C H A P T E R

5

Uncertainty and
Consumer Behavior
CHAPTER OUTLINE
5.1 Describing Risk

S

o far, we have assumed that prices, incomes, and other variables are known with certainty. However, many of the choices that people make involve considerable uncertainty. Most people, for example, borrow to finance large purchases, such as a house or a college education, and plan to pay for them out of future income. But for most of us, future incomes are uncertain. Our earnings can go up or down; we can be promoted or demoted, or even lose our jobs. And if we delay buying a house or investing in a college education, we risk price increases that could make such purchases less affordable. How should we take these uncertainties into account when making major consumption or investment decisions?
Sometimes we must choose how much risk to bear. What, for example, should you do with your savings? Should you invest your money in something safe, such as a savings account, or something riskier but potentially more lucrative, such as the stock market? Another example is the choice of a job or career. Is it better to work for a large, stable company with job security but slim chance for advancement, or is it better to join (or form) a new venture that offers less job security but more opportunity for advancement?
To answer such questions, we must examine the ways that people can compare and choose among risky alternatives. We will do this by taking the following steps:
1. In order to compare the riskiness of alternative choices, we need to quantify risk. We therefore begin this chapter by discussing measures of risk.
2. We will examine people’s preferences toward risk. Most people find risk undesirable, but some people find it more undesirable than others.
3. We will see how people can sometimes reduce or eliminate risk.
Sometimes risk can be reduced by diversification, by buying insurance, or by investing in additional information.
4. In some situations, people must choose the amount of risk they wish to bear. A good example is investing in stocks or bonds. We will see that such investments involve trade-offs between the monetary gain that one can expect and the riskiness of that gain.
5. Sometimes demand for a good is driven partly or entirely by speculation—people buy the good because they think its price will rise.

160

5.2 Preferences Toward Risk
165

5.3 Reducing Risk
170

*5.4 The Demand for Risky Assets
176

5.5 Bubbles
185

5.6 Behavioral Economics
189

LIST OF EXAMPLES
5.1 Deterring Crime
164

5.2 Business Executives and the Choice of Risk
169

5.3 The Value of Title Insurance
When Buying a House
173

5.4 The Value of Information in an Online Consumer
Electronics Market
175

5.5 Doctors, Patients, and the
Value of Information
175

5.6 Investing in the Stock Market
183

5.7 The Housing Price Bubble (I)
186

5.8 The Housing Price Bubble (II)
188

5.9 Selling a House
192

5.10 New York City Taxicab
Drivers
196

159

160 PART 2 • Producers, Consumers, and Competitive Markets
We will see how this can lead to a bubble, where more and more people, convinced that the price will keep rising, buy the good and push its price up further—until eventually the bubble bursts and the price plummets.
In a world of uncertainty, individual behavior may sometimes seem unpredictable, even irrational, and perhaps contrary to the basic assumptions of consumer theory. In the final section of this chapter, we offer an overview of the flourishing field of behavioral economics, which, by introducing important ideas from psychology, has broadened and enriched the study of microeconomics.

5.1 Describing Risk
To describe risk quantitatively, we begin by listing all the possible outcomes of a particular action or event, as well as the likelihood that each outcome will occur.1 Suppose, for example, that you are considering investing in a company that explores for offshore oil. If the exploration effort is successful, the company’s stock will increase from $30 to $40 per share; if not, the price will fall to $20 per share. Thus there are two possible future outcomes: a $40-per-share price and a $20-per-share price.

Probability
• probability Likelihood that a given outcome will occur.

Probability is the likelihood that a given outcome will occur. In our example, the probability that the oil exploration project will be successful might be 1/4 and the probability that it is unsuccessful 3/4. (Note that the probabilities for all possible events must add up to 1.)
Our interpretation of probability can depend on the nature of the uncertain event, on the beliefs of the people involved, or both. One objective interpretation of probability relies on the frequency with which certain events tend to occur.
Suppose we know that of the last 100 offshore oil explorations, 25 have succeeded and 75 failed. In that case, the probability of success of 1/4 is objective because it is based directly on the frequency of similar experiences.
But what if there are no similar past experiences to help measure probability? In such instances, objective measures of probability cannot be deduced and more subjective measures are needed. Subjective probability is the perception that an outcome will occur. This perception may be based on a person’s judgment or experience, but not necessarily on the frequency with which a particular outcome has actually occurred in the past. When probabilities are subjectively determined, different people may attach different probabilities to different outcomes and thereby make different choices. For example, if the search for oil were to take place in an area where no previous searches had ever occurred, I might attach a higher subjective probability than you to the chance that the project will succeed: Perhaps I know more about the project or I have a better understanding of the oil business and can therefore make better use of our common information. Either different information or different abilities to process the same information can cause subjective probabilities to vary among individuals.

1

Some people distinguish between uncertainty and risk along the lines suggested some 60 years ago by economist Frank Knight. Uncertainty can refer to situations in which many outcomes are possible but the likelihood of each is unknown. Risk then refers to situations in which we can list all possible outcomes and know the likelihood of each occurring. In this chapter, we will always refer to risky situations, but will simplify the discussion by using uncertainty and risk interchangeably.

CHAPTER 5 • Uncertainty and Consumer Behavior 161

Regardless of the interpretation of probability, it is used in calculating two important measures that help us describe and compare risky choices. One measure tells us the expected value and the other the variability of the possible outcomes.

Expected Value
The expected value associated with an uncertain situation is a weighted average of the payoffs or values associated with all possible outcomes. The probabilities of each outcome are used as weights. Thus the expected value measures the central tendency—the payoff or value that we would expect on average.
Our offshore oil exploration example had two possible outcomes: Success yields a payoff of $40 per share, failure a payoff of $20 per share. Denoting
“probability of” by Pr, we express the expected value in this case as

• expected value Probabilityweighted average of the payoffs associated with all possible outcomes. • payoff Value associated with a possible outcome.

Expected value = Pr(success)($40/share) + Pr(failure)($20/share)
= (1/4)($40/share) + (3/4)($20/share) = $25/share
More generally, if there are two possible outcomes having payoffs X1 and X2 and if the probabilities of each outcome are given by Pr1 and Pr2, then the expected value is
E(X) = Pr1X1 + Pr2X2
When there are n possible outcomes, the expected value becomes
E(X) = Pr1X1 + Pr2X2 + c + PrnXn

Variability
Variability is the extent to which the possible outcomes of an uncertain situation differ. To see why variability is important, suppose you are choosing between two part-time summer sales jobs that have the same expected income ($1500).
The first job is based entirely on commission—the income earned depends on how much you sell. There are two equally likely payoffs for this job: $2000 for a successful sales effort and $1000 for one that is less successful. The second job is salaried. It is very likely (.99 probability) that you will earn $1510, but there is a .01 probability that the company will go out of business, in which case you would earn only $510 in severance pay. Table 5.1 summarizes these possible outcomes, their payoffs, and their probabilities.
Note that these two jobs have the same expected income. For Job 1, expected income is .5($2000) ϩ .5($1000) ϭ $1500; for Job 2, it is .99($1510) ϩ .01($510) ϭ
$1500. However, the variability of the possible payoffs is different. We measure

TABLE 5.1

INCOME FROM SALES JOBS
OUTCOME 1

OUTCOME 2
PROBABILITY

INCOME ($)

EXPECTED
INCOME ($)

2000

.5

1000

1500

1510

.01

510

1500

PROBABILITY

INCOME ($)

Job 1: Commission

.5

Job 2: Fixed Salary

.99

• variability Extent to which possible outcomes of an uncertain event differ.

162 PART 2 • Producers, Consumers, and Competitive Markets
TABLE 5.2

DEVIATIONS FROM EXPECTED INCOME ($)
OUTCOME 1

DEVIATION

OUTCOME 2

DEVIATION

Job 1

• standard deviation Square root of the weighted average of the squares of the deviations of the payoffs associated with each outcome from their expected values. 500

1000

−500

Job 2

• deviation Difference between expected payoff and actual payoff.

2000
1510

10

510

−990

variability by recognizing that large differences between actual and expected payoffs (whether positive or negative) imply greater risk. We call these differences deviations. Table 5.2 shows the deviations of the possible income from the expected income from each job.
By themselves, deviations do not provide a measure of variability. Why?
Because they are sometimes positive and sometimes negative, and as you can see from Table 5.2, the average of the probability-weighted deviations is always 0.2
To get around this problem, we square each deviation, yielding numbers that are always positive. We then measure variability by calculating the standard deviation: the square root of the average of the squares of the deviations of the payoffs associated with each outcome from their expected values.3
Table 5.3 shows the calculation of the standard deviation for our example.
Note that the average of the squared deviations under Job 1 is given by
.5($250,000) + .5($250,000) = $250,000
The standard deviation is therefore equal to the square root of $250,000, or $500.
Likewise, the probability-weighted average of the squared deviations under Job 2 is
.99($100) + .01($980,100) = $9900
The standard deviation is the square root of $9900, or $99.50. Thus the second job is much less risky than the first; the standard deviation of the incomes is much lower.4
The concept of standard deviation applies equally well when there are many outcomes rather than just two. Suppose, for example, that the first summer job yields incomes ranging from $1000 to $2000 in increments of $100 that are all equally likely. The second job yields incomes from $1300 to $1700 (again in increments of $100) that are also equally likely. Figure 5.1 shows the alternatives

TABLE 5.3

CALCULATING VARIANCE ($)
OUTCOME 1

DEVIATION
SQUARED

OUTCOME 2

DEVIATION
SQUARED

WEIGHTED AVERAGE
DEVIATION SQUARED

Job 1

2000

250,000

1000

250,000

250,000

Job 2

1510

100

510

980,100

9900

STANDARD
DEVIATION
500
99.50

2

For Job 1, the average deviation is .5($500) ϩ .5(−$500) ϭ 0; for Job 2 it is .99($10) ϩ .01(−$990) ϭ 0.

3

Another measure of variability, variance, is the square of the standard deviation.

4

In general, when there are two outcomes with payoffs X1 and X2, occurring with probability Pr1 and Pr2, and E(X) is the expected value of the outcomes, the standard deviation is given by s, where s 2 = Pr1[(X1 - E(X))2] + Pr2[(X2 - E(X))2]

CHAPTER 5 • Uncertainty and Consumer Behavior 163

Probability

F IGURE 5.1

OUTCOME PROBABILITIES FOR TWO
JOBS

0.2
Job 2
0.1
Job 1

$1000

$1500

$2000

The distribution of payoffs associated with Job
1 has a greater spread and a greater standard deviation than the distribution of payoffs associated with Job 2. Both distributions are flat because all outcomes are equally likely.

Income

graphically. (If there had been only two equally probable outcomes, then the figure would be drawn as two vertical lines, each with a height of 0.5.)
You can see from Figure 5.1 that the first job is riskier than the second. The
“spread” of possible payoffs for the first job is much greater than the spread for the second. As a result, the standard deviation of the payoffs associated with the first job is greater than that associated with the second.
In this particular example, all payoffs are equally likely. Thus the curves describing the probabilities for each job are flat. In many cases, however, some payoffs are more likely than others. Figure 5.2 shows a situation in which the most extreme payoffs are the least likely. Again, the salary from Job 1 has a greater standard deviation. From this point on, we will use the standard deviation of payoffs to measure the degree of risk.

Decision Making
Suppose you are choosing between the two sales jobs described in our original example. Which job would you take? If you dislike risk, you will take the second job: It offers the same expected income as the first but with less risk. But suppose we add $100 to each of the payoffs in the first job, so that the expected payoff increases from $1500 to $1600. Table 5.4 gives the new earnings and the squared deviations.

Probability
0.3

F IGURE 5.2

0.2

UNEQUAL PROBABILITY OUTCOMES

Job 2

0.1

Job 1
$1000

$1500

$2000

Income

The distribution of payoffs associated with Job 1 has a greater spread and a greater standard deviation than the distribution of payoffs associated with Job 2. Both distributions are peaked because the extreme payoffs are less likely than those near the middle of the distribution.

164 PART 2 • Producers, Consumers, and Competitive Markets
TABLE 5.4

INCOMES FROM SALES JOBS—MODIFIED ($)

OUTCOME 1

DEVIATION
SQUARED

OUTCOME 2

DEVIATION
SQUARED

EXPECTED
INCOME

Job 1

2100

250,000

1100

250,000

1600

Job 2

1510

100

510

980,100

1500

STANDARD
DEVIATION
500
99.50

The two jobs can now be described as follows:
Job 1:

Expected Income ϭ $1600

Standard Deviation ϭ $500

Job 2:

Expected Income ϭ $1500

Standard Deviation ϭ $99.50

Job 1 offers a higher expected income but is much riskier than Job 2. Which job is preferred depends on the individual. While an aggressive entrepreneur who doesn’t mind taking risks might choose Job 1, with the higher expected income and higher standard deviation, a more conservative person might choose the second job.
People’s attitudes toward risk affect many of the decisions they make. In
Example 5.1 we will see how attitudes toward risk affect people’s willingness to break the law, and how this has implications for the fines that should be set for various violations. Then in Section 5.2, we will further develop our theory of consumer choice by examining people’s risk preferences in greater detail.

