Underlying Utility Function Research Articles

Ordinal utility and economic price indices

In economic price index theory, a reference level of utility is needed for measuring the change in the cost of living oetween a base period and a comparison period. A reference level function can be used to derive this reference utility level from the utilities attained at the base and at the comparison prices. Depending on the scale type of the underlying utility function, the reference level function has to satisfy certain invariance conditions. In this paper, these conditions are formulated as functional equations for interval scales and for ordinal utility scales. By solving these equations, we characterize the class of admissible reference level functions for the respective scale type.

Intertemporal Substitution in Macroeconomics: Consumption, Labor Supply, and Money Demand

This paper introduces money into the consumption-leisure based intertemporal substitution model. The optimization problem poses that the household chooses consumption, labor supply, money demand, and wealth. Holdings of real money balances along with consumption and leisure determine utility. The constant decomposes wealth into money and an alternative asset. The authors estimate the derived semireduced-form equations using per capita U.S. data. The findings indicate significant interest-rate intertemporal substitution in labor supply, but weak effects in consumption and money demand. The empirical evidence supports contemporaneous nonseparability of consumption, money, and leisure within a well-behaved underlying utility function. Copyright 1992 by MIT Press.

Structural Change in the Demand for Money

A two-stage nonparametric and parametric approach to identifying structural change in the underlying utility function for monetary assets proves useful in exploring the existence, timing, direction, and extent of structural breaks over the 1969-85 period. Divisia monetary aggregates were constructed after applying the generalized axiom of revealed preference to identify least violation subutility functions. The nonparametric procedure shows utility function inconsistencies in 1975.IV and 1982.III. A translog utility function with structural change represented by time-varying multiplicative parameters was developed and estimated. The results show that the breaks were statistically significant and measure the impacts on monetary asset demand over the period. Copyright 1992 by Ohio State University Press.

Benefit functions and duality

This paper studies a new representation of individual preferences termed the benefit function. The benefit function b( g; x, u) measures the amount that an individual is willing to trade, in terms of a specific reference commodity bundle g, for the opportunity to move from utility level u to a consumption bundle x. The benefit function is therefore a generalization of the willingness-to-pay concept. This paper studies properties of this function, including its continuity and structural properties and its indirect relation to the underlying utility function. A very important property of the benefit function is that it is the natural precursor of the expenditure function, in the sense that the expenditure function is a (special) dual of the benefit function. This duality is shown to be complete by proving that when appropriate convexity properties hold, the (correspondingly special) dual of the expenditure function is, in fact, the benefit function. The duality makes the benefit function a powerful tool for analysis of welfare issues.

A numerical methods approach to calculating cost-of-living indices

The method developed in this paper deviates from the main approaches of thecost-of-living literature. We argue that, from the perspective of the econometrician, we would like to choose a system of demands which best fits the data. However, this may require estimating a demand system for which the underlying utility function is not known or a demand system for which compensated income cannot easily be computed. We demonstrate applicability of Vartia's (1983) algorithm for calculating a Konüs cost-of-living index for a demand system that previously could not be used in applied welfare work due to these deficiencies.

A Semi-Variance Model for Incorporating Risk into Capital Investment Analysis

ABSTRACT Most traditional approaches to capital expenditure analysis have been partially successful in explicitly accounting for risk. A utilitarian model for risk treatment is described in this paper. Specifically, we address two major aspects of the utilitarian approach: (1) the mathematical legitimacy of the underlying utility function with respect to its domain of economic significance and (2) the way “Expectancy-Variance” and “Expectancy-Semivariance” compare as risk/return trade-off criteria. In particular, we have shown how commonly used quadratic utility functions present some theoretical and practical inconveniences from an economic standpoint. Then, a hybrid utility function is introduced as a more legitimate and often more realistic model where semi-variance, rather than variance, is used as a measure of the investment riskiness.

An interactive MCDM weight space reduction method utilizing a tchebycheff utility function

Employing a Tchebycheff utility function to locally approximate the underlying utility function, we develop an interactive method to solve multiple-objective linear programming problems involving a single decision maker. We utilize selected and consistent weights in an augmented Tchebycheff linear programming formulation to obtain nondominated alternatives. Based on pairwise comparisons between alternatives, we generate constraints on the weights used to combine the decision maker's objectives. The constraints, formed to be consistent with a Tchebycheff function, lead to multiple disjoint convex regions in weight space. An algorithm is presented, and its performance is compared to the Zionts-Walenius method for various true underlying utility functions.

