Form Of Utility Function Research Articles

Forms of Utility Function for Residential Behavior Analysis and Neighborhood Benefits Estimation

The main objective of this paper is to answer the question of what form of utility function is best for forecasting residential behavior and estimating the benefits of various neighborhood changes. This question is a key factor when consistently analyzing the impacts of residential environmental changes on residential behavior and measuring the benefits, because the magnitude and sensitivity of such impacts and benefits vary with the specified utility function forms. In this paper, first, residential behavior is formulated and then benefits of residential environmental changes are rigorously defined emphasizing the importance of estimating the utility function. Second, four utility function forms, namely, linear, log-linear, CES (constant elasticity of substitution), and VES (variable elasticity of substitution), are adopted, and a method for estimating the parameters of the specified utility functions is proposed. Based on a case study, it is concluded that the CES form is best in terms both of analyzing residential behavior and of estimating the benefits of various neighborhood changes.

Modeling the Societal Impact of Fatal Accidents

A number of proposals have been put forth regarding the proper way to model the societal impact of fatal accidents. Most of these proposals are based on some form of utility function asserting that the social cost (or disutility) of N lives lost in a single accident is a function of Nα. A common view is that a single large accident is more serious than many small accidents producing the same number of fatalities, hence α > 1. Drawing upon a number of empirical studies, we argue that there is insufficient justification for using any function of N fatalities to model societal impacts. The inadequacy of such models is attributed, in part, to the fact that accidents are signals of future trouble. The societal impact of an accident is determined to an important degree by what it signifies or portends. An accident that causes little direct harm may have immense consequences if it increases the judged probability and seriousness of future accidents. We propose that models based solely on functions of N be abandoned in favor of models that elaborate in detail the significant events and consequences likely to result from an accident.

A NOTE ON INVESTMENT DECISION RULES BASED ON UTILITY FUNCTIONS

Many investment decision models are formulated on the basis of certain assumptions regarding investor's tastes combined with the assumed objective of expected utility maximization. The rules are often expressed in the form of a finite number of moments of the returns distributions, depending on the specific utility function restrictions imposed. For example, mean/variance decisions have been derived using the assumption of a quadratic preference function. Borch (1969) and many others have demonstrated the ambiguity of mean/variance decision rules based on this specific utility functional form. In this note, Borch's findings are extended t o all investment decision rules based on the assumption of any finite order utility function for a general class of risk averters.

Dealing with envy

This paper argues that if envy matters, then it should enter directly into the utility functions. The Pareto sets based on the envious utilities are natural candidates for the socially optimal allocations. Three forms of envious utility functions are considered, and their Pareto sets compared to the usual definition of the fair set where the notion of non-envy is imposed on non-envious utilities. It is shown that very rarely will the fair set coincide with any envious Pareto set, and for certain types of envious utilities, no outcome in the fair set is Pareto optimal.

The structure of intercity travel demands in Canada: Theory tests and empirical results

This paper presents results of an econometric study study of intercity travel demands in Canada, 1961–1976. A translog form of reciprocal indirect utility function is used to test the structure of preferences in five demand sectors: three travel modes, goods and other services. Travel sector preferences are found to be time- and season varying but independent of average weekly work hours. The aggregate results indicate that the demands for all three passenger modes are price-elastic; bus and rail exhibit moderate complementarity, while rail and air are weakly complementary. The most important result derived from our tests of separability was that the demand system for the three passenger modes is inextricably tied to the rest of the economy, and therefore, may not be studied in isolation from the goods and other services sectors.

Travel Demand and the Evaluation of Transportation System Change: A Reconsideration of the Random Utility Approach

Williams formulated a consistent analytic representation of the trip decision process and developed compatible measures of user benefit arising from the transportation system change within the framework of random utility theory. Here, the random utility approach is reconsidered and reformulated with the aim of describing individual behavior more precisely and more realistically. The model introduces explicitly the income-time constraint imposed on an individual and permits an individual to choose multiple destinations and determine the number of trips freely. Special attention is also paid to the form of utility function which allows the consumer's surplus to be rigorously defined and to be exactly measured by the area under the demand curve.

