices and quantities, are derived. By analyzing compensated (or substitution) effects and uncompensated effects, the relationships between mixed demand functions and conditional (or rationed) demands are examined. This provides insights on the behavioral implications of consumer theory for alternative demand specifications.     

A reformulation of the theory of demand by compensated demand functions

We present a formal approach to consumer demand by compensated demand functions. In accordance with the integrability theory or with the theory of revealed preference, we do not require the existence of a utility function, but we do assume certain hypotheses concerning functions describing rational behavior. In view of their properties, these functions can be interpreted as compensated demand functions. According to traditional neoclassical consumer theory, Shephard's lemma and the symmetry and negative semidefiniteness of the Slutsky-Hicks matrix can be shown. We shall also see that a convex, continuous, and monotonic preference ordering, which is representable by income compensation functions, can be introduced. It can also be shown that the existence of a compensated equilibrium can be derived within this approach by compensated demand functions. In order to obtain the existence of a compensated equilibrium under less stringent conditions we finally generalize the axioms assuming that a compensated demand correspondence is given.     

On the characterization of excess demand functions

Summary. In this paper, we give the necessary and sufficient conditions that characterize the individual excess demand function when it depends smoothly on prices and endowments. A given function is an excess demand function if and only if it satisfies, in addition to Walras law and zero homogeneity in prices, a set of first order partial differential equations, its substitution matrix is symmetric and negative semidefinite. Moreover, we show that these conditions are equivalent to the symmetry and negative semidefiniteness of Slutsky matrix, Walras law and zero homogeneity of Marshallian demand functions.Received: 25 November 2002, Revised: 11 March 2004, JEL Classification Numbers: D11.Marwan Aloqeili: I would like to thank an anonymous referee for helpful comments.     

Characterizing C2 aggregate excess demand functions

Summary. We integrate and sharpen two characterizations of aggregate excess demand functions: we obtain Mas-Colell's (1977) equilibrium invariance, and strengthen Geanakoplos' (1984) weakly concave utility functions to strictly concave ones. Our proofs modify and extend Geanakoplos' utility-construction. We note two applications: a sharper characterization of equilibrium price sets (cf. Mas-Colell (1977)), and a basis for the studies of computable economies (Richter and Wong (1996)). Received: July 29, 1996; revised version: February 20, 1997     

Homothetic preferences and community excess demand functions

It has recently been shown that microeconomic theory imposes almost no restriction on community excess demand functions besides Walras' Law, if the economy contains no more commodities than consumers.It is shown that the same result is true if the preferences of the consumers are further restricted by the seemingly strong requirement that they be homothetic, even when the distribution of initial endowments is a set of independent points in commodity space fixed in advance except for a scaling factor which is common to all consumers.     

Engel curves and systems of demand functions

The functional forms of the Engel curves implied by several popular complete systems of demand functions are discussed. Among the systems are those generated by generalized quadratic indirect utility (the translog system, the generalized Leontief system, etc.), the linear and quadratic expenditure systems, and Deaton and Muellbauer's PIGL and AIDS. A new system, which can produce the Engel curves of all these systems as special cases, is suggested. The different Engel curves are tested against data from a Norwegian survey of consumer expenditure. This is done both in a complete system of Engel curves for eight commodities and commodity by commodity.     

Remarks concerning concave utility functions on finite sets

Summary. A direct construction of concave utility functions representing convex preferences on finite sets is presented. An alternative construction in which at first directions of supergradients (prices) are found, and then utility levels and lengths of those supergradients are computed, is exhibited as well. The concept of a least concave utility function is problematic in this context.Received: 28 November 2002, Revised: 28 June 2004, JEL Classification Numbers: D11, C60.I am indebted to an anonymous referee, Marcel K. Richter and Kam-Chau Wong, for many valuable remarks and suggestions.     

Modeling non-monotone risk aversion using SAHARA utility functions

We develop a new class of utility functions, SAHARA utility, with the distinguishing feature that it allows absolute risk aversion to be non-monotone and implements the assumption that agents may become less risk averse for very low values of wealth. The class contains the well-known exponential and power utility functions as limiting cases. We investigate the optimal investment problem under SAHARA utility and derive the optimal strategies in an explicit form using dual optimization methods. We also show how SAHARA utility functions extend the class of contingent claims that can be valued using indifference pricing in incomplete markets.     

Characterizing stochastically monotone functions by multiattribute utility theory

The research of Peter Wakker has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.     

Preferences over characteristics and utility functions over commodities

Following Lancaster, preferences are defined over a set of characteristics, while commodities vectors are transformed into characteristics by a production function. We assume that both the preferences over the characteristics and the production functions are “neoclassical” and we characterize the set utility functions over the consumption space derived as the composition of preferences over characteristics and production functions. We prove that, under regularity conditions, any function can be derived by such a composition. Thus, the theories of characteristics does not impose any restrictions on derived utility functions. We thank an anonymous referee for helpful suggestions. The research of Aldo Rustichini was supported by the NSF grant NSF/SES-0136556. Paolo Siconolfi acknowledges the support of the Graduate School of Business, Columbia University.     

Excess demand functions when new assets are introduced

We demonstrate that information on the aggregate excess demand function of an incomplete real asset market economy is not helpful toward predicting the equilibrium of a new economy to which unredundant assets are added. An innovation of assets can completely change the aggregate excess demand functions.     

Market clearing, utility functions, and securities prices

Summary. We prove the existence of equilibrium in a continuous-time finance model; our results include the case of dynamically incomplete markets as well as dynamically complete markets. In addition, we derive explicitly the stochastic process describing securities prices. The price process depends on the risk-aversion characteristics of the utility function, as well as on the presence of additional sources of wealth (including endowments and other securities). With a single stock, zero endowment in the terminal period, and Constant Relative Risk Aversion (CRRA) utility, the price process is geometric Brownian motion; in essentially any other situation, the price process is not a geometric Brownian motion.JEL Classification Numbers: D52.This paper is part of my Dissertation (UC Berkeley). I am very grateful to my advisor Professor Robert M. Anderson. I also would like to thank Steve Evans, Roger Purves, Jacob Sagi, Chris Shannon and the participants of the 2002 NBER General Equilibrium Conference at the University of Minnesota (Minneapolis) for very helpful discussions and comments. This work was supported by Grant SES-9710424 from the National Science Foundation.     

Specification and testing of count data recreation demand functions

This article examines the effects of alternative formulations of count data recreation demand models on parameter estimates, model selection, and consumer surplus. The results indicate that large parameter and consumer surplus differences exists across the various count model formulations. More importantly, the results show that distributional assumptions, heteroscedastic functional forms, and overdispersion can have a substantial effect on consumer surplus estimates.