# UTILITY THEORY Photo by: JohnKwan

Utility theory provides a methodological framework for the evaluation of alternative choices made by individuals, firms and organizations. Utility refers to the satisfaction that each choice provides to the decision maker. Thus, utility theory assumes that any decision is made on the basis of the utility maximization principle, according to which the best choice is the one that provides the highest utility (satisfaction) to the decision maker.

## UTILITY THEORY IN CONSUMER BEHAVIOR

Utility theory is often used to explain the behavior of individual consumers. In this case the consumer plays the role of the decision maker that must decide how much of each of the many different goods and services to consume so as to secure the highest possible level of total utility subject to his/her available income and the prices of the goods/services.

## UTILITY THEORY AND DEMAND

In addition to providing an explanation of consumer disposition of income, utility theory is useful in establishing individual consumer demand curves for goods and services. A consumer's demand curve for a good or service shows the different quantities that consumers purchase at various alternative prices. Factors that are held constant are consumers' tastes and preferences, income, and price.

## UTILITY FUNCTIONS

In all cases the utility that the decision maker gets from selecting a specific choice is measure by a utility function U, which is a mathematical representation of the decision maker's system of preferences such that: U(x) > U(y), where choice x is preferred over choice y or U(x) = U(y), where choice x is indifferent from choice y—both choices are equally preferred.

Utility functions can be either cardinal or ordinal. In the former case, a utility function is used to derive a numerical score for each choice that represents the utility of this choice. In this setting the utilities (scores) assigned to different choices are directly comparable. For instance, a utility of 100 units towards a cup of tea is twice as desirable as a cup of coffee with a utility level of 50 units. In the ordinal case, the magnitude of the utilities (scores) are not important; only the ordering of the choices as implied by their utilities matters. For instance, a utility of 100 towards a cup of tea and a utility level of 50 units for a cup of coffee simply state that a cup of coffee is preferred to a cup of tea, but it cannot be argued that a cup of tea is twice as desirable as a cup of coffee. Within this setting, it is important to note that an ordinal utility function is not unique, since any monotonic increasing transformation of an ordinal utility function will still provide the same ordering for the choices.

## ASSUMPTIONS ON PREFERENCES

Irrespective of the type of utility function, utility theory assumes that preferences are complete, reflexive and transitive. The preferences are said to be complete if for any pair of choices x and y, one and only one of the following be stated: (1) x is preferred to y, (2) y is preferred to x, or (3) x and y are equally preferred. The preferences are said to be reflexive if for any pair of choices x and y such that x equally preferred to y, it is concluded that y is also equally preferred to x. Finally, the preferences are said to be transitive if for any three choices x, y, z such that x is preferred over y, and y is preferred over z, it is concluded that x is preferred over z. The hypotheses on reflexivity and transitivity imply that the decision maker is consistent (rational).

## MARGINAL RATE OF SUBSTITUTION

A further assumption of utility theory is that decision makers are willing to trade one choice for another. The existing trade-offs define the marginal rate of substitution. As example suppose that two investment projects are considered by a decision maker. Project x has a return of 6 percent and a risk of 4 percent, whereas the return for project y is 5 percent and its risk is 2 percent. Furthermore assume that the decision maker considers both projects to be equally preferred. With this assumption it is clear that the decision maker is willing to increase the risk by 2 percent in order to improve return by 1 percent. Therefore, the marginal rate of substitution of risk for return is 2. In real world situations, the marginal rates of substitution are often decreasing. Such situations correspond to diminishing marginal utilities (marginal utility is defined as the change in total utility resulting from a one-unit change in consumption of the good or service). In the above example, we can assume that the decision maker is willing to take higher risks in order to get higher return, but only up to a specific point which is called saturation point. Once the risk has reached that point, the decision maker would not be willing to take any higher risk to increase return and therefore the marginal rate of substitution at this risk level would be zero.

## MULTI-ATTRIBUTE UTILITY THEORY

The traditional framework of utility theory has been extended over the past three decades to the multi-attribute case, in which decisions are taken by multiple criteria. Multi-attribute utility theory has been evolved as one of the most important topics in multiple criteria decision making with many real world applications in complex real world problems.

The concept of utility can be used to analyze individual consumer behavior, to explain individual consumer demand curves as well as in modeling the decision makers' preferences. In all cases, it is assumed that some choices are evaluated and the best one is identified as the choice that maximizes the utility or satisfaction. The utility theory has been a research topic of major importance for the development of economics, decision theory, and management and it still attracts the interest of both practitioners and academic researchers.

Michael Doumpos and

Constantin Zopounidis

Aleskerov, F., and B. Monjardet. Utility Maximization, Choice and Preference. Heidelberg: Springer Verlag, 2002.

Belton, V. and T.J. Stewart. Multiple Criteria Decision Analysis: An Integrated Approach. Dordrecht: Kluwer Academic Publishers, 2002.

Hammond, J.S, R.L. Keeney, and H. Raiffa. Smart Choices: A Practical Guide to Making Better Decisions. Boston: Harvard Business School Press, 2002.

Keeney, R.L. and H. Raiffa. Decisions with Multiple Objectives: Preference and Value Tradeoffs. Cambridge University Press, Cambridge, 1993.