An Interactive Approach to Multiple Criteria Decisionmaking Based on Statistical Inference

An interactive algorithm is proposed for the problem of selecting one of a finite number of alternatives where each is evaluated in terms of a number of conflicting criteria. A simple form of utility function is assumed, and the possibility is modeled probabilistically that the decisionmaker may at any time indicate a preference between alternatives in conflict with his true utility. On this basis, a formal Bayesian inferential procedure is applied to a sequence of pairwise choices between alternatives made by the decisionmaker to yield estimates of the unknown parameters of the utility function. This ultimately implies probability distributions on the utilities of each alternative. The sequence of pairwise comparisons continues until a satisfactorily short list of alternatives remains after elimination of those inferred to be significantly worse than the best.

An econometric model of tenure choice and demand for housing as a joint decision

This paper models a household's choice of tenure and demand for housing services as a joint decision imposing the restriction that both discrete and continuous decisions are derived from a single preference ordering. The utility index for households is the translog form of the reciprocal indirect utility function allowing for random preferences. Each household chooses between the two main tenures, the owner-occupied and subsidised rental sectors, but households may be rationed in either or both of these sectors and refused admission, in which case they are assumed to enter the third sector, uncontrolled rental. The model is estimated on UK data for 5895 households.

Multiattribute Utility Functions: Decompositions Using Interpolation

Methodologies developed in the last several years allow formal inclusion of two sources of complexity in the analysis of a decision problem—uncertainty and multiple conflicting objectives. Uncertainty can be handled by assessing the decision maker's attitude towards risk in the form of a von Neumann-Morgenstern utility function. Conflicting objectives may be handled by making the utility function multidimensional. A problem that then arises is in devising assessment protocols for these multidimensional (multiattribute) functions that make efficient use of the decision maker's time and effort. Mostly, such methods have concentrated on identifying structural properties of the function, such as separability, by asking questions of a general nature about the preferences and tradeoffs of the decision maker. These methods have been applied successfully on such problems as facilities siting, selection of appropriate medical treatment, optimal pest control and the evaluation of R&D proposals. The problem addressed in this paper is that of what to do about the assessment if no useful decomposition of the utility function can be identified. One possiblity is to make use of some of the properties that were most nearly satisfied and then attempt to support the resulting recommendations with a sensitivity analysis. This paper provides the analyst with an efficient, routine method of approximating the utility function to any degree of accuracy that the decision maker or the problem requires. The idea is to assess the function exactly only on a multidimensional grid and then to interpolate other values of the utility function from those on the grid. Evidently, a finer grid will, in general, provide a better approximation. The resulting utility function is continuous. It is not anticipated that many of the problems in which conflicting objectives are a factor will need this level of sophistication. But just as there are problems that require a substantial modelling effort to identify feasible consequences so, occasionally, an analysis would benefit from an accurate modelling of the objective function.

A Behavioral Model of Bureaucracy

From a traditional viewpoint, government growth is thought to be a response to population expansion and the increasing complexities of the economy engendered by externalities and various other market failure. In the literature, Buchanan [1] first explains the decision-making process of the government by postulating a utility function for the bureaucracy that has income level and size of bureaucracy as arguments. Thus, this form of utility function is similar to that of a profit maximizing firm. (Note that a hyperbolic utility function implies that government bureaucrats will maximize wages above the market rate times the size of output of bureau services. This is identical to profit maximization.) To achieve these goals, the government bureaus which behave as monopolies must under-produce government services. Hence at the utility maximizing output, it is impossible to have over-size bureaus.1 To amend this, we have to assume that for the utility function of the bureaucracy, more favor is attached to the size of the bureaucracy than to the income of the bureaucrats. Niskanen [6] justifies the latter by assuming the sole objective of government bureaucrats is to maximize the budget allocation. He then demonstrates that this assumption would result in an over-expansion of bureaucracy. Tullock [7; 8] has noted that the above analysis has an obvious drawback in that voters participation is omitted. The introduction of voters in our analysis also introduces competition into the public sector. Downs [3] argues that the sole objective in the decision-making process of government bureaucrats is to maximize political support; that is, ensure re-election. Hence, when government bureaucrats are faced with a group of conscientious voters,

Utility maximisation, demand systems, and functional form in transport demand analysis

