4.1 The Consumer’s Preferences and the Concept of Utility

Consumers’ preferences underlie every decision they make. Economists think of consumers as making rational choices about what they like best, given the constraints they face.

Assumptions about Consumer Preferences

Consumers make many choices every day about what to buy and what not to buy. These choices involve many different goods: Buy a giant bag of Twizzlers and walk home, or buy a bus ticket and leave a sweet tooth unsatisfied? Buy a new video game or buy a new water pump for the car? Buy a ticket to the ball game or go to a bar for drinks with friends and watch the game on TV? To understand how consumers form their preferences for thousands of goods and services, we need to make some simplifying assumptions. Specifically, we assume that all decisions about what to buy share four properties that help consumers determine their preferences about all the possible combinations of goods and services they can buy.

consumption bundle

A set of goods or services a consumer considers purchasing.

  1. Completeness and rankability. This assumption implies that consumers can make comparisons across all sets of goods that they consider. Economists use the term consumption bundle (or just bundle) to describe any collection of these goods. The assumption means that, given any two bundles, a consumer can decide which she prefers (or whether she is indifferent, meaning she likes them the same). This assumption is important because it means that we can apply economic theory to any bundle of goods we want to discuss. Whether the bundle includes sapphires and SUVs; movies, motorcycles, modern art, and marshmallows; or iPads, Ikea furniture, and iceberg lettuce, the consumer can decide which bundle she likes better.

    Note, however, that this assumption does not tell us what kinds of bundles the consumer will like more than others. It just implies she is able to determine if one is better than the other.

  2. For most goods, more is better than less (or at least more is no worse than less). In general, more of a good thing is good. If we like a car that is safe in a crash, we would like that same car even better if it were even safer.1

    1 There may come a point at which more of a good thing stops being better. Economists call this a satiation point. For instance, the first jelly bean may make us happy, but the 1,437th jelly bean might actually make us sick if we ate it, making us worse off than had we eaten only 1,436. However, because people can sometimes save extra jelly beans for later, trade them with someone else for something they want, or just give them away, satiation points tend not to be very important in practice.

    In addition, to keep things relatively simple, we also assume that consumers can discard unwanted goods at no cost, a concept economists call “free disposal.”

    107

  3. Transitivity. For any three bundles of goods (call them A, B, and C), if a consumer prefers A to B and also prefers B to C, then she prefers A to C. If you prefer apples to oranges, and you prefer oranges to bananas, then transitivity implies that you must also prefer an apple to a banana. Note that, as always, we are holding everything else constant when making these comparisons. Transitivity does not mean that you prefer apples to bananas in all situations, only that, at a given moment, you prefer apples to bananas. Transitivity imposes logical consistency on the preferences.

  4. The more a consumer has of a particular good, the less she is willing to give up of something else to get even more of that good. The idea behind this assumption is that consumers like variety. If you like birthday cake and haven’t had cake lately, you might be willing to give up a lot for some cake. You might pay a high price for a cake, take the afternoon to bake a cake, or trade away your last carton of milk for some cake. On the other hand, if you’ve just polished off two-thirds of a cake, you are unlikely to be willing to pay much money for more, and you may very well want to trade the rest of the cake to get back some of that carton of milk.2

    2 In some special cases, this might not be right. Most people would prefer having a second water ski or a second snow ski to having one of each, for example. But it’s almost always true and makes the analysis much simpler.

The Concept of Utility

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.

utility

A measure of how satisfied a consumer is.

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.

utility function

A mathematical function that describes the relationship between what consumers actually consume and their level of well-being.

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 = J0.7K0.3. 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.

108

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).

Marginal Utility

marginal utility

The additional utility a consumer receives from an additional unit of a good or service.

One of the most important concepts related to utility functions is marginal utility, the extra utility a consumer receives from a 1-unit increase in consumption.3 Each good in a utility function has its own marginal utility. Using the Junior Mints and Kit Kats utility function, for example, the marginal utility of Junior Mints, MUJ, would be

3 Marginal utility can be calculated for any given utility function.

image

where ΔJ is the small (1-unit) change in the number of Junior Mints the consumer eats and ΔU(J, K) is the change in utility she gets from doing so. Likewise, the marginal utility of consuming Kit Kats is given by

image

Later in this chapter, we see that marginal utility is the key to understanding the consumption choices a person makes.

Utility and Comparisons

One important point about utility and the four preference assumptions we started with is that they allow us to rank all bundles of goods for a particular consumer, but they do not allow us to determine how much more a consumer likes one bundle than another. In mathematical terms, we have an ordinal ranking of bundles (we can line them up from best to worst), but not a cardinal ranking (which would allow us to say by exactly how much a consumer prefers one bundle to another). The reason for this is that the units in which we measure utility are essentially arbitrary.

An example will make this clearer. Let’s say we define a unit of measurement for utility that we call a “util.” And let’s say we have three bundles: A, B, and C, and a consumer who likes bundle A the most and bundle C the least. We might then assign these three bundles values of 8, 7, and 6 utils, respectively. The difficulty is that we just as easily could have assigned the bundles values of 8, 7, and 2 utils (or 19, 17, and 16 utils; or 67, 64, and 62 utils, etc.) and this would still perfectly describe the situation. You can say that you like something better, but how can you describe how happy it makes you, objectively? There is no real-world unit of measurement like dollars, grams, or inches with which to measure utility, so we can shift, stretch, or squeeze a utility function without altering any of its observable implications, as long as we don’t change the ordering of preferences over bundles.4

4 In mathematical parlance, these order-preserving shifts, squeezes, or stretches of a utility function are called monotonic transformations. Any monotonic transformation of a utility function will imply exactly the same preferences for the consumer as the original utility function. Consider our first example of a utility function from consuming Junior Mints and Kit Kats, U = J × K. Suppose that it were U = 8J × K + 12 instead. For any possible bundle of Junior Mints and Kit Kats, this new utility function will imply the same ordering of the consumer’s utility levels as would the old function. (You can put in a few specific numbers to test this.) Because the consumer’s relative preferences don’t change, she will make the same decisions on how much of each good to consume with either utility function.

109

It often doesn’t really matter that we have only an ordinal ranking of utility. We can still provide answers to the important questions about how consumers behave and how this behavior results in a downward-sloping demand curve.

welfare economics

The area of economics concerned with the economic well-being of society as a whole.

One set of questions we will not be able to answer, though, are questions that make interpersonal comparisons, meaning comparisons of one consumer’s utility to another’s. We can say that if one person prefers Concert A tickets to Concert B tickets and the other person prefers the reverse, then both will be better off if the first person gets the A tickets and the second person gets the Bs. But if they both prefer A, we have no easy way to tell who would be better off getting the A tickets. (These types of questions relate to the area known as welfare economics, which we discuss in several places later in the book. For now, however, we focus on the preferences of one consumer at a time.)

Just as important as the assumptions we make when analyzing utility functions are the assumptions that we do not make. For one, we do not impose particular preferences on consumers. An individual is free to prefer dogs or ferrets as pets, just as long as they follow the four preference assumptions. We don’t make value judgments about what consumers should or shouldn’t prefer. Even if it is Justin Bieber music, preferences are just a description of how a person feels. We also don’t require that preferences remain constant over time. Someone may prefer sleeping to seeing a movie tonight, but tomorrow prefer the opposite.

The concepts of utility and utility functions are general enough to account for a consumer’s preferences over any number of goods and the various bundles into which they can be combined. As we proceed in building our model of consumer behavior, however, we focus on a simple model in which a consumer buys a bundle with only two goods. This approach is an easy way to see how things work, and the ideas still apply in the more complicated situations.