Given these assumptions about preferences, we could create a list of all the consumer’s preferences between any possible bundles for every decision. But because such a list would include billions of possible bundles, it would be basically useless as a decision aid.

Instead, economists use the concept of utility and a mathematical description called a utility function to describe preferences more simply. Utility describes how satisfied a consumer is. For practical purposes, you can think of utility as a fancy word for happiness or well-being. It is important to realize that utility is not a measure of how rich a consumer is. Income may affect utility, but it is just one of many factors that do so.

A utility function summarizes the relationship between what consumers consume and their level of well-being. A function is a mathematical relationship that links a set of inputs to an output. For instance, if you combine the inputs eggs, flour, sugar, vanilla, butter, frosting, and candles in just the right way, you end up with the output of a birthday cake. In consumer behavior, the inputs to a utility function are the different things that can give a person utility. Examples of inputs to the utility function include traditional goods and services like cars, candy bars, health club memberships, and airplane rides. But there are many other types of inputs to utility as well, including scenic views, a good night’s sleep, spending time with friends, and the pleasure that comes from giving to charity. The output of the utility function is the consumer’s utility level. By mapping the bundles a consumer considers to measures of the consumer’s level of well-being—this bundle provides so much utility, that bundle provides so much utility, and so on—a utility function gives us a concise way to rank a consumer’s bundles.

Utility functions can take a variety of mathematical forms. Let’s look at the utility someone enjoys from consuming Junior Mints and Kit Kats. Generically, we can write this utility level as U = U(J, K), where U(J, K) is the utility function and J and K are, respectively, the number of Junior Mints and Kit Kats the consumer eats. An example of a specific utility function for this consumer is U = J × K. In this case, utility equals the product of the number of Junior Mints and Kit Kats she eats. But it could instead be that the consumer’s utility equals the total number of Junior Mints and Kit Kats eaten. In that case, the utility function is U = J + K. Yet another possibility is that the consumer’s utility is given by U = J^0.7K^0.3. Because the exponent on Junior Mints (0.7) is larger than that on Kit Kats (0.3), this utility function implies that a given percentage increase in Junior Mints consumed will raise utility more than the same percentage increase in Kit Kats.

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These are just a few examples from the large variety of possible utility functions we could imagine consumers having for these or any other combination of goods. At this point in our analysis of consumer behavior, we don’t have to be too restrictive about the form any particular utility function takes. Because utility functions are used to represent preferences, however, they have to conform to our four assumptions about preferences (rankability and completeness, more is better, transitivity, and variety is important).