Testing for Structural Change: The Demand for Meat

AbstractRecent research on meat demand demonstrates the importance in empirical demand analyses of identifying and measuring structural changes. This paper develops and applies a method of analyzing structural changes in preferences using parameters from empirical demand equations derived from an underlying utility function. Structural changes alter the marginal rate of substitution between goods at fixed points of prices and quantities. The evolution of preference changes is measured by time‐varying multiplicative terms in a translog utility function. The application to meat concludes that structural change occurred in the 1970s and provides measures of the time pattern of demand shifts.

An interactive method for bicriteria integer programming

An efficient interactive solution framework for bicriteria integer programming is developed. The proposed methodology follows the implicit utility maximization approach. The decision maker's underlying utility function is assumed to be pseudoconcave and nondecreasing, and the problem is solved using an interactive branch-and-bound methodology. Several new concepts on bicriteria integer programming that offer great efficiency in the solution process are developed. The framework has been tested extensively, and results with problems having up to 80 variables and 40 constraints are presented. The results show that the methodology is an effective approach to solving practical bicriteria problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Preference Structure Representation Using Convex Cones in Multicriteria Integer Programming

A new efficient system of representing the decision-maker's preference structure in solving multicriteria integer programming problems is developed. The problem is solved by an interactive branch-and-bound method that employs the procedure of Zionts and Wallenius (Zionts, S., J. Wallenius. 1983. An interactive multiple objective linear programming method for a class of underlying nonlinear utility functions. Management Sci. 29(5).) for multicriteria linear programming. The decision-maker's underlying utility function is assumed to be pseudoconcave, and his pairwise comparisons of decision alternatives are used to determine his preference structure in terms of certain convex cones in the objective function space and constraints on the weights on the objectives in the weight space. The two forms of preference structure representation are interrelated, and their underlying theory is developed. The primary objective of a representation scheme is exactness, and, in this respect, it is shown that the constraints on the weights are not adequate for representing nonlinear utility functions. On the other hand, the convex cones exactly represent any quasiconcave utility function and clearly avoid the approximations and inaccuracies in other utility assessment systems. Accordingly, an efficient ordered representation using convex cones is developed. An algorithmic framework for multicriteria integer programming that integrates the representation using convex cones with the branch-and-bound solution procedure is developed. Computational experience with bicriteria problems having up to 80 variables and 40 constraints is presented.

Interactive multicriteria linear programming: An extension of the method of Zionts and Wallenius

This article presents an extension of the interactive multicriteria linear-programming method of Zionts and Wallenius [see Management Science, 29(5) (1983)]. The decision maker's underlying utility function is assumed to be pseudoconcave, and his preference structure is assessed through pairwise comparison questions. In the method of Zionts and Wallenius, the decision maker's preference structure is represented as constraints on the weights on the objectives derived from his responses. This representation is only a linear approximation to the underlying nonlinear utility function. Accordingly, inconsistency among the constraints on the weights arises while solving the problem. Therefore, some of the constraints have to be dropped, resulting in a loss of information on the preference structure, and hence an increase in the total number of questions. In this article we develop a hybrid representation scheme to avoid this problem. The proposed scheme is implemented within the algorithmic framework of the method of Zionts and Wallenius, and its underlying theory is developed. Computational results show that the number of questions required by the Zionts and Wallenius method can be sinificantly reduced using the proposed scheme.

Objective Benefit Versus Subjective Perception in the Theory of Risk-Sensitive Foraging

The organism's responses to variability in resource distributions is a compound effect of both the perceived (subjective) probability of the occurrence of different reward levels or benefits and the utility that results from such benefits. To date, research has focused primarily on the utility function that assigns values to different outcomes of acts. Some kinds of observed behavior (like the preference of uncertain rewards over certain rewards with equal expectation) have led behavioral ecologists to postulate that organismal utility functions are both convex and concave but over different portions of the range of rewards. Though this is a plausible and likely explanation, observed patterns of behavior and their tests cannot distinguish the effects of shifting subjective probabilities at different levels of reward expectation. If subjective probabilities are skewed such that rare favorable events are perceived to be more likely to occur than they objectively are, then organisms may show apparently risk-seeking behavior without implying a change in the curvature of the underlying utility function. Shifts in probabilities of this sort do not guarantee the concavity of utility, nor does the existence of such shifts exclude the possibility that utility is both convex and concave. The two problems are separate, but only one (the shape of utility) has received attention. I present a graphical method for partitioning these effects on the basis of the concept of "acceptance sets." The method leads to testable predictions that relate easily to the experimental systems commonly employed in the analysis of risk-sensitive foraging.