Summary In this paper, we have examined the basic theory of utility maximisation and its use in the generation of demand systems which significantly reduce the parameter space within which the researcher must work. For a specific utility representation we show how a particularly popular demand system known as the linear expenditure system (LES) is derived and proceed to examine a generalisation known as the S‐branch system. This S‐branch system has been used by Kraft and Kraft4 in the analysis of intercity travel with some success and may lead to further analysis of travel demand using complete demand systems. However, the restrictions on parameter estimates yielded by demand systems based on additive preferences (as is the LES and its variants) may lead one to reject this approach in favour of an a priori approach to demand function specification. If this is the case, recent work on generalised functional form based on the early developments of Box and Cox is suggested as being possibly quite useful. We ...

Risk Invariance and Ordinally Additive Utility Functions

This study introduces ordinally additive, ordinally linear, and ordinally Cobb-Douglas utility functions for the analysis of risky decisions when the uncertainty affects several attributes. Practical algorithms for the determination of utility functions with these forms are provided. Further, the study offers several risk invariance axioms on choice behavior under multidimensional risk. These axioms, for the first time, extend to the multidimensional context the heuristic correspondence between risk aversion and subjective wealth, heretofore familiar in only one dimension. In addition, the consequences of these new risk invariance axioms for utility functional forms in the multi-dimensional context are investigated. The result is a sequence of theorems which show that ordinally linear, ordinally Cobb-Douglas, and ordinally additive von Neumann-Morgenstern utility functions are characterized by the risk invariance axioms. IN THE STUDY OF DECISION MAKING under uncertainty, it is well known that plausible sets of axioms imply that the decision maker acts as if he maximizes his expected von Neumann-Morgenstern utility. (See [1], for example.) If the uncertain outcomes are multidimensional, then the appropriate utility concept is a function of many variables. This is the case, for example, for a firm choosing marketing policies which will affect sales and profits, for an individual faced with investment choices which will affect consumption during several years, and for a government deciding among projects which differ in their costs, outputs, and environmental impacts. In grappling with such problems, decision analysts have found it impossibly difficult to proceed with utility measured by a general function of the outcome variables. Instead, they have used multi-attribute utility functions with special forms, and found that their conclusions are sensitive to the particular form utilized. (See [13], for example.) Thus, it falls to theorists to develop testable hypotheses about risky choice which are equivalent to special (and, hopefully, convenient) functional forms for multiattribute utility. Fishburn [2, 3, and 4], Keeney [5 and 6], and Pollak [9, 10, and 11] have made contributions in this vein. This study introduces ordinally additive von Neumann-Morgenstern utility functions (i.e., those which are a monotonic transformation of a sum of functions, each of one variable) to the literature. I show that they should be well suited to practical decision analysis by presenting algorithms for their use. I propose several risk invariance axioms which plausibly extend to the multidimensional context the intuitive link between risk aversion and wealth in one dimension. These axioms are shown to characterize (in the presence of some other assumptions) ordinally additive, ordinally linear, and ordinally Cobb-Douglas von NeumannMorgenstern utility functions.

Risk Aversion and Consumer Preferences

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 (e.g., 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 (e.g., 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.

On the Formation of Travel Demand Models and Economic Evaluation Measures of User Benefit

This paper examines a variety of issues within the context of two main themes: the formation of travel demand models and economic evaluation measures which are mutually consistent within a theory of rational choice; and a consideration of the structure of models which are representations of the trip decision process over several dimensions: location, mode, and route. Random utility theory is invoked to explore both the role and properties of composite costs or index prices in the ‘recursive’ approach to the structuring of travel choice models, and their significance in the economic evaluation problem. It is shown that the specification of these costs must be made very precisely, with respect to the demand model form chosen, in order to retain the underlying assumption that the traveller is an optimal decisionmaker. It is argued that the structure of ‘simultaneous’ models currently in use is inconsistent with the form of utility function assumed to generate those models. Furthermore, it is shown that the ‘simultaneous’ and ‘recursive’ forms are special cases of a more general choice model structure which takes specific account of correlation or ‘commonality’ of trip attributes. A number of applications are discussed in which consistent demand models and perceived user benefit measures are constructed. These include the formation of strategic transport planning models and of models for mixed-mode, multimode, and multiroute systems. The formalism allows definitive answers to be given to a number of problems of current interest in transportation planning, which have been incorrectly or incompletely treated.