E XA MPLE 5.1 DETERRING CRIME
Fines may be better than incarceration in deterring certain types of crimes, such as speeding, doubleparking, tax evasion, and air polluting.5 A person choosing to violate the law in these ways has good information and can reasonably be assumed to be behaving rationally.
Other things being equal, the greater the fine, the more a potential criminal will be discouraged from committing the crime. For example, if it cost nothing to catch criminals, and if the crime imposed a calculable cost of $1000 on society, we might choose to catch all violations and impose a fine of $1000 on each. This practice would discourage people whose benefit from engaging in the activity was less than the $1000 fine.
In practice, however, it is very costly to catch lawbreakers. Therefore, we save on administrative costs by imposing relatively high fines (which are no more costly to collect than low fines), while allocating

5

resources so that only a fraction of the violators are apprehended. Thus the size of the fine that must be imposed to discourage criminal behavior depends on the attitudes toward risk of potential violators.
Suppose that a city wants to deter people from double-parking. By double-parking, a typical resident saves $5 in terms of his own time for engaging in activities that are more pleasant than searching for a parking space. If it costs nothing to catch a double-parker, a fine of just over $5—say, $6— should be assessed every time he double-parks.
This policy will ensure that the net benefit of double-parking (the $5 benefit less the $6 fine) would be less than zero. Our citizen will therefore choose to obey the law. In fact, all potential violators whose benefit was less than or equal to $5 would be discouraged, while a few whose benefit was greater than $5 (say, someone who double-parks because of an emergency) would violate the law.

This discussion builds indirectly on Gary S. Becker, “Crime and Punishment: An Economic
Approach,” Journal of Political Economy (March/April 1968): 169–217. See also A. Mitchell Polinsky and Steven Shavell, “The Optimal Tradeoff Between the Probability and the Magnitude of Fines,”
American Economic Review 69 (December 1979): 880–91.

CHAPTER 5 • Uncertainty and Consumer Behavior 165

In practice, it is too costly to catch all violators.
Fortunately, it’s also unnecessary. The same deterrence effect can be obtained by assessing a fine of
$50 and catching only one in ten violators (or perhaps a fine of $500 with a one-in-100 chance of being caught). In each case, the expected penalty is $5, i.e.,
[$50][.1] or [$500][.01]. A policy that combines a high fine and a low probability of apprehension is likely to reduce enforcement costs. This approach is especially effective if drivers don’t like to take risks. In our example, a $50 fine with a .1 probability of being

caught might discourage most people from violating the law. We will examine attitudes toward risk in the next section.
A new type of crime that has become a serious problem for music and movie producers is digital piracy; it is particularly difficult to catch and fines are rarely imposed. Nevertheless, fines that are levied are often very high. In 2009, a woman was fined $1.9 million for illegally downloading
24 songs. That amounts to a fine of $80,000 per song. 5.2 Preferences Toward Risk
We used a job example to show how people might evaluate risky outcomes, but the principles apply equally well to other choices. In this section, we concentrate on consumer choices generally and on the utility that consumers obtain from choosing among risky alternatives. To simplify things, we’ll consider the utility that a consumer gets from his or her income—or, more appropriately, the market basket that the consumer’s income can buy. We now measure payoffs, therefore, in terms of utility rather than dollars.
Figure 5.3 (a) shows how we can describe one woman’s preferences toward risk. The curve 0E, which gives her utility function, tells us the level of utility
(on the vertical axis) that she can attain for each level of income (measured in thousands of dollars on the horizontal axis). The level of utility increases from
10 to 16 to 18 as income increases from $10,000 to $20,000 to $30,000. But note that marginal utility is diminishing, falling from 10 when income increases from
0 to $10,000, to 6 when income increases from $10,000 to $20,000, and to 2 when income increases from $20,000 to $30,000.
Now suppose that our consumer has an income of $15,000 and is considering a new but risky sales job that will either double her income to $30,000 or cause it to fall to $10,000. Each possibility has a probability of .5. As Figure 5.3 (a) shows, the utility level associated with an income of $10,000 is 10 (at point A) and the utility level associated with an income of $30,000 is 18 (at E). The risky job must be compared with the current $15,000 job, for which the utility is 13.5 (at B).
To evaluate the new job, she can calculate the expected value of the resulting income. Because we are measuring value in terms of her utility, we must calculate the expected utility E(u) that she can obtain. The expected utility is the sum of the utilities associated with all possible outcomes, weighted by the probability that each outcome will occur. In this case expected utility is
E(u) = (1/2)u($10,000) + (1/2)u($30,000) = 0.5(10) + 0.5(18) = 14
The risky new job is thus preferred to the original job because the expected utility of 14 is greater than the original utility of 13.5.
The old job involved no risk—it guaranteed an income of $15,000 and a utility level of 13.5. The new job is risky but offers both a higher expected income
($20,000) and, more importantly, a higher expected utility. If the woman wishes to increase her expected utility, she will take the risky job.

In §3.1, we explained that a utility function assigns a level of utility to each possible market basket.

In §3.5, marginal utility is described as the additional satisfaction obtained by consuming an additional amount of a good.

• expected utility Sum of the utilities associated with all possible outcomes, weighted by the probability that each outcome will occur.

166 PART 2 • Producers, Consumers, and Competitive Markets

Different Preferences Toward Risk
• risk averse Condition of preferring a certain income to a risky income with the same expected value.

• risk neutral Condition of being indifferent between a certain income and an uncertain income with the same expected value. • risk loving Condition of preferring a risky income to a certain income with the same expected value.

People differ in their willingness to bear risk. Some are risk averse, some risk loving, and some risk neutral. An individual who is risk averse prefers a certain given income to a risky income with the same expected value. (Such a person has a diminishing marginal utility of income.) Risk aversion is the most common attitude toward risk. To see that most people are risk averse most of the time, note that most people not only buy life insurance, health insurance, and car insurance, but also seek occupations with relatively stable wages.
Figure 5.3 (a) applies to a woman who is risk averse. Suppose hypothetically that she can have either a certain income of $20,000, or a job yielding an income of $30,000 with probability .5 and an income of $10,000 with probability .5 (so that the expected income is also $20,000). As we saw, the expected utility of the uncertain income is 14—an average of the utility at point A(10) and the utility at
E(18)—and is shown by F. Now we can compare the expected utility associated with the risky job to the utility generated if $20,000 were earned without risk.
This latter utility level, 16, is given by D in Figure 5.3 (a). It is clearly greater than the expected utility of 14 associated with the risky job.
For a risk-averse person, losses are more important (in terms of the change in utility) than gains. Again, this can be seen from Figure 5.3 (a). A $10,000 increase in income, from $20,000 to $30,000, generates an increase in utility of two units; a $10,000 decrease in income, from $20,000 to $10,000, creates a loss of utility of six units.
A person who is risk neutral is indifferent between a certain income and an uncertain income with the same expected value. In Figure 5.3 (c) the utility associated with a job generating an income of either $10,000 or $30,000 with equal probability is 12, as is the utility of receiving a certain income of $20,000.
As you can see from the figure, the marginal utility of income is constant for a risk-neutral person.6
Finally, an individual who is risk loving prefers an uncertain income to a certain one, even if the expected value of the uncertain income is less than that of the certain income. Figure 5.3 (b) shows this third possibility. In this case, the expected utility of an uncertain income, which will be either $10,000 with probability .5 or $30,000 with probability .5, is higher than the utility associated with a certain income of $20,000. Numerically,
E(u) = .5u($10,000) + .5u($30,000) = .5(3) + .5(18) = 10.5 7 u($20,000) = 8
Of course, some people may be averse to some risks and act like risk lovers with respect to others. For example, many people purchase life insurance and are conservative with respect to their choice of jobs, but still enjoy gambling. Some criminologists might describe criminals as risk lovers, especially if they commit crimes despite a high prospect of apprehension and punishment. Except for such special cases, however, few people are risk loving, at least with respect to major purchases or large amounts of income or wealth.

• risk premium Maximum amount of money that a riskaverse person will pay to avoid taking a risk.

RISK PREMIUM The risk premium is the maximum amount of money that a risk-averse person will pay to avoid taking a risk. In general, the magnitude
6

Thus, when people are risk neutral, the income they earn can be used as an indicator of well-being.
A government policy that doubles incomes would then also double their utility. At the same time, government policies that alter the risks that people face, without changing their expected incomes, would not affect their well-being. Risk neutrality allows a person to avoid the complications that might be associated with the effects of governmental actions on the riskiness of outcomes.

CHAPTER 5 • Uncertainty and Consumer Behavior 167

of the risk premium depends on the risky alternatives that the person faces.
To determine the risk premium, we have reproduced the utility function of
Figure 5.3 (a) in Figure 5.4 and extended it to an income of $40,000. Recall that an expected utility of 14 is achieved by a woman who is going to take a risky job with an expected income of $20,000. This outcome is shown graphically by drawing a horizontal line to the vertical axis from point F, which bisects straight

Utility
E
18
D

16

C

14
13.5

B

F

A
10

0

10

15 16

20

30
Income ($1000)

(a)
Utility

Utility
E

E

18

18

C

12
C

8

6

A

A
3

0

10

20

30

0

10

20

(b)

30
Income ($1000)

Income ($1000)
(c)

F IGURE 5.3

RISK AVERSE, RISK LOVING, AND RISK NEUTRAL
People differ in their preferences toward risk. In (a), a consumer’s marginal utility diminishes as income increases.
The consumer is risk averse because she would prefer a certain income of $20,000 (with a utility of 16) to a gamble with a .5 probability of $10,000 and a .5 probability of $30,000 (and expected utility of 14). In (b), the consumer is risk loving: She would prefer the same gamble (with expected utility of 10.5) to the certain income
(with a utility of 8). Finally, the consumer in (c) is risk neutral and indifferent between certain and uncertain events with the same expected income.

168 PART 2 • Producers, Consumers, and Competitive Markets

Utility

G

20
18

E
C

14

F
Risk Premium

A
10

10

16

20
Income ($1000)

30

40

F IGURE 5.4

RISK PREMIUM
The risk premium, CF, measures the amount of income that an individual would give up to leave her indifferent between a risky choice and a certain one. Here, the risk premium is $4000 because a certain income of $16,000 (at point C) gives her the same expected utility (14) as the uncertain income (a .5 probability of being at point A and a .5 probability of being at point E) that has an expected value of $20,000.

line AE (thus representing an average of $10,000 and $30,000). But the utility level of 14 can also be achieved if the woman has a certain income of $16,000, as shown by dropping a vertical line from point C. Thus, the risk premium of $4000, given by line segment CF, is the amount of expected income ($20,000 minus
$16,000) that she would give up in order to remain indifferent between the risky job and a hypothetical job that would pay her a certain income of $16,000.
RISK AVERSION AND INCOME The extent of an individual’s risk aversion depends on the nature of the risk and on the person’s income. Other things being equal, risk-averse people prefer a smaller variability of outcomes. We saw that when there are two outcomes—an income of $10,000 and an income of $30,000—the risk premium is $4000. Now consider a second risky job, also illustrated in Figure 5.4.
With this job, there is a .5 probability of receiving an income of $40,000, with a utility level of 20, and a .5 probability of getting an income of $0, with a utility level of 0.
The expected income is again $20,000, but the expected utility is only 10:
Expected utility = .5u($0) + .5u($40,000) = 0 + .5(20) = 10
Compared to a hypothetical job that pays $20,000 with certainty, the person holding this risky job gets 6 fewer units of expected utility: 10 rather than 16 units.
At the same time, however, this person could also get 10 units of utility from a job that pays $10,000 with certainty. Thus the risk premium in this case is $10,000, because this person would be willing to give up $10,000 of her $20,000 expected income to avoid bearing the risk of an uncertain income. The greater the variability of income, the more the person would be willing to pay to avoid the risky situation.

CHAPTER 5 • Uncertainty and Consumer Behavior 169

Expected income Expected income U3
U2
U1

U3
U2
U1

Standard deviation of income
(a)

Standard deviation of income
(b)

F IGURE 5.5

RISK AVERSION AND INDIFFERENCE CURVES
Part (a) applies to a person who is highly risk averse: An increase in this individual’s standard deviation of income requires a large increase in expected income if he or she is to remain equally well off. Part (b) applies to a person who is only slightly risk averse: An increase in the standard deviation of income requires only a small increase in expected income if he or she is to remain equally well off.

