In order to provide a foundation for our study of utility, we need to make three assumptions about behavior that seem quite reasonable. These are intended to provide a simple framework for what we mean when we say people make choices in a rational and consistent way.
Completeness
When faced with two options, A or B, it seems reasonable that a person can say whether he or she prefers A to B, or B to A, or finds them equally attractive. In other words, we assume that people are not paralyzed by indecision—that they can actually state what they prefer. This assumption rules out the situation of the mythical jackass who, finding himself halfway between a bale of hay and a sack of oats, starved to death because he was unable to decide which one to choose.
We can extend this example a bit by assuming that people can make such preference judgements about any possible options presented to them. That is, we will assume preferences arecomplete. For any options presented, a person always is able to state which is preferred.
Complete preferences The assumption that an individual is able to state which of any two options is preferred.
A P P L I C A T I O N 2 . 1 Can Money Buy Health and Happiness?
Although measuring utility directly may be impossible, econ- omists have been quite willing to explore various approxi- mations. Perhaps the most widely used measure is annual income. As the old joke goes, even if money can’t buy happiness, it can buy you any kind of sadness you want.
Here we focus specifically on the connections between income, health, and happiness.
Income and Health
An individual’s health is certainly one aspect of his or her utility, and the relationship between income and health has been intensively studied. Virtually all of these studies con- clude that people who have higher incomes enjoy better health. For example, comparing men of equal ages, life expectancy is about 7 years shorter for those with incomes in the bottom quarter of the population than for those in the top quarter. Similar differences show up in the preva- lence of various diseases—rates of heart disease and can- cer are much lower for those in the upper-income group.
Clearly it appears that money can ‘‘buy’’ good health.
There is less agreement among economists about why more income ‘‘buys’’ good health.1The standard explana- tion is that higher incomes allow people greater access to health care. Higher incomes may also be associated with taking fewer health-related risks (e.g., smoking or excessive alcohol consumption). In fact, these factors play relatively little role in determining an individual’s health. For example, the connection between income and health persists in coun- tries with extensive national health insurance systems and after controlling for the risky things people do. These find- ings have led some economists to question the precise causality in the income-health linkage. Is it possible that the health is affecting income rather than vice versa? There are two general ways in which a person’s health may affect his or her income. First, health may affect the kinds or amount of work that a person can do. Disabilities that limit a person’s hours of work or that prevent people from taking some good-paying jobs can have a major negative effect on income. Similarly, large health-related expenses can prevent a person from accumulating wealth, thereby reducing the income that might be received in the form of dividends or interest. As in many economic situations where the causal
connection between two variables runs both ways, sorting out the precise relationship between income and health from the available data can be difficult.
Income and Happiness
A more general approach to the relationship between income and utility asks people to rank how happy they are on a numerical scale. Although people’s answers show con- siderable variability, the data do show certain regularities.
People with higher incomes report that they are happier than are those with lower incomes in virtually every survey. For example, the economic historian Richard Easterlin reports on measured happiness in the United States on a 4-point scale.
He finds that people with incomes above $75,000 per year have an average happiness ranking of 2.8, whereas those with incomes below $20,000 per year have a ranking below 2.0.2 Surveys from other countries show much the same result.
One puzzle in the association between income and happiness is that a person’s happiness does not seem to rise as he or she becomes more affluent during his or her lifetime. But people always seem to think they are better off than they were in the past and will be even better off in the future. Easterlin argues that such findings can be explained by the fact that people’s aspirations rise with their incomes—
getting richer as one gets older is offset by rising expecta- tions in its total effect on happiness.
TOTHINKABOUT
1. A higher income makes it possible for a person to con- sume bundles of goods that were previously unafford- able. He or she must necessarily be better off. Isn’t that all we need to know?
2. Sometimes people are said to be poor if they have to spend more than, say, 25 percent of their income on food. Why would spending a large fraction of one’s income on food tend to indicate some degree of eco- nomic deprivation? How would you want to adjust the 25 percent figure for factors such as family size or the number of meals eaten in restaurants?
1For a more complete discussion of the issues raised in this section, see James P. Smith, ‘‘Healthy Bodies and Thick Wallets: The Dual Relationship between Health and Economic Status,’’Journal of Eco- nomic Perspectives(Spring 1999): 145–166.
2Richard A. Easterlin, ‘‘Income and Happiness: Toward a Unified Theory’’Economic Journal, July 2001: 465–484.
Transitivity
In addition to assuming that people can state their preferences clearly and completely, we also might expect these preferences to exhibit some sort of internal consistency. That is, we would not expect a person to say contradictory things about what he or she likes. This presumption can be formalized by the assumption that preferences aretransitive. If a person states, ‘‘I prefer A to B’’ and
‘‘I prefer B to C,’’ we would expect that he or she would also say, ‘‘I prefer A to C.’’ A person who instead stated the contrary (‘‘I prefer C to A’’) would appear to be hopelessly confused. Economists do not believe people suffer from such confusions (at least not on a regular basis), so they generally assume them away for most purposes.
More Is Better: Defining an Economic ‘‘Good’’
A third assumption we make about preferences is that a person prefers more of a good to less. In Figure 2.1, all points in the darkly shaded area are preferred to the amounts ofX* of goodXandY*of goodY. Movement from pointX*,Y* to any point in the shaded area is an unambiguous improvement, since in this area this person gets more of one good without taking less of another. This idea leads us to
F I G U R E 2 . 1
Mor e o f a Go od Is Pr e f er r ed t o Les s Quantity of Y
per week
Y*
Quantity of X per week
?
?
X*
0
The darkly shaded area represents those combinations ofXandYthat are unambiguously preferred to the combinationX*,Y*. This is why goods are called ‘‘goods’’; individuals prefer having more of any good rather than less. Combinations ofXandYin the lightly shaded area are inferior to the combinationX*,Y*, whereas those in the questionable areas may or may not be superior toX*,Y*.
Transitivity of preferences
The property that ifAis preferred toB,andBis preferred toC,thenA must be preferred toC.
define an ‘‘economic good’’ as an item that yields positive benefits to people.1That is, more of a good is, by definition, better. Combinations of goods in the lightly shaded area of Figure 2.1 are definitely inferior toX*,Y* since they offer less of bothgoods.
These three assumptions about preferences are about enough to justify our use of the simple utility function that we introduced earlier. That is, if people obey these assumptions, they will make choices in a way consistent with using such a function. Notice that economists do not claim that people actually consult a utility function when deciding, say, what brand of toothpaste to buy. Instead, we assume that people have relatively well-defined preferences and make decisionsas ifthey consulted such a function. Remember Friedman’s pool player analogy from Chapter 1—the laws of physics can explain his or her shots even though the player knows nothing about physics. Similarly, the theory of utility can explain economic choices even though no one actually has a utility function embedded in his or her brain. Whether economists actually have to consider exactly what does go on in the brains of people has become a topic of some debate in recent years. In Application 2.2: Should Economists Care about How the Mind Works? we provide a first look at that debate.