A utility approach to the analytic hierarchy process

This paper attempts to examine the utility foundation of the Analytic Hierarchy Process (AHP). It identifies the conditions under which the selection of an alternative is consistent with the maximization of an underlying utility function, or more precisely, the conditions under which the AHP-recommended choice corresponds with the solution attained from maximizing the respondent's utility function.

How ‘exact’ are exact measures of welfare loss?

This paper examines the sensitivity of exact measures of welfare loss to changes in the assumed form of the underlying utility function.

Homogeneous Premium Calculation Principles

AbstractA premium calculation principle π is called positively homogeneous if π(cX) = cπ(X) for all c &gt; 0 and all random variables X. For all known principles it is shown that this condition is fulfilled if it is satisfied for two specific values of c only, say c = 2 and c = 3, and for only all two point random variables X. In the case of the Esscher principle one value of c suffices. In short this means that local homogeneity implies global homogeneity. From this it follows that in the case of the zero utility principle or Swiss premium calculation principle, the underlying utility function is of a very specific type.A very general theorem on premium calculation principles which satisfy a weak continuity condition, is added. Among others the proof uses Kroneckers Theorem on Diophantine Approximations.

An improved method for solving multiple criteria problems involving discrete alternatives

An approach is presented for solving a discrete-multiple-criteria problem. The approach asks pairwise comparisons of a decision-maker. Under mild assumptions, the method obtains the most preferred alternative. The required number of pairwise comparisons is generally modest. The authors' experience with the method indicates that for reasonable underlying utility functions, a heuristic stopping rule generally yields the most preferred alternative after several comparisons, usually fewer than 20.

Nonparametric Tests of Models of Investor Behavior

The standard models of consumer behavior under uncertainty are the expected utility model and the mean-variance model. As with any models involving unobservables one might well ask about the empirical content of these hypotheses: what restrictions on observed behavior do these models impose? How can one test observed behavior for consistency with these models? How can one recover the underlying utility function and forecast behavior in new situations?

Model Misspecification in Multiattribute Parameter Estimation

Most applications of conjoint analysis have emphasized main-effects models, largely because fewer data points are needed to fit that type of model at the individual level. The authors suggest that such simplifications can lead to poor predictions when the underlying utility functions depart from the simplicity of a main-effects model. They also show how compromise designs, which allow orthogonal estimation of selected two-way interactions (as well as main effects), can provide a more general experimental design in cases where a specified set of two-way interactions is suspected.

A Note on Iterative Premium Calculation Principles

Gerber (1974) has given a characterization of the exponential utility function by proving the fact that a premium calculation principle of zero utility is iterative iff the underlying utility function is linear or exponential. In the present note we prove the more general result that the premium calculation principle introduced by Bühlmann, Gagliardi, Gerber and Straub (1977) is iterative iff the underlying function v is linear or exponential or when the principle is a mean value principle.

Stochastic Dominance Tests for Selecting Acceptable Debt Issuance Strategies

The use of the Stochastic Dominance (SD) ordering rules in selecting a set of acceptable debt issuance strategies is examined. A procedure for selecting among alternative strategies on both the timing of issuance and maturity composition of a portfolio of liabilities is formulated. An application of the SD rules provides an effective analytical alternative to subjective judgment in determining debt timing policy when there are uncertain future costs. The SD approach enables a choice of strategies where there are specific stated assumptions on the nature of the underlying utility functions; the decisions are not based on subjective estimates of utility. An application of the ordering rules to the debt timing decision requires the use of a solution procedure applicable to a multi-period case having nonstationary probability functions over time. An application of the model to a small sample problem indicates the information requirements, SD test results, and the evaluation of the tests.