RISK AVERSION AND INDIFFERENCE CURVES We can also describe the extent of a person’s risk aversion in terms of indifference curves that relate expected income to the variability of income, where the latter is measured by the standard deviation. Figure 5.5 shows such indifference curves for two individuals, one who is highly risk averse and another who is only slightly risk averse. Each indifference curve shows the combinations of expected income and standard deviation of income that give the individual the same amount of utility. Observe that all of the indifference curves are upward sloping: Because risk is undesirable, the greater the amount of risk, the greater the expected income needed to make the individual equally well off.
Figure 5.5 (a) describes an individual who is highly risk averse. Observe that in order to leave this person equally well off, an increase in the standard deviation of income requires a large increase in expected income. Figure 5.5 (b) applies to a slightly risk-averse person. In this case, a large increase in the standard deviation of income requires only a small increase in expected income.

In §3.1, we define an indifference curve as all market baskets that generate the same level of satisfaction for a consumer.

EX AMPLE 5. 2 BUSINESS EXECUTIVES AND THE CHOICE OF RISK
Are business executives more risk loving than most people? When they are presented with alternative strategies, some risky, some safe, which do they choose? In one study, 464 executives were asked

7

to respond to a questionnaire describing risky situations that an individual might face as vice president of a hypothetical company.7 Respondents were presented with four risky events, each of which had a

This example is based on Kenneth R. MacCrimmon and Donald A. Wehrung, “The Risk In-Basket,”
Journal of Business 57 (1984): 367–87.

170 PART 2 • Producers, Consumers, and Competitive Markets given probability of a favorable and unfavorable outcome. The payoffs and probabilities were chosen so that each event had the same expected value. In increasing order of the risk involved (as measured by the difference between the favorable and unfavorable outcomes), the four items were:
1. A lawsuit involving a patent violation
2. A customer threatening to buy from a competitor
3. A union dispute
4. A joint venture with a competitor
To gauge their willingness to take or avoid risks, researchers asked respondents a series of questions regarding business strategy. In one situation, they could pursue a risky strategy with the possibility of a high return right away or delay making a choice until the outcomes became more certain and the risk was reduced. In another situation, respondents could opt for an immediately risky but potentially profitable strategy that could lead to a promotion, or they could delegate the decision to someone else, which

would protect their job but eliminate the promotion possibility. The study found that executives vary substantially in their preferences toward risk. Roughly 20 percent indicated that they were relatively risk neutral; 40 percent opted for the more risky alternatives; and
20 percent were clearly risk averse (20 percent did not respond). More importantly, executives (including those who chose risky alternatives) typically made efforts to reduce or eliminate risk, usually by delaying decisions and collecting more information.
Some have argued that a cause of the financial crisis of 2008 was excessive risk-taking by bankers and Wall Street executives who could earn huge bonuses if their ventures succeeded but faced very little downside if the ventures failed. The
U.S. Treasury Department’s Troubled Asset Relief
Program (TARP) bailed out some of the banks, but so far has been unable to impose constraints on
“unnecessary and excessive” risk-taking by banks’ executives. We will return to the use of indifference curves as a means of describing risk aversion in Section 5.4, where we discuss the demand for risky assets. First, however, we will turn to the ways in which an individual can reduce risk.

5.3 Reducing Risk
As the recent growth in state lotteries shows, people sometimes choose risky alternatives that suggest risk-loving rather than risk-averse behavior. Most people, however, spend relatively small amounts on lottery tickets and casinos.
When more important decisions are involved, they are generally risk averse. In this section, we describe three ways by which both consumers and businesses commonly reduce risks: diversification, insurance, and obtaining more information about choices and payoffs.

Diversification
• diversification Practice of reducing risk by allocating resources to a variety of activities whose outcomes are not closely related. Recall the old saying, “Don’t put all your eggs in one basket.” Ignoring this advice is unnecessarily risky: If your basket turns out to be a bad bet, all will be lost. Instead, you can reduce risk through diversification: allocating your resources to a variety of activities whose outcomes are not closely related.
Suppose, for example, that you plan to take a part-time job selling appliances on a commission basis. You can decide to sell only air conditioners or only heaters, or you can spend half your time selling each. Of course, you can’t be sure how hot or cold the weather will be next year. How should you apportion your time in order to minimize the risk involved?
Risk can be minimized by diversification—by allocating your time so that you sell two or more products (whose sales are not closely related) rather than a

CHAPTER 5 • Uncertainty and Consumer Behavior 171

TABLE 5.5

INCOME FROM SALES OF APPLIANCES ($)
HOT WEATHER

COLD WEATHER

Air conditioner sales

30,000

12,000

Heater sales

12,000

30,000

single product. Suppose there is a 0.5 probability that it will be a relatively hot year, and a 0.5 probability that it will be cold. Table 5.5 gives the earnings that you can make selling air conditioners and heaters.
If you sell only air conditioners or only heaters, your actual income will be either $12,000 or $30,000, but your expected income will be $21,000 (.5[$30,000] ϩ .5[$12,000]). But suppose you diversify by dividing your time evenly between the two products. In that case, your income will certainly be $21,000, regardless of the weather. If the weather is hot, you will earn $15,000 from air conditioner sales and $6000 from heater sales; if it is cold, you will earn $6000 from air conditioners and $15,000 from heaters. In this instance, diversification eliminates all risk.
Of course, diversification is not always this easy. In our example, heater and air conditioner sales are negatively correlated variables—they tend to move in opposite directions; whenever sales of one are strong, sales of the other are weak. But the principle of diversification is a general one: As long as you can allocate your resources toward a variety of activities whose outcomes are not closely related, you can eliminate some risk.
THE STOCK MARKET Diversification is especially important for people who invest in the stock market. On any given day, the price of an individual stock can go up or down by a large amount, but some stocks rise in price while others fall. An individual who invests all her money in a single stock (i.e., puts all her eggs in one basket) is therefore taking much more risk than necessary. Risk can be reduced—although not eliminated—by investing in a portfolio of ten or twenty different stocks. Likewise, you can diversify by buying shares in mutual funds: organizations that pool funds of individual investors to buy a large number of different stocks. There are thousands of mutual funds available today for both stocks and bonds. These funds are popular because they reduce risk through diversification and because their fees are typically much lower than the cost of assembling one’s own portfolio of stocks.
In the case of the stock market, not all risk is diversifiable. Although some stocks go up in price when others go down, stock prices are to some extent positively correlated variables: They tend to move in the same direction in response to changes in economic conditions. For example, the onset of a severe recession, which is likely to reduce the profits of many companies, may be accompanied by a decline in the overall market. Even with a diversified portfolio of stocks, therefore, you still face some risk.

Insurance
We have seen that risk-averse people are willing to pay to avoid risk. In fact, if the cost of insurance is equal to the expected loss (e.g., a policy with an expected loss of $1000 will cost $1000), risk-averse people will buy enough insurance to recover fully from any financial losses they might suffer.

• negatively correlated variables Variables having a tendency to move in opposite directions. • mutual fund Organization that pools funds of individual investors to buy a large number of different stocks or other financial assets.

• positively correlated variables Variables having a tendency to move in the same direction. 172 PART 2 • Producers, Consumers, and Competitive Markets
Why? The answer is implicit in our discussion of risk aversion. Buying insurance assures a person of having the same income whether or not there is a loss.
Because the insurance cost is equal to the expected loss, this certain income is equal to the expected income from the risky situation. For a risk-averse consumer, the guarantee of the same income regardless of the outcome generates more utility than would be the case if that person had a high income when there was no loss and a low income when a loss occurred.
To clarify this point, let’s suppose a homeowner faces a 10-percent probability that his house will be burglarized and he will suffer a $10,000 loss. Let’s assume he has $50,000 worth of property. Table 5.6 shows his wealth in two situations—with insurance costing $1000 and without insurance.
Note that expected wealth is the same ($49,000) in both situations. The variability, however, is quite different. As the table shows, with no insurance the standard deviation of wealth is $3000; with insurance, it is 0. If there is no burglary, the uninsured homeowner gains $1000 relative to the insured homeowner. But with a burglary, the uninsured homeowner loses $9000 relative to the insured homeowner. Remember: for a risk-averse individual, losses count more (in terms of changes in utility) than gains. A risk-averse homeowner, therefore, will enjoy higher utility by purchasing insurance.
THE LAW OF LARGE NUMBERS Consumers usually buy insurance from companies that specialize in selling it. Insurance companies are firms that offer insurance because they know that when they sell a large number of policies, they face relatively little risk. The ability to avoid risk by operating on a large scale is based on the law of large numbers, which tells us that although single events may be random and largely unpredictable, the average outcome of many similar events can be predicted. For example, I may not be able to predict whether a coin toss will come out heads or tails, but I know that when many coins are flipped, approximately half will turn up heads and half tails.
Likewise, if I am selling automobile insurance, I cannot predict whether a particular driver will have an accident, but I can be reasonably sure, judging from past experience, what fraction of a large group of drivers will have accidents. ACTUARIAL FAIRNESS By operating on a large scale, insurance companies can be sure that over a sufficiently large number of events, total premiums paid in will be equal to the total amount of money paid out. Let’s return to our burglary example. A man knows that there is a 10-percent probability that his house will be burgled; if it is, he will suffer a $10,000 loss. Prior to facing this risk, he calculates the expected loss to be $1000 (.10 ϫ $10,000). The risk involved is considerable, however, because there is a 10-percent probability of

TABLE 5.6

THE DECISION TO INSURE ($)

INSURANCE

BURGLARY
(PR ‫)1. ؍‬

NO BURGLARY
(PR ‫)9. ؍‬

EXPECTED
WEALTH

STANDARD
DEVIATION

No

40,000

50,000

49,000

3000

Yes

49,000

49,000

49,000

0

CHAPTER 5 • Uncertainty and Consumer Behavior 173

a large loss. Now suppose that 100 people are similarly situated and that all of them buy burglary insurance from the same company. Because they all face a
10-percent probability of a $10,000 loss, the insurance company might charge each of them a premium of $1000. This $1000 premium generates an insurance fund of $100,000 from which losses can be paid. The insurance company can rely on the law of large numbers, which holds that the expected loss to the 100 individuals as a whole is likely to be very close to $1000 each. The total payout, therefore, will be close to $100,000, and the company need not worry about losing more than that.
When the insurance premium is equal to the expected payout, as in the example above, we say that the insurance is actuarially fair. But because they must cover administrative costs and make some profit, insurance companies typically charge premiums above expected losses. If there are a sufficient number of insurance companies to make the market competitive, these premiums will be close to actuarially fair levels. In some states, however, insurance premiums are regulated in order to protect consumers from “excessive” premiums. We will examine government regulation of markets in detail in Chapters 9 and 10 of this book. In recent years, some insurance companies have come to the view that catastrophic disasters such as earthquakes are so unique and unpredictable that they cannot be viewed as diversifiable risks. Indeed, as a result of losses from past disasters, these companies do not feel that they can determine actuarially fair insurance rates. In California, for example, the state itself has had to enter the insurance business to fill the gap created when private companies refused to sell earthquake insurance. The state-run pool offers less insurance coverage at higher rates than was previously offered by private insurers.

• actuarially fair
Characterizing a situation in which an insurance premium is equal to the expected payout.

EX AMPLE 5. 3 THE VALUE OF TITLE INSURANCE WHEN BUYING A HOUSE
Suppose you are buying your first house. To close the sale, you will need a deed that gives you clear “title.” Without such a clear title, there is always a chance that the seller of the house is not its true owner. Of course, the seller could be engaging in fraud, but it is more likely that the seller is unaware of the exact nature of his or her ownership rights. For example, the owner may have borrowed heavily, using the house as “collateral” for a loan. Or the property might carry with it a legal requirement that limits the use to which it may be put.
Suppose you are willing to pay $300,000 for the house, but you believe there is a one-in-twenty chance that careful research will reveal that the seller does not actually own the property. The property

would then be worth nothing. If there were no insurance available, a risk-neutral person would bid at most $285,000 for the property
(.95[$300,000] + .05[0]). However, if you expect to tie up most of your assets in the house, you would probably be risk averse and, therefore, bid much less—say, $230,000.
In situations such as this, it is clearly in the interest of the buyer to be sure that there is no risk of a lack of full ownership. The buyer does this by purchasing “title insurance.” The title insurance company researches the history of the property, checks to see whether any legal liabilities are attached to it, and generally assures itself that there is no ownership problem. The insurance company then agrees to bear any remaining risk that might exist.

