ECON 2210 Chapter Notes - Chapter 5: Risk Neutral, Moral Hazard, Risk Premium
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Chapter 5
Uncertainty and Consumer Behavior
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?
A risk-averse person has a diminishing marginal utility of income and prefers a certain income to a
gamble with the same expected income. A risk lover has an increasing marginal utility of income and
prefers an uncertain income to a certain income when the expected value of the uncertain income
equals the certain income. To some extent, a person’s risk preferences are like preferences for different
vegetables. They may be inborn or learned from parents or others, and we cannot easily say why
some people are risk averse while others like taking risks. But there are some economic factors that
can affect risk preferences. For example, a wealthy person is more likely to take risks than a moderately
well-off person, because the wealthy person can better handle losses. Also, people are more likely to
take risks when the stakes are low (like office pools around NCAA basketball time) than when stakes
are high (like losing a house to fire).
2. Why is the variance a better measure of variability than the range?
Range is the difference between the highest possible outcome and the lowest possible outcome.
Range ignores all outcomes except the highest and lowest, and it does not consider how likely each
outcome is. Variance, on the other hand, is based on all the outcomes and how likely they are to occur.
Variance weights the difference of each outcome from the mean outcome by its probability, and thus
is a more comprehensive 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% and
the expected return on mutual fund B is 10%. Should George pick mutual fund A or fund B?
George’s decision will depend not only on the expected return for each fund, but also on the variability
of each fund’s returns and on George’s risk preferences. For example, if fund A has a higher standard
deviation than fund B, and George is risk averse, then he may prefer fund B even though it has a
lower expected return. If George is not particularly risk averse he may choose fund A even if its
return is more variable.
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?
To maximize expected utility means that the individual chooses the option that yields the highest
average utility, where average utility is the probability-weighted sum of all utilities. This theory
requires that the consumer knows each possible outcome that may occur and the probability of each
outcome. Sometimes consumers either do not know all possible outcomes and the relevant probabilities,
or they have difficulty evaluating low-probability, extreme-payoff events. In some cases, consumers
cannot assign a utility level to these extreme-payoff events, such as when the payoff is the loss of the
consumer’s life. In cases like this, consumers may make choices based on other criteria such as risk
avoidance.
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Chapter 5 Uncertainty and Consumer Behavior 79
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall.
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?
Risk averse people have declining marginal utility, and this means that the pain of a loss increases at
an increasing rate as the size of the loss increases. As a result, they are willing to pay more than the
expected value of the loss to insure against suffering the loss. For example, consider a homeowner
who owns a house worth $200,000. Suppose there is a small 0.001 probability that the house will
burn to the ground and be a total loss and a high probability of 0.999 that there will be no loss. The
expected loss is 0.001(200,000) 0.999(0) $200. Many risk averse homeowners would be willing
to pay a lot more than $200 (like $400 or $500) to buy insurance that will replace the house if it burns.
They do this because the disutility of losing their $200,000 house is more than 1000 times larger than
the disutility of paying the insurance premium.
6. Why is an insurance company likely to behave as if it were risk neutral even if its managers are
risk-averse individuals?
A large insurance company sells hundreds of thousands of policies, and the company’s managers
know they will have to pay for losses incurred by some of their policyholders even though they do
not know which particular policies will result in claims. Because of the law of large numbers,
however, the company can estimate the total number of claims quite accurately. Therefore, it can
make very precise estimates of the total amount it will have to pay in claims. This means the
company faces very little risk overall and consequently behaves essentially as if it were risk neutral.
Each manager, on the other hand, cannot diversify his or her own personal risks to the same extent,
and thus each faces greater risk and behaves in a much more risk-averse manner.
7. When is it worth paying to obtain more information to reduce uncertainty?
It is worth paying for information if the information leads the consumer to make different choices
than she would have made without the information, and the expected utility of the payoffs (deducting
the cost of the information) is greater with the information than the expected utility of the payoffs
received when making the best choices without knowing the information.