Multivariate Risk Aversion, Utility Independence and Separable Utility Functions

This paper concerns utility functions for more than one attribute. A new type of risk aversion found only in muitivariate utility functions is defined. Certain behavioral assumptions, which are necessary and sufficient for one of three forms of separable utility functions including the well-known additive form, are given. It is shown that only one of these separable forms, the “negative multiplicative form,” possesses this new type of risk aversion and in particular that the additive form does not.

Solution of Capital Budgeting Problems Having Chance Constraints; Heuristic and Exact Methods

Abstract The capital budgeting heuristic (CBH) algorithm for solving capital budgeting problems is extended to solve problems with chance constraints of the form Pr where each αi is specified. The objective function is linear, being the expectation-variance form of utility function. Computational experience is described using the modified CBH to solve a set of 24 problems, each having 30 independent projects and 5 budget periods.

Comparison of Moment and Stochastic Dominance Ranking Methods

Since the appearance in 1969 of Kadar and Russell's paper [1] and in 1970 of Whitmore's paper [4] extending stochastic dominance to the second and third degrees, a considerable interest has developed in stochastic dominance methods as an alternative to moment methods in investment ranking models. The particular attraction of stochastic dominance is that its results are consistent with the expected utility hypothesis without depending on a particular mathematical form of utility function or on a specific type of distribution of investment returns. Although both stochastic dominance ranking models and moment ranking models are based on probability distributions of investment returns, it has been difficult to relate the two types of models mathematically for a complete comparison of results. In this paper the common moments are expressed in terms of successive integrals of a probability density function to allow a systematic comparison of the two methods.

Portfolio Choice and Saving in an Optimal Consumption-Leisure Plan

Economists have for some time been interested in analysis of a consumer's choice of savings rate and portfolio composition in the presence of uncertain returns. Theorems have been proved for a large number of cases involving utility functions with various special functional forms.3 There are no papers in the literature which prove theorems which hold for the class of all continuous, increasing, strictly quasi-concave utility of consumption and leisure functions.4 This is in marked contrast to the situation in the theory of consumer demand under certainty where the general case,5 as well as various special cases,6 has received considerable attention. The paucity of theorems which hold for the general case is somewhat surprising since strict quasi-concavity of utility functions has a particularly appealing interpretation in models which admit uncertain outcomes. This interpretation is that of the weakest form of risk-aversion [5, p. 101]. The present paper is concerned with the implications of the strict quasi-concavity hypothesis for the consumer's choice of savings rate and portfolio composition.7 The only results in the uncertainty literature which do not require hypotheses about the form of a consumer's utility function 8 which are stronger than strict quasi-concavity are general equilibrium theorems, such as those of Arrow and Debreu.9 The authors who use the Arrow-Debreu contingent commodity approach in the analysis of a consumer's

Convex stochastic dominance with finite consequence sets

Stochastic dominance is a notion in expected-utility decision theory which has been developed to facilitate the analysis of risky or uncertain decision alternatives when the full form of the decision maker's von Neumann-Morgenstern utility function on the consequence space X is not completely specified. For example, if f and g are probability functions on X which correspond to two risky alternatives, then f first-degree stochastically dominates g if, for every consequence x in X, the chance of getting a consequence that is preferred to x is as great under f as under g. When this is true, the expected utility of f must be as great as the expected utility of g. Most work in stochastic dominance has been based on increasing utility functions on X with X an interval on the real line. The present paper, following [1], formulates appropriate notions of first-degree and second-degree stochastic dominance when X is an arbitrary finite set. The only ‘structure’ imposed on X arises from the decision maker's preferences. It is shown how typical analyses with stochastic dominance can be enriched by applying the notion to convex combinations of probability functions. The potential applications of convex stochastic dominance include analyses of simple-majority voting on risky alternatives when voters have similar preference orders on the consequences.

Functional form for utility, demand systems, and the aggregate consumption function

Alternative utility specifications are imbedded in a simple calculus of variations problem to obtain complete sets of demand equations and their associated aggregate consumption function. In three cases, the resulting consumption functions are linear in prices and income with no intercept. For parameter identification, empirical work should be based upon the underlying demand systems.