174 PART 2 • Producers, Consumers, and Competitive Markets
Because the title insurance company is a specialist in such insurance and can collect the relevant information relatively easily, the cost of title insurance is often less than the expected value of the loss involved. A fee of $1500 for title insurance is not unusual, even though the expected loss can be much higher. It is also in the interest of sellers to provide title insurance, because

all but the most risk-loving buyers will pay much more for a house when it is insured than when it is not. In fact, most states require sellers to provide title insurance before a sale can be completed.
In addition, because mortgage lenders are all concerned about such risks, they usually require new buyers to have title insurance before issuing a mortgage.

The Value of Information
• value of complete information Difference between the expected value of a choice when there is complete information and the expected value when information is incomplete. People often make decisions based on limited information. If more information were available, one could make better predictions and reduce risk. Because information is a valuable commodity, people will pay for it. The value of complete information is the difference between the expected value of a choice when there is complete information and the expected value when information is incomplete.
To see how information can be valuable, suppose you manage a clothing store and must decide how many suits to order for the fall season. If you order 100 suits, your cost is $180 per suit. If you order only 50 suits, your cost increases to $200.
You know that you will be selling suits for $300 each, but you are not sure how many you can sell. All suits not sold can be returned, but for only half of what you paid for them. Without additional information, you will act on your belief that there is a .5 probability that you will sell 100 suits and a .5 probability that you will sell 50. Table 5.7 gives the profit that you would earn in each of these two cases.
Without additional information, you would choose to buy 100 suits if you were risk neutral, taking the chance that your profit might be either $12,000 or
$1500. But if you were risk averse, you might buy 50 suits: In that case, you would know for sure that your profit would be $5000.
With complete information, you can place the correct order regardless of future sales. If sales were going to be 50 and you ordered 50 suits, your profits would be $5000. If, on the other hand, sales were going to be 100 and you ordered 100 suits, your profits would be $12,000. Because both outcomes are equally likely, your expected profit with complete information would be $8500.
The value of information is computed as
Expected value with complete information:
Less: Expected value with uncertainty (buy 100 suits):
Equals: Value of complete information

$8500
- 6750
$1750

Thus it is worth paying up to $1750 to obtain an accurate prediction of sales.
Even though forecasting is inevitably imperfect, it may be worth investing in a marketing study that provides a reasonable forecast of next year’s sales.

TABLE 5.7

PROFITS FROM SALES OF SUITS ($)
SALES OF 50

SALES OF 100

EXPECTED PROFIT

Buy 50 suits

5000

5000

5000

Buy 100 suits

1500

12,000

6750

CHAPTER 5 • Uncertainty and Consumer Behavior 175

EX AMPLE 5. 4 THE VALUE OF INFORMATION IN AN ONLINE CONSUMER
ELECTRONICS MARKET
Internet-based price comparison sites offer a valuable informational resource to consumers, as shown by a study of a leading price-comparison website,
Shopper.com. Researchers studied price information provided to consumers on over 1,000 topselling electronics products for an 8-month period.
They found that consumers saved about 16% when using this website versus shopping in the store, because the website significantly reduced the cost of finding the lowest priced product.8
The value of price comparison information is not the same for everyone and for every product. Competition matters. The study found that when only two firms list prices on Shopper.com,

consumers save 11%. But the savings increase with the number of competitors, jumping to 20% when more than 30 companies list prices.
One might think that the Internet will generate so much information about prices that only the lowestprice products will be sold in the long run, causing the value of such information to eventually decline to zero. So far, this has not been the case. There are fixed costs for parties to both transmit and to acquire information over the Internet. These include the costs of maintaining servers and the fees that sites such as Shopper.com charge to list prices at their sites.
The result is that prices are likely to continue to vary widely as the Internet continues to grow and mature.

You might think that more information is always a good thing. As the following example shows, however, that is not always the case.

EX AMPLE 5. 5 DOCTORS, PATIENTS, AND THE VALUE OF INFORMATION
Suppose you were seriously ill and required major surgery. Assuming you wanted to get the best care possible, how would you go about choosing a surgeon and a hospital to provide that care? Many people would ask their friends or their primary-care physician for a recommendation. Although this might be helpful, a truly informed decision would probably require more detailed information. For example, how successful has a recommended surgeon and her affiliated hospital been in performing the particular operation that you need? How many of her patients have died or had serious complications from the operation, and how do these numbers compare with those for other surgeons and hospitals? This kind of information is likely to be difficult or impossible for most patients to obtain. Would patients be better off if detailed information about the performance records of doctors and hospitals were readily available?

Not necessarily. More information is often, but not always, better.
Interestingly in this case, access to performance information could actually lead to worse health outcomes. Why?
Because access to such information would create two different incentives that would affect the behavior of both doctors and patients. First, it would allow patients to choose doctors with better performance records, which creates an incentive for doctors to perform better. That is a good thing. But second, it would encourage doctors to limit their practices to patients who are in relatively good health.
The reason is that very old or very sick patients are more likely to have complications or die as a result of treatment; doctors who treat such patients are likely to have worse performance records (other factors being equal). To the extent that doctors would be judged according to performance, they would

8
Michael Baye, John Morgan, and Patrick Scholten,” The Value of Information in an Online
Electronics Market.”Journal of Public Policy and Marketing, vol. 22 (2003): 17–25.

176 PART 2 • Producers, Consumers, and Competitive Markets have an incentive to avoid treating very old or sick patients. As a result, such patients would find it difficult or impossible to obtain treatment.
Whether more information is better depends on which effect dominates—the ability of patients to make more informed choices versus the incentive for doctors to avoid very sick patients. In a recent study, economists examined the impact of the mandatory “report cards” introduced in New York and Pennsylvania in the early 1990s to evaluate outcomes of coronary bypass surgeries.9 They analyzed hospital choices and outcomes for all elderly heart attack patients and patients receiving coronary bypass surgery in the United States from 1987 through 1994. By comparing trends in
New York and Pennsylvania to the trends in other states, they could determine the effect of the increased information made possible by the availability of report cards. They found that although report cards improved matching of patients with

hospitals and doctors, they also caused a shift in treatment from sicker patients towards healthier ones. Overall, this led to worse outcomes, especially among sicker patients. Thus the study concluded that report cards reduced welfare.
The medical profession has responded to this problem to some extent. For example, in 2010, cardiac surgery programs across the country voluntarily reported the results of coronary-artery bypass grafting procedures. Each program was rated with one to three stars, but this time the ratings were “risk adjusted” to reduce the incentive for doctors to choose less risky patients.
More information often improves welfare because it allows people to reduce risk and to take actions that might reduce the effect of bad outcomes.
However, as this example makes clear, information can cause people to change their behavior in undesirable ways. We will discuss this issue further in Chapter 17.

*5.4 The Demand for Risky Assets
Most people are risk averse. Given a choice, they prefer fixed monthly incomes to those which, though equally large on average, fluctuate randomly from month to month. Yet many of these same people will invest all or part of their savings in stocks, bonds, and other assets that carry some risk. Why do riskaverse people invest in the stock market and thereby risk losing part or all of their investments?10 How do people decide how much risk to bear when making investments and planning for the future? To answer these questions, we must examine the demand for risky assets.

Assets
• asset Something that provides a flow of money or services to its owner.

An asset is something that provides a flow of money or services to its owner. A home, an apartment building, a savings account, or shares of General Motors stock are all assets. A home, for example, provides a flow of housing services to its owner, and, if the owner did not wish to live there, could be rented out, thereby providing a monetary flow. Likewise, apartments can be rented out, providing a flow of rental income to the owner of the building. A savings account pays interest
(usually every day or every month), which is usually reinvested in the account.
9

David Dranove, Daniel Kessler, Mark McClennan, and Mark Satterthwaite, “Is More Information
Better? The Effects of ’Report Cards’ on Health Care Providers,” Journal of Political Economy
3 (June 2003): 555–558.

10

Most Americans have at least some money invested in stocks or other risky assets, though often indirectly. For example, many people who hold full-time jobs have shares in pension funds underwritten in part by their own salary contributions and in part by employer contributions. Usually such funds are partly invested in the stock market.

CHAPTER 5 • Uncertainty and Consumer Behavior 177

The monetary flow that one receives from asset ownership can take the form of an explicit payment, such as the rental income from an apartment building: Every month, the landlord receives rent checks from the tenants. Another form of explicit payment is the dividend on shares of common stock: Every three months, the owner of a share of General Motors stock receives a quarterly dividend payment.
But sometimes the monetary flow from ownership of an asset is implicit: It takes the form of an increase or decrease in the price or value of the asset. An increase in the value of an asset is a capital gain; a decrease is a capital loss. For example, as the population of a city grows, the value of an apartment building may increase. The owner of the building will then earn a capital gain beyond the rental income. The capital gain is unrealized until the building is sold because no money is actually received until then. There is, however, an implicit monetary flow because the building could be sold at any time. The monetary flow from owning General Motors stock is also partly implicit. The price of the stock changes from day to day, and each time it does, owners gain or lose.

Risky and Riskless Assets
A risky asset provides a monetary flow that is at least in part random. In other words, the monetary flow is not known with certainty in advance. A share of General
Motors stock is an obvious example of a risky asset: You cannot know whether the price of the stock will rise or fall over time, nor can you even be sure that the company will continue to pay the same (or any) dividend per share. Although people often associate risk with the stock market, most other assets are also risky.
An apartment building is one example. You cannot know how much land values will rise or fall, whether the building will be fully rented all the time, or even whether the tenants will pay their rents promptly. Corporate bonds are another example—the issuing corporation could go bankrupt and fail to pay bond owners their interest and principal. Even long-term U.S. government bonds that mature in 10 or 20 years are risky. Although it is highly unlikely that the federal government will go bankrupt, the rate of inflation could unexpectedly increase and make future interest payments and the eventual repayment of principal worth less in real terms, thereby reducing the value of the bonds.
In contrast, a riskless (or risk-free) asset pays a monetary flow that is known with certainty. Short-term U.S. government bonds—called Treasury bills—are riskless, or almost riskless. Because they mature in a few months, there is very little risk from an unexpected increase in the rate of inflation. You can also be reasonably confident that the U.S. government will not default on the bond (i.e., refuse to pay back the holder when the bond comes due). Other examples of riskless or almost riskless assets include passbook savings accounts and shortterm certificates of deposit.

• risky asset Asset that provides an uncertain flow of money or services to its owner.

• riskless (or risk-free) asset Asset that provides a flow of money or services that is known with certainty.

Asset Returns
People buy and hold assets because of the monetary flows they provide. To compare assets with each other, it helps to think of this monetary flow relative to an asset’s price or value. The return on an asset is the total monetary flow it yields—including capital gains or losses—as a fraction of its price. For example, a bond worth $1000 today that pays out $100 this year (and every year) has a return of

• return Total monetary flow of an asset as a fraction of its price. 178 PART 2 • Producers, Consumers, and Competitive Markets

• real return Simple (or nominal) return on an asset, less the rate of inflation.

• expected return Return that an asset should earn on average. • actual return Return that an asset earns.

10 percent.11 If an apartment building was worth $10 million last year, increased in value to $11 million this year, and also provided rental income (after expenses) of $0.5 million, it would have yielded a return of 15 percent over the past year. If a share of General Motors stock was worth $80 at the beginning of the year, fell to
$72 by the end of the year, and paid a dividend of $4, it will have yielded a return of -5 percent (the dividend yield of 5 percent less the capital loss of 10 percent).
When people invest their savings in stocks, bonds, land, or other assets, they usually hope to earn a return that exceeds the rate of inflation. Thus, by delaying consumption, they can buy more in the future than they can by spending all their income now. Consequently, we often express the return on an asset in real—i.e., inflation-adjusted—terms. The real return on an asset is its simple (or nominal) return less the rate of inflation. For example, with an annual inflation rate of 5 percent, our bond, apartment building, and share of GM stock have yielded real returns of 5 percent, 10 percent, and −10 percent, respectively.
EXPECTED VERSUS ACTUAL RETURNS Because most assets are risky, an investor cannot know in advance what returns they will yield over the coming year. For example, our apartment building might have depreciated in value instead of appreciating, and the price of GM stock might have risen instead of fallen. However, we can still compare assets by looking at their expected returns.
The expected return on an asset is the expected value of its return, i.e., the return that it should earn on average. In some years, an asset’s actual return may be much higher than its expected return and in some years much lower. Over a long period, however, the average return should be close to the expected return.
Different assets have different expected returns. Table 5.8, for example, shows that while the expected real return of a U.S. Treasury bill has been less than 1 percent, the expected real return on a group of representative stocks on the New
York Stock Exchange has been more than 9 percent.12 Why would anyone buy a Treasury bill when the expected return on stocks is so much higher? Because the demand for an asset depends not just on its expected return, but also on its risk: Although stocks have a higher expected return than Treasury bills, they also carry much more risk. One measure of risk, the standard deviation of the real annual return, is equal to 20.4 percent for common stocks, 8.3 percent for corporate bonds, and only 3.1 percent for U.S. Treasury bills.
The numbers in Table 5.8 suggest that the higher the expected return on an investment, the greater the risk involved. Assuming that one’s investments are well diversified, this is indeed the case.13 As a result, the risk-averse investor must balance expected return against risk. We examine this trade-off in more detail in the next section.

