Chapter 2
In This Chapter
Getting to grips with utility
Understanding how economists model a representative consumer
Looking at people’s buying preferences
Consumer choice is the backbone of market economies. Today you can choose to buy from among more items than at any time in the past, and people are certainly taking advantage of the opportunity. In the United States, consumer spending accounts for roughly 70 percent of Gross Domestic Product, which is a hefty $12.4 trillion expenditure. When you look at the importance of consumer spending in our economy, you quickly see why economists want to understand the consumer as much as possible.
Consumers are people with individual preferences, ideas, backgrounds, histories, identities, and all manner of complicated personalities that can make understanding what they like and don’t like difficult. This could be a problem if you want to understand what makes a person tick, but what we want to understand is how people, given those tastes and preferences, decide what to buy and how markets respond to consumers’ choices.
Ultimately, microeconomists want to lay out a set of conditions that explain how consumers come to their decisions in a way that makes sense — we describe what we specifically mean by “makes sense” in this chapter — and how that then affects their behavior in the marketplace. This chapter shows you how to set the foundations of the microeconomist’s view of consumers — how they behave and why — which you can use when building more complicated models (such as the ones in Chapters 4 through 6).
There are many views about why people choose what they do, with psychologists and sociologists approaching the question in their own ways. In turn, microeconomists focus on one explanation for people making a given choice over another one: that the choice delivers more utility.
Consider the following example of a consumer to illustrate the two utility options in practice. Allan has three possible goods (tea, coffee, and cocoa) and has measured (in his own way) the utility he receives from consuming a unit of the three delicious hot beverages available (see Table 2-1). For a system of cardinal utility, you need to be able to ascribe a level of utility to each unit consumed, just as Allan does.
Table 2-1 Example of Cardinal Utility
Good |
Utility from Consuming the Good |
Tea |
10 |
Coffee |
7 |
Cocoa |
5 |
As the table shows, Allan prefers tea to coffee, and coffee to cocoa. Therefore, you can rewrite the table so that Allan’s preferences are expressed as ranks to provide the ordinal utility (see Table 2-2).
Table 2-2 Example of Ordinal Utility
Good |
Utility from Consuming the Good |
Rank of Choice |
Tea |
10 |
1 |
Coffee |
7 |
2 |
Cocoa |
5 |
3 |
As you can see, the ordinal utility preferences preserve the ranking of the preferences without using a particular value for utility. Crucially, therefore, you can easily transfer any representation of utility that’s cardinal into an ordinal representation — just by writing down the numbers in order. For cardinal utility, you need to know something more exact about what a person values than economists usually know about a person, and so by the principle of fewest assumptions, you encounter ordinal utility more often than cardinal.
Making assumptions is necessary as a first stage of modeling anything. A model doesn’t attempt to replicate everything in the world, but represents a simplified view of the world so that you can draw enough conclusions to make a reasoned argument. As a result, modeling begins by making some restrictions and looks at the small picture where those restrictions are binding (some of them can be relaxed later, after you develop an intuitive feeling for what’s going on in the model, and some of them hold throughout most models).
Economists begin with a model that has rational agents — in the sense that they are logically consistent in their behavior — and they make the fewest assumptions about the tastes or preferences of these agents. Because economists don’t know very much about the people they’re modeling — there are 7 billion people on Earth, after all — starting with what you think is common to them all makes sense.
A criticism sometimes leveled at the economists’ view of a representative “person” is that such a construction could describe a psychopath, in the sense that representative consumers follow their own interests and make a rational choice between options that allows them to maximize their own utility.
We aren’t psychiatrists and so can’t give a medical view on whether this description satisfies the conditions for diagnosing a psychopath, but we do want to point out a couple of flaws in this view of what economists think of as a representative agent:
We don’t mean to imply that the way economists model preferences has no issues. In fact, in the later section “Noting issues with the preference model,” we introduce a few points of criticism. We only mean that the psychopath objection isn’t really one of them.
Microeconomists want to look at the different ways in which a consumer may prefer one bundle of goods over another. This requires them to examine people’s preferences.
To illustrate how economists use these relations, let’s consider Allan’s preferences in hot beverages. In both the cardinal or the ordinal model, Allan prefers tea to coffee (see the earlier section “Contrasting two ways of approaching utility: Cardinal and ordinal”). In fact, Allan gets more utility from tea than from coffee, and so in this case Allan strongly prefers tea to coffee. Economists express this preference as follows:
If Allan were to get at least as much utility from tea (and possibly more) as he does from coffee, you’d say that the preference was weak and write:
If he were indifferent between the two, you’d write:
Indifference curves are a popular tool among economists for analyzing why consumers choose one option over another (Chapters 4 through 6 use them to look at how consumers choose, given a budget constraint). Here we explain the concept briefly and describe what these curves can tell you.
We plot a simple indifference curve in Figure 2-1: here are a few things you’re looking at. We imagine that over the course of a week, Allan allocates his consumption to tea and coffee so that each point of the indifference curve is a combination of a week’s tea and coffee usage that yields Allan exactly the same utility.
