Utility theoryA theory postulated in economics to explain behavior of individuals based on the premise people can consistently order rank their choices depending upon their preferences. bases its beliefs upon individuals’ preferences. It is a theory postulated in economics to explain behavior of individuals based on the premise people can consistently rank order their choices depending upon their preferences. Each individual will show different preferences, which appear to be hard-wired within each individual. We can thus state that individuals’ preferences are intrinsic. Any theory, which proposes to capture preferences, is, by necessity, abstraction based on certain assumptions. Utility theory is a positive theoryTheory that seeks to explain an individual’s observed behavior and choices. that seeks to explain the individuals’ observed behavior and choices.The distinction between normative and positive aspects of a theory is very important in the discipline of economics. Some people argue that economic theories should be normative, which means they should be prescriptive and tell people what to do. Others argue, often successfully, that economic theories are designed to be explanations of observed behavior of agents in the market, hence positive in that sense. This contrasts with a normative theoryTheory that dictates that people should behave in the manner prescribed by it., one that dictates that people should behave in the manner prescribed by it. Instead, it is only since the theory itself is positive, after observing the choices that individuals make, we can draw inferences about their preferences. When we place certain restrictions on those preferences, we can represent them analytically using a utility functionA mathematical formulation that ranks the preferences of the individual in terms of satisfaction different consumption bundles provide.—a mathematical formulation that ranks the preferences of the individual in terms of satisfaction different consumption bundles provide. Thus, under the assumptions of utility theory, we can assume that people behaved as if they had a utility function and acted according to it. Therefore, the fact that a person does not know his/her utility function, or even denies its existence, does not contradict the theory. Economists have used experiments to decipher individuals’ utility functions and the behavior that underlies individuals’ utility.
To begin, assume that an individual faces a set of consumption “bundles.” We assume that individuals have clear preferences that enable them to “rank order” all bundles based on desirability, that is, the level of satisfaction each bundle shall provide to each individual. This rank ordering based on preferences tells us the theory itself has ordinal utilityUtility that can only represent relative levels of satisfaction between two or more alternatives, that is, rank orders them.—it is designed to study relative satisfaction levels. As we noted earlier, absolute satisfaction depends upon conditions; thus, the theory by default cannot have cardinal utilityUtility that can represent the absolute level of satisfaction., or utility that can represent the absolute level of satisfaction. To make this theory concrete, imagine that consumption bundles comprise food and clothing for a week in all different combinations, that is, food for half a week, clothing for half a week, and all other possible combinations.
The utility theory then makes the following assumptions:
If one thinks of preference orderings as comparative relationships, then it becomes simpler to construct examples where this assumption is violated. So, in “beats”—as in A beat B in college football. These are relationships that are easy to see. For example, if University of Florida beats Ohio State, and Ohio State beats Georgia Tech, it does not mean that Florida beats Georgia Tech. Despite the restrictive nature of the assumption, it is a critical one. In mathematics, it is called the assumption of transitivity of preferences.
Whenever these four assumptions are satisfied, then the preferences of the individual can be represented by a well-behaved utility functionA representation of the preferences of the individual that satisfies the assumptions of completeness, monotonicity, mix-is-better, and rationality..The assumption of convexity of preferences is not required for a utility function representation of an individual’s preferences to exist. But it is necessary if we want that function to be well behaved. Note that the assumptions lead to “a” function, not “the” function. Therefore, the way that individuals represent preferences under a particular utility function may not be unique. Well-behaved utility functions explain why any comparison of individual people’s utility functions may be a futile exercise (and the notion of cardinal utility misleading). Nonetheless, utility functions are valuable tools for representing the preferences of an individual, provided the four assumptions stated above are satisfied. For the remainder of the chapter we will assume that preferences of any individual can always be represented by a well-behaved utility function. As we mentioned earlier, well-behaved utility depends upon the amount of wealth the person owns.
Utility theory rests upon the idea that people behave as if they make decisions by assigning imaginary utility values to the original monetary values. The decision maker sees different levels of monetary values, translates these values into different, hypothetical terms (“utils”), processes the decision in utility terms (not in wealth terms), and translates the result back to monetary terms. So while we observe inputs to and results of the decision in monetary terms, the decision itself is made in utility terms. And given that utility denotes levels of satisfaction, individuals behave as if they maximize the utility, not the level of observed dollar amounts.
While this may seem counterintuitive, let’s look at an example that will enable us to appreciate this distinction better. More importantly, it demonstrates why utility maximization, rather than wealth maximization, is a viable objective. The example is called the “St. Petersburg paradox.” But before we turn to that example, we need to review some preliminaries of uncertainty: probability and statistics.