11

The price of a bond often changes during the course of a year. If the bond appreciates (or depreciates) in value during the year, its return will be greater (or less) than 10 percent. In addition, the definition of return given above should not be confused with the “internal rate of return,” which is sometimes used to compare monetary flows occurring over a period of time. We discuss other return measures in Chapter 15, when we deal with present discounted values.
12

For some stocks, the expected return is higher, and for some it is lower. Stocks of smaller companies (e.g., some of those traded on the NASDAQ) have higher expected rates of return—and higher return standard deviations.
13
It is nondiversifiable risk that matters. An individual stock may be very risky but still have a low expected return because most of the risk could be diversified away by holding a large number of such stocks. Nondiversifiable risk, which arises from the fact that individual stock prices are correlated with the overall stock market, is the risk that remains even if one holds a diversified portfolio of stocks. We discuss this point in detail in the context of the capital asset pricing model in Chapter 15.

CHAPTER 5 • Uncertainty and Consumer Behavior 179

TABLE 5.8

INVESTMENTS—RISK AND RETURN (1926–2010)
AVERAGE RATE OF
RETURN (%)

AVERAGE REAL
RATE OF RETURN
(%)

RISK (STANDARD
DEVIATION)

11.9

8.7

20.4

Long-term corporate bonds 6.2

3.3

8.3

U.S. Treasury bills

3.7

0.7

3.1

Common stocks
(S&P 500)

Source: Ibbotson® SBBI® 2001 Classic Yearbook: Market results for Stocks, Bonds, Bills, and Inflation 1926–2010.
© 2011 Morningstar.

The Trade-Off Between Risk and Return
Suppose a woman wants to invest her savings in two assets—Treasury bills, which are almost risk free, and a representative group of stocks. She must decide how much to invest in each asset. She might, for instance, invest only in Treasury bills, only in stocks, or in some combination of the two. As we will see, this problem is analogous to the consumer’s problem of allocating a budget between purchases of food and clothing.
Let’s denote the risk-free return on the Treasury bill by Rf . Because the return is risk free, the expected and actual returns are the same. In addition, let the expected return from investing in the stock market be Rm and the actual return be rm. The actual return is risky. At the time of the investment decision, we know the set of possible outcomes and the likelihood of each, but we do not know what particular outcome will occur. The risky asset will have a higher expected return than the risk-free asset (Rm 7 Rf). Otherwise, risk-averse investors would buy only Treasury bills and no stocks would be sold.
THE INVESTMENT PORTFOLIO To determine how much money the investor should put in each asset, let’s set b equal to the fraction of her savings placed in the stock market and (1 - b) the fraction used to purchase Treasury bills. The expected return on her total portfolio, Rp, is a weighted average of the expected return on the two assets:14
R p = bR m + (1 - b)R f

(5.1)

Suppose, for example, that Treasury bills pay 4 percent (Rf ϭ .04), the stock market’s expected return is 12 percent (Rm ϭ .12), and b ϭ 1/2. Then Rp ϭ 8 percent. How risky is this portfolio? One measure of riskiness is the standard deviation of its return. We will denote the standard deviation of the risky stock market investment by ␴m. With some algebra, we can show that the standard deviation of the portfolio, ␴p (with one risky and one risk-free asset) is the fraction
14

The expected value of the sum of two variables is the sum of the expected values. Therefore
R p = E[brm] + E[(1 - b)R f] = bE[rm] + (1 - b)R f = bR m + (1 - b)R f

180 PART 2 • Producers, Consumers, and Competitive Markets of the portfolio invested in the risky asset times the standard deviation of that asset:15 sp = bsm

(5.2)

The Investor’s Choice Problem

In §3.2 we explain how a budget line is determined from an individual’s income and the prices of the available goods.

We have still not determined how the investor should choose this fraction b. To do so, we must first show that she faces a risk-return trade-off analogous to a consumer’s budget line. To identify this trade-off, note that equation (5.1) for the expected return on the portfolio can be rewritten as
R p = R f + b(R m - R f)
Now, from equation (5.2) we see that b ϭ ␴p/␴m, so that

Rp = Rf +

• Price of risk Extra risk that an investor must incur to enjoy a higher expected return.

(R m - R f) sm sp

(5.3)

RISK AND THE BUDGET LINE This equation is a budget line because it describes the trade-off between risk (␴p) and expected return (Rp). Note that it is the equation for a straight line: Because Rm, Rf, and ␴m are constants, the slope (Rm − Rf)/
␴m is a constant, as is the intercept, Rf. The equation says that the expected return on the portfolio Rp increases as the standard deviation of that return ␴p increases. We call the slope of this budget line, (Rm − Rf)/␴m, the price of risk, because it tells us how much extra risk an investor must incur to enjoy a higher expected return.
The budget line is drawn in Figure 5.6. If our investor wants no risk, she can invest all her funds in Treasury bills (b ϭ 0) and earn an expected return
Rf. To receive a higher expected return, she must incur some risk. For example, she could invest all her funds in stocks (b ϭ 1), earning an expected return Rm but incurring a standard deviation ␴m. Or she might invest some fraction of her funds in each type of asset, earning an expected return somewhere between Rf and Rm and facing a standard deviation less than ␴m but greater than zero.
RISK AND INDIFFERENCE CURVES Figure 5.6 also shows the solution to the investor’s problem. Three indifference curves are drawn in the figure. Each curve describes combinations of risk and return that leave the investor equally satisfied. The curves are upward-sloping because risk is undesirable. Thus, with a greater amount of risk, it takes a greater expected return to make the investor equally well-off. Curve U3 yields the greatest amount of satisfaction and U1 the least amount: For a given amount of risk, the investor earns a higher expected return on U3 than on U2 and a higher expected return on U2 than on U1.
15

To see why, we observe from footnote 4 that we can write the variance of the portfolio return as s 2 = E[brm + (1 - b)R f - R p]2 p Substituting equation (5.1) for the expected return on the portfolio, Rp, we have s 2 = E[brm + (1 - b)R f - bR m - (1 - b)R f]2 = E[b(rm - R m)]2 = b 2s 2 p m
Because the standard deviation of a random variable is the square root of its variance, sp = bsm.

CHAPTER 5 • Uncertainty and Consumer Behavior 181

Expected return, Rp

U3
U2
U1

Rm
Budget Line

R*

Rf

0

σ*

σm

Standard deviation of return, σp

F IGURE 5.6

CHOOSING BETWEEN RISK AND RETURN
An investor is dividing her funds between two assets—Treasury bills, which are risk free, and stocks. The budget line describes the trade-off between the expected return and its riskiness, as measured by the standard deviation of the return. The slope of the budget line is (Rm− R f )/␴m, which is the price of risk. Three indifference curves are drawn, each showing combinations of risk and return that leave an investor equally satisfied.
The curves are upward-sloping because a risk-averse investor will require a higher expected return if she is to bear a greater amount of risk. The utility-maximizing investment portfolio is at the point where indifference curve U2 is tangent to the budget line.

Of the three indifference curves, the investor would prefer to be on U3. This position, however, is not feasible, because U3 does not touch the budget line.
Curve U1 is feasible, but the investor can do better. Like the consumer choosing quantities of food and clothing, our investor does best by choosing a combination of risk and return at the point where an indifference curve (in this case U2) is tangent to the budget line. At that point, the investor’s return has an expected value R* and a standard deviation ␴*.
Naturally, people differ in their attitudes toward risk. This fact is illustrated in Figure 5.7, which shows how two different investors choose their portfolios.
Investor A is quite risk averse. Because his indifference curve UA is tangent to the budget line at a point of low risk, he will invest almost all of his funds in
Treasury bills and earn an expected return RA just slightly larger than the riskfree return Rf. Investor B is less risk averse. She will invest most of her funds in stocks, and while the return on her portfolio will have a higher expected value
RB, it will also have a higher standard deviation ␴B.
If Investor B has a sufficiently low level of risk aversion, she might buy stocks on margin: that is, she would borrow money from a brokerage firm in order

182 PART 2 • Producers, Consumers, and Competitive Markets

Expected return, Rp

F IGURE 5.7

THE CHOICES OF TWO
DIFFERENT INVESTORS

UB

Rm

Investor A is highly risk averse.
Because his portfolio will consist mostly of the risk-free asset, his expected return RA will be only slightly greater than the risk-free return.
His risk ␴A, however, will be small.
Investor B is less risk averse. She will invest a large fraction of her funds in stocks. Although the expected return on her portfolio RB will be larger, it will also be riskier.

UA

RB

Budget Line

RA
Rf

0

σA

σB

σm

Standard deviation of return, σp

to invest more than she actually owns in the stock market. In effect, a person who buys stocks on margin holds a portfolio with more than 100 percent of the portfolio’s value invested in stocks. This situation is illustrated in Figure 5.8, which shows indifference curves for two investors. Investor A, who is relatively risk-averse, invests about half of his funds in stocks. Investor B, however, has an indifference curve that is relatively flat and tangent with the budget line at

F IGURE 5.8

BUYING STOCKS ON
MARGIN
Because Investor A is risk averse, his portfolio contains a mixture of stocks and risk-free Treasury bills. Investor B, however, has a very low degree of risk aversion. Her indifference curve, UB, is tangent to the budget line at a point where the expected return and standard deviation for her portfolio exceed those for the stock market overall. This implies that she would like to invest more than 100 percent of her wealth in the stock market. She does so by buying stocks on margin—i.e., by borrowing from a brokerage firm to help finance her investment.

UB
UA
RB

Budget
Line

Rm

RA

Rf

0

σA

σm

σB

CHAPTER 5 • Uncertainty and Consumer Behavior 183

a point where the expected return on the portfolio exceeds the expected return on the stock market. In order to hold this portfolio, the investor must borrow money because she wants to invest more than 100 percent of her wealth in the stock market. Buying stocks on margin in this way is a form of leverage: the investor increases her expected return above that for the overall stock market, but at the cost of increased risk.
In Chapters 3 and 4, we simplified the problem of consumer choice by assuming that the consumer had only two goods from which to choose— food and clothing. In the same spirit, we have simplified the investor ’s choice by limiting it to Treasury bills and stocks. The basic principles, however, would be the same if we had more assets (e.g., corporate bonds, land, and different types of stocks). Every investor faces a trade-off between risk and return.16 The degree of extra risk that each is willing to bear in order to earn a higher expected return depends on how risk averse he or she is. Less risk-averse investors tend to include a larger fraction of risky assets in their portfolios. EX AMPLE 5. 6 INVESTING IN THE STOCK MARKET
The 1990s witnessed a shift in the investing behavior of Americans.
First, many people started investing in the stock market for the first time. In 1989, about 32 percent of families in the United
States had part of their wealth invested in the stock market, either directly (by owning individual stocks) or indirectly (through mutual funds or pension plans invested in stocks). By 1998, that fraction had risen to 49 percent. In addition, the share of wealth invested in stocks increased from about 26 percent to about 54 percent during the same period.17 Much of this shift is attributable to younger investors. For those under the age of
35, participation in the stock market increased from about 22 percent in 1989 to about 41 percent in 1998. In most respects, household investing behavior has stabilized after the 1990s shift.
The percent of families with investments in the stock market was 51.1% in 2007. However, older
Americans have become much more active. By

2007, 40 percent of people over age 75 held stocks, up from 29 percent in 1998.
Why have more people started investing in the stock market?
One reason is the advent of online trading, which has made investing much easier. Another reason may be the considerable increase in stock prices that occurred during the late 1990s, driven in part by the so-called
“dot com euphoria.” These increases may have convinced some investors that prices could only continue to rise in the future. As one analyst put it, “The market’s relentless seven-year climb, the popularity of mutual funds, the shift by employers to self-directed retirement plans, and the avalanche of do-it-yourself investment publications all have combined to create a nation of financial know-it-alls.”18 Figure 5.9 shows the dividend yield and price/ earnings (P/E) ratio for the S&P 500 (an index of stocks of 500 large corporations) over the period

16

As mentioned earlier, what matters is nondiversifiable risk, because investors can eliminate diversifiable risk by holding many different stocks (e.g., via mutual funds). We discuss diversifiable versus nondiversifiable risk in Chapter 15.
17

Data are from the Federal Reserve Bulletin, January 2000, and the Survey of Consumer Finances, 2011.