8. How does the diversification of an investor’s portfolio avoid risk?
An investor reduces risk by investing in many assets whose returns are not highly correlated and,
even better, some whose returns are negatively correlated. A mutual fund, for example, is a portfolio
of stocks of many different companies. If the rate of return on each company’s stock is not highly
related to the rates of return earned on the other stocks in the portfolio, the portfolio will have a lower
variance than any of the individual stocks. This occurs because low returns on some stocks tend to be
offset by high returns on others. As the number of stocks in the portfolio increases, the portfolio’s
variance decreases. While there is less risk in a portfolio of stocks, risk cannot be completely
avoided; there is still some market risk in holding a portfolio of stocks compared to a low-risk asset,
such as a U.S. government bond.
9. Why do some investors put a large portion of their portfolios into risky assets, while others
invest largely in risk-free alternatives? (Hint: Do the two investors receive exactly the same
return on average? If so, why?)
Most investors are risk averse, but some are more risk averse than others. Investors who are highly
risk averse will invest largely in risk-free alternatives while those who are less risk averse will put a
larger portion of their portfolios into risky assets. Of course, because investors are risk averse, they
will demand higher rates of return on investments that have higher levels of risk (i.e., higher variances).
So investors who put larger amounts into risky assets expect to earn greater rates of return than those
who invest primarily in risk-free assets.
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80 Pindyck/Rubinfeld, Microeconomics, Eighth Edition
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall.
10. What is an endowment effect? Give an example of such an effect.
An endowment effect exists if an individual places a higher value on an item that is in her possession
as compared to the value she places on the same item when it is not in her possession. For example,
some people might refuse to pay $5 for a simple coffee mug but would also refuse to sell the same
mug for $5 if they already owned it or had just gotten it for free.
11. Jennifer is shopping and sees an attractive shirt. However, the price of $50 is more than she is
willing to pay. A few weeks later, she finds the same shirt on sale for $25 and buys it. When a
friend offers her $50 for the shirt, she refuses to sell it. Explain Jennifer’s behavior.
To help explain Jennifer’s behavior, we need to look at the reference point from which she is making
the decision. In the first instance, she does not own the shirt so she is not willing to pay the $50 to
buy the shirt. In the second instance, she will not accept $50 for the shirt from her friend because her
reference point has changed. Once she owns the shirt, the value she attaches to it increases.
Individuals often value goods more when they own them than when they do not. This is called the
endowment effect.
Exercises
1. Consider a lottery with three possible outcomes:
● $125 will be received with probability 0.2
● $100 will be received with probability 0.3
● $50 will be received with probability 0.5
a. What is the expected value of the lottery?
The expected value, EV, of the lottery is equal to the sum of the returns weighted by their
probabilities:
EV (0.2)($125) (0.3)($100) (0.5)($50) $80.
b. What is the variance of the outcomes?
The variance,
2, is the sum of the squared deviations from the mean, $80, weighted by their
probabilities:
2 (0.2)(125 80)2 (0.3)(100 80)2 (0.5)(50 80)2 $975.
c. What would a risk-neutral person pay to play the lottery?
A risk-neutral person would pay the expected value of the lottery: $80.
2. Suppose you have invested in a new computer company whose profitability depends on two
factors: (1) whether the U.S. Congress passes a tariff raising the cost of Japanese computers
and (2) whether the U.S. economy grows slowly or quickly. What are the four mutually
exclusive states of the world that you should be concerned about?
The four mutually exclusive states may be represented as:
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Document Summary
A risk-averse person has a diminishing marginal utility of income and prefers a certain income to a gamble with the same expected income. A risk lover has an increasing marginal utility of income and prefers an uncertain income to a certain income when the expected value of the uncertain income equals the certain income. To some extent, a person"s risk preferences are like preferences for different vegetables. They may be inborn or learned from parents or others, and we cannot easily say why some people are risk averse while others like taking risks. But there are some economic factors that can affect risk preferences. For example, a wealthy person is more likely to take risks than a moderately well-off person, because the wealthy person can better handle losses. Also, people are more likely to take risks when the stakes are low (like office pools around ncaa basketball time) than when stakes are high (like losing a house to fire).