Figure 2-1 shows that if he wants to maintain the same utility while increasing his consumption of tea, he can only do so by reducing his consumption of coffee. An indifference curve tells you that the total utility from achieving coffee and tea must be a constant, so if tea goes up, coffee must come down. The slope of the indifference curve at any given point expresses this as the economic concept called the marginal rate of substitution (MRS). All points on the curve yield the same amount of utility, but the combinations of tea and coffee must yield a constant level of utility along the curve.
Figure 2-2 draws the MRS and annotates the original indifference curve to show how you depict it on a graph. Mathematically, the slope of the indifference curve at any given point is the MRS of Good 1 for Good 2 at that point. The tangent is a straight line with the same slope as the indifference curve at the point or at the number of cups of tea and coffee you’re evaluating. Both the tangent and the indifference curve have the same slope — which equals the marginal rate of substitution of tea for coffee at that point:
Indifference curves cannot cross. Figure 2-3 shows two indifference curves, which theoretically show the same level of utility along each curve. Bundles X and Y are along the same curve, I1. However, look at Bundle Z: It delivers a higher level of utility than Bundle Y and therefore can’t lie on the same line as Bundles X and Y. And yet, because the two curves cross, where they cross they must yield the same level of utility as each other. Thus, Bundle Z can’t be on the same indifference curve as both X and Y, and therefore can’t be on a curve that crosses I1.
Indifference curves tend to be convex, which means they have the scooped bow shape shown in Figures 2-1 through 2-3, where the marginal rate of substitution is negative along the entire curve. At any given point, getting more of Good 2 requires a greater sacrifice of Good 1, and the more of Good 2 you desire, the more of Good 1 you have to give up.
Two limiting cases apply (see Figure 2-4):
Mostly, though, unless disutility is involved, as may be in the case of goods that economists call bads, indifference curves are convex. In fact, in some cases they can be strictly convex, which means that the weighted average of a bundle of goods is preferred to an extreme bundle where only one of the two goods is consumed. For example, if the goods are health care and housing, it is not unreasonable to assume that people want some amount of both goods — they can’t live on health care or housing alone.
If you are sitting in on a seminar of economists, you may hear utility functions described as monotonic (note, not monotonous).
Relatedly, a monotonic transformation of an indifference curve or utility function is one that preserves the order of any particular ranking of utility of any bundles consumed. Table 2-3 shows Allan’s original utility (from Table 2-1) under three possible monotonic transformations: adding a number, multiplying by two, or cubing the number, and as you can see, the rank order is preserved.
Table 2-3 Example Utility after Three Monotonic Transformations
Good |
Utility from Consuming the Good |
Transformation (Adding 1) |
Transformation (Multiplying by 2) |
Transformation (Cubing) |
Tea |
10 |
11 |
20 |
1,000 |
Coffee |
7 |
8 |
16 |
343 |
Cocoa |
5 |
6 |
10 |
125 |
We want to examine briefly a couple of issues that people have raised with the model of consumer preferences. For now, please note them, and even if you fully accept them, keep in mind that using the preference model is still useful as a yardstick to compare with other versions — it may after all be worth knowing how models differ and from what they differ.
Lack of rationality: Experiments tend to confirm that when uncertainty is introduced into the choices, an individual’s weighting of utility may not be rational (as we describe rational in the earlier section “Acting rationally in economic terms: A mathematical tool”). For instance, take an offer of $10 now versus entry in a lottery where you have a 1 in 10 chance of earning $100. The expected gain from both offers is $10. The first offer gives $10 with a probability of 1, whereas the expected outcome of the second is 0.1 (that is, 1 in 10) times 100, which equals, yes that’s right, $10. If someone is strictly rational, as we have described rationality, that person will be indifferent between the two offers. But relatively few people would accept that the offer of $10 with certainty is the same as the option of $100 with a one in ten chance. So, people faced with uncertainty in their choices may not be rational in the way we have described.
A number of similar experiments show some quite consistent biases. One, for instance, is that people tend to value the prospect of losses more negatively than they value the prospect of gains positively, which means that they tend to do irrational things such as throwing money at a losing position rather than doing as rationality suggests and closing down their trading book and walking away.
Bounded rationality: People can be bounded by a number of constraints in their lives, including time, which may mean they can’t figure out their preferences and so they can’t optimize their utility. Instead, they go for “good enough,” because the time taken to make a decision, or their resources or their ability to think is constrained. Bounded rationality is becoming more widely used in economics, particularly in complex systems models. The key implication of the bounded rationality approach is that the inference economists make from applying utility and preference theory to markets isn’t always correct. Chapter 5 talks more about constraints.
By contrast, the behavioral economics approach seeks to map and explore the differences between the results the utility and preference models predict and what happens in reality. It does so by using lab experiments and real-world data and testing how preferences really work in people. Some results already show the existence of persistent biases in people’s reasoning. The example where people attach more weight to losses than their potential gains is one such bias.
Both these approaches — the behavioral and the bounded rationality approach — make some specific challenges to the model that we present. The key one is that people may not have such well-behaved preferences as economists like to ascribe to them, and therefore the results of such preferences may be less robust than economists would like them to be.