18
“We’re All Bulls Here: Strong Market Makes Everybody an Expert,” Wall Street Journal, September
12, 1997.

184 PART 2 • Producers, Consumers, and Competitive Markets

7

50
45

6

Dividend Yield
40

P/E Ratio

30

4

25
3

20
15

2

Dividend Yield (percent)

5

35

10
1
5
0
1970

P/E Ratio
1974

1978

1982

1986

1990 1994
Year

1998

2002

2006

2010

0

F IGURE 5.9

DIVIDEND YIELD AND P/E RATIO FOR S&P 500
The dividend yield for the S&P 500 (the annual dividend divided by the stock price) has fallen dramatically, while the price/earnings ratio (the stock price divided by the annual earningsper-share) rose from 1980 to 2002 and then dropped.

1970 to 2011. Observe that the dividend yield
(the annual dividend divided by the stock price) fell from about 5 percent in 1980 to below 2 percent by 2000. Meanwhile, however, the price/ earnings ratio (the share price divided by annual earnings per share) increased from about 8 in
1980 to over 40 in 2002, before falling to around
20 between 2005 and 2007 and then increasing through 2011. In retrospect, the increase in the
P/E ratio could only have occurred if investors believed that corporate profits would continue to grow rapidly in the coming decade. This suggests that in the late 1990s, many investors had a low degree of risk aversion, were quite optimistic about the economy, or both. Alternatively, some economists have argued that the run-up of stock

19

prices during the 1990s was the result of “herd behavior,” in which investors rushed to get into the market after hearing of the successful experiences of others.19
The psychological motivations that explain herd behavior can help to explain stock market bubbles.
However, they go far beyond the stock market.
They also apply to the behavior of consumers and firm managers in a wide variety of settings. Such behavior cannot always be captured by the simplified assumptions that we have made up to this point about consumer choice. In the next section, we will discuss these aspects of behavior in detail, and we will see how the traditional models of Chapters 3 and 4 can be expanded to help us understand this behavior. See, for example, Robert Shiller, Irrational Exuberance, Princeton University Press, 2000.

CHAPTER 5 • Uncertainty and Consumer Behavior 185

5.5 Bubbles
During 1995 to 2000, the stock prices of many Internet companies rose sharply. What was behind these sharp price increases? One could argue—as many stock analysts, investment advisors, and ordinary investors did at the time—that these price increases were justified by fundamentals. Many people thought that the Internet’s potential was virtually unbounded, particularly as high-speed Internet access became more widely available. After all, more and more goods and services were being bought online through companies such as Amazon.com, Craigslist.org, Ticketmaster.com, Fandango. com, and a host of others. In addition, more and more people began to read the news online rather than buying physical newspapers and magazines, and more and more information became available online through sources like
Google, Bing, Wikipedia, and WebMD. And as a result, companies began to shift more and more of their advertising from newspapers and television to the Internet.
Yes, the Internet has certainly changed the way most of us live. (In fact, some of you may be reading the electronic version of this book, which you downloaded from the Pearson website and hopefully paid for!) But does that mean that any company with a name that ends in “.com” is sure to make high profits in the future? Probably not. And yet many investors (perhaps “speculators” is a better word) bought the stocks of Internet companies at very high prices, prices that were increasingly difficult to justify based on fundamentals, i.e., based on rational projections of future profitability. The result was the Internet bubble, an increase in the prices of Internet stocks based not on the fundamentals of business profitability, but instead on the belief that the prices of those stocks would keep going up. The bubble burst when people started to realize that the profitability of these companies was far from a sure thing, and that prices that go up can also come down.
Bubbles are often the result of irrational behavior. People stop thinking straight. They buy something because the price has been going up, and they believe (perhaps encouraged by their friends) that the price will keep going up, so that making a profit is a sure thing. If you ask these people whether the price might at some point drop, they typically will answer “Yes, but I will sell before the price drops.” And if you push them further by asking how they will know when the price is about to drop, the answer might be “I’ll just know.” But, of course, most of the time they won’t know; they will sell after the price has dropped, and they will lose at least part of their investment.
(There might be a silver lining—perhaps they will learn some economics from the experience.)
Bubbles are often harmless in the sense that while people lose money, there is no lasting damage to the overall economy. But that is not always the case.
The United States experienced a prolonged housing price bubble that burst in
2008, causing financial losses to large banks that had sold mortgages to home buyers who could not afford to make their monthly payments (but thought housing prices would keep rising). Some of these banks were given large government bailouts to keep them from going bankrupt, but many homeowners were less fortunate, and facing foreclosure, they lost their homes. By the end of 2008, the United States was in its worst recession since the Great Depression of the 1930s. The housing price bubble, far from harmless, was partly to blame for this.

• bubble An increase in the price of a good based not on the fundamentals of demand or value, but instead on a belief that the price will keep going up.

Recall from Section 4.3 that speculative demand is driven not by the direct benefits one obtains from owning or consuming a good but instead is driven by an expectation that the price of the good will increase.

186 PART 2 • Producers, Consumers, and Competitive Markets

E XA MPLE 5.7 THE HOUSING PRICE BUBBLE (I)
Starting around 1998, U.S. housing prices began rising sharply.
Figure 5.10 shows the S&P/CaseShiller housing price index at the national level.20 From 1987 (when the Index was first published) to
1998, the index rose around 3 percent per year in nominal terms. (In real terms, i.e., net of inflation, the index dropped about 0.5 percent per year.) This was a normal rate of price increase, roughly commensurate with population and income growth and with inflation. But then prices started rising much more rapidly, with the index increasing about 10 percent per year until it reached its peak of 190 in
2006. During that 8-year period from 1998 to 2006,

many people bought into the myth that housing was a sure-fire investment, and that prices could only keep going up. Many banks also bought into this myth and offered mortgages to people with incomes well below what it would take to make the monthly interest and principal payments over the long term. The demand for housing increased sharply, with some people buying four or five houses under the assumption that they could “flip” them in a year and make a quick profit. This speculative demand served to push prices up further.
However, in 2006 something funny happened.
Prices stopped going up. In fact, during 2006, prices

190

Home Price Index

170
Housing Price Index
(nominal)

150
130
110
90
70

Housing Price Index
(real)

50
1987

1989

1991

1993

1995

1997

1999
Year

2001

2003

2005

2007

2009

2011

F IGURE 5.10

S&P/CASE-SHILLER HOUSING PRICE INDEX
The Index shows the average home price in the United States at the national level. Note the increase in the index from 1998 to 2007, and then the sharp decline.

20
The S&P/Case-Shiller index measures the change in housing prices by tracking repeat sales of single family homes in 20 cities across the United States. By comparing a home’s original sale price with its price in subsequent sales, the index is able to control for other variables (i.e., size, location, style) that might also lead to rising home prices.

CHAPTER 5 • Uncertainty and Consumer Behavior 187

actually fell slightly (about 2 percent in nominal terms).
Then, in 2007 prices started falling rapidly, and by 2008 it had become clear that the great housing boom was just a bubble, and the bubble had burst. From its peak in early 2006 through 2011, housing prices fell by over
33 percent in nominal terms. (In real terms they fell by nearly 40% percent.) And this drop is an average for the United States as a whole. In some states, such as Florida, Arizona, and Nevada, the bubble was far worse, with prices dropping by over 50 percent.
The United States was not the only country to experience a housing price bubble. More or less the same thing happened in Europe. In Ireland, for

example, a booming economy and increasing foreign investment—along with widespread speculation— pushed housing prices up 305% between 1995 and 2007 (641% between 1987 and 2007—both in nominal terms). After over a decade of above average growth, Ireland’s bubble burst. By 2010, housing prices had fallen over 28% from their 2007 peak. Spain and other European countries suffered similar fates, contributing to a worldwide debt crisis. Other apparent bubbles have yet to deflate. Many Chinese cities, including Shanghai and Beijing, have seen rapidly rising housing and land prices, with some apartments reportedly doubling in value in mere months.21

Informational Cascades
Suppose you are considering investing in the stock of Ajax Corp., which is trading at $20 per share. Ajax is a biotech company that is working on a radically new approach to the treatment of chronic boredom (a disease that often afflicts students of economics). You find it difficult to evaluate the company’s prospects, but $20 seems like a reasonable price. But now you see the price is increasing—to $21, $22, then a jump to $25 per share. In fact, some friends of yours have just bought in at $25. Now the price reaches $30. Other investors must know something. Perhaps they consulted biochemists who can better evaluate the company’s prospects. So you decide to buy the stock at $30. You believe that positive information drove the actions of other investors, and you acted accordingly.
Was buying the stock of Ajax at $30 a rational decision, or were you simply buying into a bubble? It might indeed be rational. After all, it is reasonable to expect that other investors tried to value the company as best they could and that their analyses might have been more thorough or better informed than yours. Thus the actions of other investors could well be informative and lead you to rationally adjust your own valuation of the company.
Note that in this example, your investment decisions are based not on fundamental information that you have obtained (e.g., regarding the likelihood that
Ajax’s R&D will be successful), but rather on the investment decisions of others.
And note that you are implicitly assuming that: (i) these investment decisions of others are based on fundamental information that they have obtained; or (ii) these investment decisions of others are based on the investment decisions of others still, which are based on fundamental information that they have obtained; or
(iii) these investment decisions of others are based on the investment decisions of others still, which in turn are based on the investment decisions of still more others, which are based on fundamental information that they obtained; or . . . etc., etc. You get the idea. Maybe the “others” at the end of the chain based their investment decisions on weak information that was no more informative than the information you started with when you began thinking about Ajax. In other
21
Fearing a sudden collapse, the Chinese government took steps to curtail skyrocketing housing prices, tightening lending requirements and requiring purchasers to put more money down. See http://www.businessinsider.com/the-chinese-real-estate-bubble-is-the-most-obvious-bubbleever-2010-1#prices-are-way-out-of-whack-compared-to-global-standards-3. 188 PART 2 • Producers, Consumers, and Competitive Markets

E XA MPLE 5.8 THE HOUSING PRICE BUBBLE (II)
Informational cascades may help to explain the housing bubbles that occurred in the U.S. and other countries. For example, from 1999 to
2006, home prices in Miami nearly tripled. Would it have been completely irrational to buy real estate in Miami in 2006? In the years prior to 2006, some analysts projected large increases in the demand for housing in Miami and other parts of
Florida, based in part on a growing number of aging retirees that want to move to someplace warm, and in part on an influx of immigrants with family or other roots in Miami. If other investors acted on the belief that these analysts had done their homework, investing might have been rational. Informational cascades may also help explain the housing bubbles that took place in other parts of the U.S., notably
Arizona, Nevada, and California. (See
Figure 5.11.) There, too, some analysts had projected large increases in demand.
On the other hand, few analysts projected large demand increases in cities like Cleveland (not exactly a retirement paradise), and indeed such cities experienced little in the way of a bubble.
Was it rational to buy real estate in Miami in
2006? Rational or not, investors should have known that considerable risk was involved in buying real estate there (or elsewhere in Florida, Arizona,
Nevada, and California). Looking back, we now know that many of these investors lost their shirts
(not to mention their homes).

500
450

Home Price Index of Cities

400
350
300
250
200
150
100
50
1987

1989

1991

1993

Los Angeles

1995

Miami

1997

1999
Year

2001

Las Vegas

2003

2005

New York

2007

2009

2011

Cleveland

F IGURE 5.11

S&P/CASE-SHILLER HOUSING PRICE INDEX FOR FIVE CITIES
The Index shows the average home price for each of five cities (in nominal terms). For some cities, the housing bubble was much worse than for others. Los Angeles, Miami, and Las Vegas experienced some of the sharpest increases in home prices, and then starting in 2007, prices plummeted. Cleveland, on the other hand, largely avoided the bubble, with home prices increasing, and then falling, only moderately.

CHAPTER 5 • Uncertainty and Consumer Behavior 189

words, your own investment decisions might be the result of an informational cascade—actions based on actions based on actions . . . , etc., driven by very limited fundamental information.
The bubble that results from an informational cascade can in fact be rational in the sense that there is a basis for believing that investing in the bubble will yield a positive return. The reason is that if investors early in the chain indeed obtained positive information and based their decisions on that information, the expected gain to an investor down the chain will be positive.22 However, the risk involved will be considerable, and it is likely that at least some investors will underestimate that risk.

5.6 Behavioral Economics
Recall that the basic theory of consumer demand is based on three assumptions:
(1) consumers have clear preferences for some goods over others; (2) consumers face budget constraints; and (3) given their preferences, limited incomes, and the prices of different goods, consumers choose to buy combinations of goods that maximize their satisfaction (or utility). These assumptions, however, are not always realistic: Preferences are not always clear or might vary depending on the context in which choices are made, and consumer choices are not always utility-maximizing. Perhaps our understanding of consumer demand (as well as the decisions of firms) would be improved if we incorporated more realistic and detailed assumptions regarding human behavior. This has been the objective of the newly flourishing field of behavioral economics, which has broadened and enriched the study of microeconomics.23 We introduce this topic by highlighting some examples of consumer behavior that cannot be easily explained with the basic utility-maximizing assumptions that we have relied on so far:
• There has just been a big snowstorm, so you stop at the hardware store to buy a snow shovel. You had expected to pay $20 for the shovel—the price that the store normally charges. However, you find that the store has suddenly raised the price to $40. Although you would expect a price increase because of the storm, you feel that a doubling of the price is unfair and that the store is trying to take advantage of you. Out of spite, you do not buy the shovel.24
• Tired of being snowed in at home you decide to take a vacation in the country. On the way, you stop at a highway restaurant for lunch. Even though you are unlikely to return to that restaurant, you believe that it is fair and

22

For a reasonably simple example that makes this point (and an interesting discussion), see
S. Bikhchandani, D. Hirschleifer, and I. Welch, “Learning from the Behavior of Others: Conformity,
Fads, and Informational Cascades,” 12 Journal of Economic Perspectives, (Summer 1998): 151–170.

23

For more detailed discussion of the material presented in this section, see Stefano DellaVigna,
“Psychology and Economics: Evidence from the Field,” Journal of Economic Literature 47(2), 2009:
315–372; Colin Camerer and George Loewenstein, “Behavioral Economics: Past, Present, Future,” in Colin Camerer, George Loewenstein, and Matthew Rabin (eds.), Advances in Behavioral Economics,
Princeton University Press, 2003.
24
This example is based on Daniel Kahneman, Jack Knetsch, and Richard Thaler, “Fairness as a
Constraint on Profit Seeking: Entitlements in the Market,” American Economic Review 76 (September
1986): 728–741.

• Informational cascade
An assessment (e.g., of an investment opportunity) based in part on the actions of others, which in turn were based on the actions of others.

190 PART 2 • Producers, Consumers, and Competitive Markets appropriate to leave a 15-percent tip in appreciation of the good service that you received.
• You buy this textbook from an Internet bookseller because the price is lower than the price at your local bookstore. However, you ignore the shipping cost when comparing prices.
Each of these examples illustrates plausible behavior that cannot be explained by a model based solely on the basic assumptions described in Chapters 3 and 4.
Instead, we need to draw on insights from psychology and sociology to augment our basic assumptions about consumer behavior. These insights will enable us to account for more complex consumer preferences, for the use of simple rules in decision-making, and for the difficulty that people often have in understanding the laws of probability.
Adjustments to the standard model of consumer preferences and demand can be grouped into three categories: A tendency to value goods and services in part based on the setting one is in, a concern about the fairness of an economic transaction, and the use of simple rules of thumb as a way to cut through complex economic decisions. We examine each of these in turn.

Reference Points and Consumer Preferences

• reference point The point from which an individual makes a consumption decision.

• endowment effect
Tendency of individuals to value an item more when they own it than when they do not.

The standard model of consumer behavior assumes that consumers place unique values on the goods and services they purchase. However, psychologists and market research studies have found that perceived value depends in part on the setting in which the purchasing decision occurs. That setting creates a reference point on which preferences might be at least partly based. The reference point—the point from which the individual makes the consumption decision—can strongly affect that decision. Consider, for example, apartment prices in Pittsburgh and San Francisco. In Pittsburgh, the median monthly rent in 2006 for a two-bedroom apartment was about $650, while in
San Francisco the rent for a similar apartment was $2,125. For someone accustomed to San Francisco housing prices, Pittsburgh might seem like a bargain.
On the other hand, someone moving from Pittsburgh to San Francisco might feel “gouged”—thinking it unfair for housing to cost that much.25 In this example, the reference point is clearly different for long-time residents of Pittsburgh and San Francisco.
Reference points can develop for many reasons: our past consumption of a good, our experience in a market, our expectation about how prices should behave, and even the context in which we consume a good. Reference points can strongly affect the way people approach economic decisions. Below we describe several different examples of reference points and the way they affect consumer behavior. ENDOWMENT EFFECT A well-known example of a reference point is the endowment effect—the fact that individuals tend to value an item more when they happen to own it than when they do not. One way to think about this effect is to consider the gap between the price that a person is willing to pay for a good and the price at which she is willing to sell the same good to someone else. Our
25
This example is based on Uri Simonsohn and George Loewenstein, “Mistake #37: The Effects of
Previously Encountered Prices on Current Housing Demand,” The Economic Journal 116 (January
2006): 175–199.

CHAPTER 5 • Uncertainty and Consumer Behavior 191

basic theory of consumer behavior says that this price should be the same, but many experiments suggest that is not what happens in practice.26
In one classroom experiment, half of the students chosen at random were given a free coffee mug with a market value of $5; the other half got nothing.27
Students with the mug were asked the price at which they would sell it back to the professor; the second group was asked the minimum amount of money that they would accept in lieu of a mug. The decision faced by both groups is similar but their reference points are different. For the first group, whose reference point was possession of a mug, the average selling price was $7. For the second group, which did not have a mug, the average amount desired in lieu of a mug was $3.50. This gap in prices shows that giving up the mug was perceived to be a greater “loss” to those who had one than the “gain” from obtaining a mug for those without one. This is an endowment effect—the mug was worth more to those people who already owned it.
LOSS AVERSION The coffee mug experiment described above is also an example of loss aversion—the tendency of individuals to prefer avoiding losses over acquiring gains. The students who owned the mug and believed that its market value was indeed $5 were averse to selling it for less than $5 because doing so would have created a perceived loss. The fact that they had been given the mug for free, and thus would still have had an overall gain, didn’t matter as much.
As another example of loss aversion, people are sometimes hesitant to sell stocks at a loss, even if they could invest the proceeds in other stocks that they think are better investments. Why? Because the original price paid for the stock—which turned out to be too high given the realities of the market—acts as a reference point, and people are averse to losses. (A $1000 loss on an investment seems to “hurt” more than the perceived benefit from a $1000 gain.) While there are a variety of circumstances in which endowment effects arise, we now know that these effects tend to disappear as consumers gain relevant experience. We would not expect to see stockbrokers or other investment professionals exhibit the loss aversion described above.28
FRAMING Preferences are also influenced by framing, which is another manifestation of reference points. Framing is a tendency to rely on the context in which a choice is described when making a decision. How choices are framed—the names they are given, the context in which they are described, and their appearance—can affect the choices that individuals make. Are you more likely to buy a skin cream whose package claims that is will “slow the aging process” or one that is described as “making you feel young again.”
These products might be essentially identical except for their packaging.
Yet, in the real world where information is sometimes limited and perspective matters, many individuals would prefer to buy the product that emphasizes youth.
26

Experimental work such as this has been important to the development of behavioral economics. It is for this reason that the 2002 Nobel Prize in economics was shared by Vernon Smith, who did much of the pioneering work in the use of experiments to test economic theories.
27

Daniel Kahneman, Jack L. Knetsch, and Richard H. Thaler, “Experimental Tests of the Endowment
Effect and the Coase Theorem,” Journal of Political Economy 98, (December 1990): 1925–48.
28

John A. List, “Does Market Experience Eliminate Market Anomalies?” Quarterly Journal of Economics
118 (January 2003): 41–71.

• loss aversion Tendency for individuals to prefer avoiding losses over acquiring gains.

• framing Tendency to rely on the context in which a choice is described when making a decision. 192 PART 2 • Producers, Consumers, and Competitive Markets

E XA MPLE 5.9 SELLING A HOUSE
Homeowners sometimes sell their homes because they have to relocate for a new job, because they want to be closer to (or farther from) the city in which they work, or because they want to move to a bigger or smaller house. So they put their home on the market. But at what price? The owners can usually get a good idea of what the house will sell for by looking at the selling prices of comparable houses, or by talking with a realtor. Often, however, the owners will set an asking price that is well above any realistic expectation of what the house can actually sell for. As a result, the house may stay on the market for many months before the owners grudgingly lower the price. During that time the owners have to continue to maintain the house and pay for taxes, utilities, and insurance.
This seems irrational. Why not set an asking price closer to what the market will bear?
The endowment effect is at work here. The homeowners view their house as special; their

ownership has given them what they think is a special appreciation of its value—a value that may go beyond any price that the market will bear. If housing prices have been falling, loss aversion could also be at work. As we saw in Examples
5.7 and 5.8, U.S and European housing prices started falling around 2008, as the housing bubble deflated. As a result, some homeowners were affected by loss aversion when deciding on an asking price, especially if they bought their home at a time near the peak of the bubble. Selling the house turns a paper loss, which may not seem real, into a loss that is real. Averting that reality may serve to explain the reluctance of home owners to take that final step of selling their home. It is not surprising, therefore, to find that houses tend to stay on the market longer during economic downturns than in upturns. Fairness
People sometimes do things because they think it is appropriate or fair to do so, even though there is no financial or other material benefit. Examples include charitable giving, volunteering time, or tipping in a restaurant. Fairness likewise affected consumer behavior in our example of buying a snow shovel.
At first glance, our basic consumer theory does not appear to account for fairness. However, we can often modify our models of demand to account for the effects of fairness on consumer behavior. To see how, let’s return to our original snow shovel example. In that example, the market price of shovels was $20, but right after a snowstorm (which caused a shift in the demand curve), stores raised their price to $40. Some consumers, however, felt they were being unfairly gouged, and refused to buy a shovel.
This is illustrated in Figure 5.12. Demand curve D1 applies during normal weather. Stores have been charging $20 for a shovel, and sell a total quantity of Q1 shovels per month (because many consumers buy shovels in anticipation of snow). In fact some people would have been willing to pay much more for a shovel (the upper part of the demand curve), but they don’t have to because the market price is $20. Then the snowstorm hits, and the demand curve shifts to the right. Had the price remained $20, the quantity demanded would have increased to Q2. But note that the new demand curve (D2) does not extend up as far as the old one. Many consumers might feel that an increase in price to, say,
$25 is fair, but an increase much above that would be unfair gouging. Thus the new demand curve becomes very elastic at prices above $25, and no shovels can be sold at a price much above $30.
Note how fairness comes in to play here. In normal weather, some consumers would have been willing to pay $30 or even $40 for a shovel. But they know that

CHAPTER 5 • Uncertainty and Consumer Behavior 193

P

F IGURE 5.12

$40

DEMAND FOR SNOW SHOVELS

$25
$20

D2
D1
Q1

Q2

Demand curve D1 applies during normal weather. Stores have been charging $20 and sell Q1 shovels per month. When a snowstorm hits, the demand curve shifts to the right. Had the price remained $20, the quantity demanded would have increased to Q2. But the new demand curve (D2) does not extend up as far as the old one. Consumers view an increase in price to, say, $25 as fair, but an increase much above that as unfair gouging. The new demand curve is very elastic at prices above $25, and no shovels can be sold at a price much above $30.

Q

the price has always been $20, and they feel that a sharp increase in price after a snowstorm is unfair gouging and refuse to buy. Note also how we can modify standard demand curves to account for consumer attitudes towards fairness.
Another example of fairness arises in the ultimatum game. Imagine that, under the following rules, you are offered a chance to divide 100 one-dollar bills with a stranger whom you will never meet again: You first propose a division of the money between you and the stranger. The stranger will respond by either accepting or rejecting your proposal. If he accepts, you each get the share that you proposed. If he rejects, you both get nothing. What should you do?
Because more money means more utility, our basic theory provides a clear answer to this question. You should propose that you get $99 while the other person gets only $1. Moreover, the responder should be happy to accept this proposal, because $1 is more than he had before and more than he would get if he rejected your offer (in both cases zero). This is a beneficial deal for both of you.
Yet most people facing this choice hesitate to make such an offer because they think it unfair, and many “strangers” would reject the offer. Why? The stranger might believe that because you both received the windfall opportunity to divide
$100, a simple and fair division would be 50/50 or something close to that.
Maybe the stranger will turn down the $1 offer to teach you that greediness is not appropriate behavior. Indeed, if you believe that the stranger will feel this way, it will be rational for you to offer a greater amount. In fact, when this game is played experimentally, typical sharing proposals range between 67/33 and
50/50, and such offers are normally accepted.
The ultimatum game shows how fairness can affect economic decisions. Not surprisingly, fairness concerns can also affect negotiations between firms and their workers. A firm may offer a higher wage to employees because the managers believe that workers deserve a comfortable standard of living or because they want to foster a pleasant working environment. Moreover, workers who do

194 PART 2 • Producers, Consumers, and Competitive Markets not get a wage that they feel is fair may not put much effort into their work.29
(In Section 17.6, we will see that paying workers higher-than-market wages can also be explained by the “efficiency wage theory” of labor markets, in which fairness concerns do not apply.) Fairness also affects the ways in which firms set prices and can explain why firms can more easily raise prices in response to higher costs than to increases in demand.30
Fortunately, fairness concerns can be taken into account in the basic model of consumer behavior. If individuals moving to San Francisco believe that high apartment rents are unfair, their maximum willingness to pay for rental housing will be reduced. If a sufficient number of individuals feel this way, the resulting reduction in demand will lead to lower rental prices. Similarly, if enough workers do not feel that their wages are fair, there will be a reduction in the supply of labor, and wage rates will increase.

Rules of Thumb and Biases in Decision Making
Many economic (and everyday) decisions can be quite complex, especially if they involve choices about matters in which we have little experience. In such cases, people often resort to rule of thumb or other mental shortcuts to help them make decisions. In the tipping example, you took a mental shortcut when you decided to offer a 15-percent tip. The use of such rules of thumb, however, can introduce a bias into our economic decision making—something that our basic model does not allow.31

• anchoring Tendency to rely heavily on one prior (suggested) piece of information when making a decision.

ANCHORING The mental rules that we use in making decisions frequently depend on both the context in which the decisions are made and the information available. For example, imagine that you just received a solicitation from a new local charity to make a donation. Rather than asking for a gift of any amount, the charity asks you to choose: $20, $50, $100, $250, or “other.” The purpose of these suggestions is to induce you to anchor your final donation. Anchoring refers to the impact that a suggested (perhaps unrelated) piece of information may have on your final decision. Rather than trying to decide precisely how much to donate—say $44.52—and not wanting to appear miserly, one might simply write a check for the next higher category—$50. Another individual wishing to make only a token donation of $10 might choose the lowest stated amount, $20.
In both cases, anchoring can bias individual choices toward larger donations.
Similarly, it’s no coincidence so many price tags end with the digits 95 or 99.
Marketers understand that consumers tend to overemphasize the first digit of prices, and also to think in terms of price categories like “under $20” or “over
$20.” Thus to the consumer, who may not be thinking too carefully, $19.95 seems much cheaper than $20.01.
RULES OF THUMB A common way to economize on the effort involved in making decisions is to ignore seemingly unimportant pieces of information.
29

For a general discussion of behavioral economics and the theory of wages and employment, see
George Akerlof, “Behavioral Macroeconomics and Macroeconomic Behavior,” American Economic
Review 92 (June 2002): 411–33.

30

See, for example, Julio J. Rotemberg, “Fair Pricing,” NBER Working Paper No. W10915, 2004.

31

For an introduction to this topic see Amos Tversky and Daniel Kahneman, “Judgment under
Uncertainty: Heuristics and Biases,” Science 185 (September 1974): 1124–31.

CHAPTER 5 • Uncertainty and Consumer Behavior 195

For example, goods purchased over the Internet often involve shipping costs.
Although small, these costs should be included as part of the good’s final price when making a consumption decision. However, a recent study has shown that shipping costs are typically ignored by many consumers when deciding to buy things online. Their decisions are biased because they view the price of goods to be lower than they really are.32
Whereas depending on rules of thumb can introduce biases in decision making, it is important to understand that they do serve a useful purpose. Frequently, rules of thumb help to save time and effort and result in only small biases. Thus, they should not be dismissed outright.
Consumers often face uncertainty when making decisions, and lack the understanding of probability to make those decisions optimally. (Consider the difficulty involved, for example, in calculating expected utility.) Consumers will often use rules of thumb when making decisions, but sometimes those rules of thumb can lead to strong biases.
THE LAW OF SMALL NUMBERS People are sometimes prone to a bias called the law of small numbers: They tend to overstate the probability that certain events will occur when faced with relatively little information from recent memory. For example, many people tend to overstate the likelihood that they or someone they know will die in a plane crash or win the lottery. Recall the roulette player who bets on black after seeing red come up three times in a row:
He has ignored the laws of probability.
Research has shown that investors in the stock market are often subject to a small-numbers bias, believing that high returns over the past few years are likely to be followed by more high returns over the next few years—thereby contributing to the kind of “herd behavior” that we discussed in the previous section. In this case, investors assess the likely payoff from investing by observing the market over a short period of time. In fact, one would have to study stock market returns for many decades in order to estimate accurately the expected return on equity investments. Similarly when people assess the likelihood that housing prices will rise based on several years of data, the resulting misperceptions can result in housing price bubbles.33
Although individuals may have some understanding of true probabilities (as when flipping a coin), complications arise when probabilities are unknown. For instance, few people have an idea about the probability that they or a friend will be in a car or airplane accident. In such cases, we form subjective probability assessments about such events. Our estimation of subjective probabilities may be close to true probabilities, but often they are not.
Forming subjective probabilities is not always an easy task and people are generally prone to several biases in the process. For instance, when evaluating the likelihood of an event, the context in which the evaluation is made can be very important. If a tragedy such as a plane crash has occurred recently, many people will tend to overestimate the probability of it happening to them.
Likewise, when a probability for a particular event is very, very small, many people simply ignore that possibility in their decision making.

32

Tankim Hossain and John Morgan, “… Plus Shipping and Handling: Revenue (Non) Equivalence in Field Experiments on eBay,” Advances in Economic Analysis & Policy 6: 2 (2006).
33

See Charles Himmelberg, Christopher Mayer, and Todd Sinai, “Assessing High House Prices:
Bubbles, Fundamentals and Misperceptions,” Journal of Economic Perspectives 19 (Fall 2005): 67–92.

• law of small numbers Tendency to overstate the probability that a certain event will occur when faced with relatively little information. 196 PART 2 • Producers, Consumers, and Competitive Markets

Summing Up
Where does this leave us? Should we dispense with the traditional consumer theory discussed in Chapters 3 and 4? Not at all. In fact, the basic theory that we learned up to now works quite well in many situations. It helps us to understand and evaluate the characteristics of consumer demand and to predict the impact on demand of changes in prices or incomes. Although it does not explain all consumer decisions, it sheds light on many of them. The developing field of behavioral economics tries to explain and to elaborate on those situations that are not well explained by the basic consumer model.
If you continue to study economics, you will notice many cases in which economic models are not a perfect reflection of reality. Economists have to carefully decide, on a case-by-case basis, what features of the real world to include and what simplifying assumptions to make so that models are neither too complicated to study nor too simple to be useful.

E XA MPLE 5.10 NEW YORK CITY TAXICAB DRIVERS
Most cab drivers rent their taxicabs for a fixed daily fee from a company that owns a fleet of cars.
They can then choose to drive the cab as little or as much as they want during a 12-hour period. As with many services, business is highly variable from day to day, depending on the weather, subway breakdowns, holidays, and so on. How do cabdrivers respond to these variations, many of which are largely unpredictable?
In many cities, taxicab rates are fixed by regulation and do not change from day to day. However, on busy days drivers can earn a higher income because they do not have to spend as much time searching for riders. Traditional economic theory would predict that drivers will work longer hours on busy days than on slow days; an extra hour on a busy day might bring in
$20, whereas an extra hour on a slow day might yield only $10. Does traditional theory explain the actual behavior of taxicab drivers?
An interesting study analyzed actual taxicab trip records obtained from the New York Taxi and
Limousine Commission for the spring of 1994.34 The daily fee to rent a taxi was then $76, and gasoline cost about $15 per day. Surprisingly, the researchers

34

found that most drivers drive more hours on slow days and fewer hours on busy days. In other words, there is a negative relationship between the effective hourly wage and the number of hours worked each day; the higher the wage, the sooner the cabdrivers quit for the day. Behavioral economics can explain this result. Suppose that most taxicab drivers have an income target for each day. That target effectively serves as a reference point. Daily income targeting makes sense from a behavioral perspective. An income target provides a simple decision rule for drivers because they need only keep a record of their fares for the day. A daily target also helps drivers with potential self-control problems; without a target, a driver may choose to quit earlier on many days just to avoid the hassles of the job.
The target in the 1994 study appeared to be about
$150 per day.
Still other studies challenge this “behavioral” explanation of behavior. A different study, also of
New York City cab drivers who rented their taxis, concluded that the traditional economic model does indeed offer important insights into drivers’

Colin Camerer, Linda Babcock, George Loewenstein, and Richard Thaler, “Labor Supply of New
York City Cabdrivers: One Day at a Time,” Quarterly Journal of Economics (May 1997): 404–41. See also, Henry S. Farber, “Reference-Dependent Preferences and Labor Supply: The Case of New York
City Taxi Drivers,” American Economic Review 98 (2008): 1069–82.

CHAPTER 5 • Uncertainty and Consumer Behavior 197

behavior.35 The study concluded that daily income had only a small effect on a driver’s decision as to when to quit for the day. Rather, the decision to stop appears to be based on the cumulative number of hours already worked that day and not on hitting a specific income target.
What may soon become known as “the great taxicab driver debate” did not end here. A recent study sought to explain these two seemingly

contradictory results. Reanalyzing the same taxicab trip records, the authors found that the traditional economic model goes a long way in explaining most workday decisions of taxicab drivers, but that a behavioral model that accounts for reference points and targeted goals (for income and hours) can do even better.36 If you are interested in learning more about the taxicab industry, you can look ahead to the examples in Chapters 8, 9, and 15.

SUMMARY
1. Consumers and managers frequently make decisions in which there is uncertainty about the future. This uncertainty is characterized by the term risk, which applies when each of the possible outcomes and its probability of occurrence is known.
2. Consumers and investors are concerned about the expected value and the variability of uncertain outcomes. The expected value is a measure of the central tendency of the values of risky outcomes. Variability is frequently measured by the standard deviation of outcomes, which is the square root of the probabilityweighted average of the squares of the deviation from the expected value of each possible outcome.
3. Facing uncertain choices, consumers maximize their expected utility—an average of the utility associated with each outcome—with the associated probabilities serving as weights.
4. A person who would prefer a certain return of a given amount to a risky investment with the same expected return is risk averse. The maximum amount of money that a risk-averse person would pay to avoid taking a risk is called the risk premium. A person who is

5.
6.

7.

8.

indifferent between a risky investment and the certain receipt of the expected return on that investment is risk neutral. A risk-loving consumer would prefer a risky investment with a given expected return to the certain receipt of that expected return.
Risk can be reduced by (a) diversification, (b) insurance, and (c) additional information.
The law of large numbers enables insurance companies to provide insurance for which the premiums paid equal the expected value of the losses being insured against. We call such insurance actuarially fair.
Consumer theory can be applied to decisions to invest in risky assets. The budget line reflects the price of risk, and consumers’ indifference curves reflect their attitudes toward risk.
Individual behavior sometimes seems unpredictable, even irrational, and contrary to the assumptions that underlie the basic model of consumer choice. The study of behavioral economics enriches consumer theory by accounting for reference points, endowment effects, anchoring, fairness considerations, and deviations from the laws of probability.

QUESTIONS FOR REVIEW
1. What does it mean to say that a person is risk averse?
Why are some people likely to be risk averse while others are risk lovers?
2. Why is the variance a better measure of variability than the range?
3. George has $5000 to invest in a mutual fund. The expected return on mutual fund A is 15 percent and the expected return on mutual fund B is 10 percent.
Should George pick mutual fund A or fund B?

4. What does it mean for consumers to maximize expected utility? Can you think of a case in which a person might not maximize expected utility?
5. Why do people often want to insure fully against uncertain situations even when the premium paid exceeds the expected value of the loss being insured against?
6. Why is an insurance company likely to behave as if it were risk neutral even if its managers are risk-averse individuals? 35
Henry S. Farber, “Is Tomorrow Another Day? The Labor Supply of New York City Cabdrivers,”
Journal of Political Economy 113 (2005): 46–82.
36

See Vincent P. Crawford and Juanjuan Meng, “New York City Cab Drivers’ Labor Supply Revisited:
Reference-Dependent Preferences with Rational-Expectations Targets for Hours and Income,”
American Economic Review, 101 (August 2011): 1912–1934.