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1、CHAPTER 5UNCERTAINTY AND CONSUMER BEHAVIORTEACHING NOTESChoice under uncertainty is an important topic in microeconomic theory, but students find the concept difficult. The topic should be covered in business-oriented courses, particularly if you intend to cover the role of risk in capital markets,
2、which is discussed in Chapter 15. The primary purpose of this chapter is to encourage students to think about the influence on behavior of attitudes toward risk. The first three sections of the chapter should be covered in at least two lectures, giving the students time to absorb the basic ideas.If
3、students have not been previously exposed to probability, expected value, and variance, they will have difficulty with this chapter, particularly with Exercises (1) through (5), which illustrate these concepts. Most students without a background in probability consider risk to be the possibility of
4、loss or injury, instead of the probability of either loss or gain. Make sure they understand this distinction before further discussing uncertainty.If students have had basic probability theory before and you have covered utility theory, they should easily grasp the definition of expected utility. H
5、owever, they usually confuse the utility of an expected value with expected utility. Both concepts are needed to explain risk aversion in general and the subtleties of Exercise (7) in particular. For an empirical analysis of gambling, see Selby and Beranek, “Sweepstake Contests: Analysis, Strategies
6、, and Survey,” American Economic Review (March 1981) and Brunk, “A Test of the Friedman-Savage Gambling Model,” Quarterly Journal of Economics (May 1981). In a more theoretical class, present the derivation of the Von Neumann-Morgenstern utility function. See Copeland and Westons discussion of utili
7、ty theory under uncertainty in Chapter 4, Financial Theory and Corporate Policy (Addison-Wesley, 1979).Even if your students have not fully understood the technical aspects of choice under uncertainty, they should easily comprehend Examples 5.1 and 5.2 (the latter example leads to Exercise (8), whic
8、h is easier than it looks). This is also true of the topics presented in Section 5.3, i.e., diversification and purchasing insurance and Examples 5.3 and 5.4. Also, you might mention the problems of adverse selection and moral hazard in insurance, to be discussed in Chapter 17.The last section, 5.4,
9、 is more difficult and may be postponed until after the class has completed the discussion of risk and rates of return in Chapter 15.QUESTIONS FOR REVIEW1. 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
10、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. The economic explanation of whether an individual is risk averse
11、or risk loving depends on the shape of the individuals utility function for wealth. Also, a persons risk aversion (or risk loving) depends on the nature of the risk involved and on the persons income.2. Why is the variance a better measure of variability than the range?Range is the difference betwee
12、n the highest possible outcome and the lowest possible outcome. Range does not indicate the probabilities of observing these high or low outcomes. Variance weighs the difference of each outcome from the mean outcome by its probability and, thus, is a more useful measure of variability than the range
13、.3. George has $5,000 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?Georges decision will depend not only on the expected return for each fund, but also on the variability in the exp
14、ected return on each fund, and on Georges 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 it subjec
15、t to more variability in its expected return.4. What does it mean for consumers to maximize expected utility? Can you think of a case where a person might not maximize expected utility?The expected utility is the sum of the utilities associated with all possible outcomes, weighted by the probability
16、 that each outcome will occur. To maximize expected utility means that the individual chooses the option that yields the highest average utility, where average utility is a probability-weighted sum of all utilities. This theory requires that the consumer knows the probability of every outcome. At ti
17、mes, consumers either do not know the relevant probabilities or have difficulty in evaluating low-probability, high-payoff events. In some cases, consumers cannot assign a utility level to these high-payoff events, such as when the payoff is the loss of the consumers life.5. Why do people often want
18、 to insure fully against uncertain situations even when the premium paid exceeds the expected value of the loss being insured against?If the cost of insurance is equal to the expected loss, (i.e., if the insurance is actuarially fair), risk-averse individuals will fully insure against monetary loss.
19、 The insurance premium assures the individual of having the same income regardless of whether or not a loss occurs. Because the insurance is actuarially fair, this certain income is equal to the expected income if the individual takes the risky option of not purchasing insurance. This guarantee of t
20、he same income, whatever the outcome, generates more utility for a risk-averse person than the average utility of a high income when there was no loss and the utility of a low income with a loss (i.e., because of risk aversion, EU(x) U(Ex).6. Why is an insurance company likely to behave as if it is
21、risk neutral even if its managers are risk-averse individuals? Most large companies have opportunities for diversifying risk. Managers acting for the owners of a company choose a portfolio of independent, profitable projects at different levels of risk. Of course, shareholders may diversify their ri
22、sk by investing in several projects in the same way that the insurance company itself diversifies risk by insuring many people. By operating on a sufficiently large scale, insurance companies can assure themselves that over many outcomes the total premiums paid to the company will be equal to the to
23、tal amount of money paid out to compensate the losses of the insured. Thus, the insurance company behaves as if it is risk neutral, while the managers, as individuals, might be risk averse.7. When is it worth paying to obtain more information to reduce uncertainty?Individuals are willing to pay more
24、 for information when the utility of the choice with more information, including the cost of gathering the information, is greater than the expected utility of the choice without the information.8. How does the diversification of an investors portfolio avoid risk?An investor reduces risk by investin
25、g in many inversely related assets. For example, a mutual fund is a portfolio of stocks of independent companies. If the variance of the return on one companys stock is inversely related to the variance of the return on another companys stock, a portfolio of both stocks will have a lower variance th
26、an either stock held separately. As the number of stocks increases, the variance in the rate of return on the portfolio as a whole decreases. While there is less risk in a portfolio of stocks, risk is not eliminated altogether; there is still some market risk in holding such a portfolio, compared to
27、 a low-risk asset, such as a U.S. government savings 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? Why?)In a market for risky asse
28、ts, where investors are risk averse, investors demand a higher return on investments that have a higher level of risk (a higher variance in returns). Although some individuals are willing to accept a higher level of risk in exchange for a higher rate of return, this does not mean that these individu
29、als are less risk averse. On the contrary, they will not invest in risky assets unless they are compensated for the increased risk.10. What is an endowment effect? Give an example of such an effect.An endowment effect exists if an individual places a greater value on an item that is in her possessio
30、n as compared to the value she places on the same item when it is not in her possession. For example, many people would refuse to pay $5 for a simple coffee mug but would also refuse to sell a simple coffee mug they won in a contest for the same price even though they got it for free. 11. Jennifer i
31、s 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 Jennifer $50 for the shirt, she refuses to sell it. Explain Jennifers behavior.To help explain Jennifer
32、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
33、 has changed. Once she owns the shirt, she changed the amount by which she valued the shirt. Individuals often value goods more when they own them than when they do not.EXERCISES1. Consider a lottery with three possible outcomes: $125 will be received with probability .2, $100 with probability .3, a
34、nd $50 with probability .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 of the lottery?The variance, s2, i
35、s the sum of the squared deviations from the mean, $80, weighted by their probabilities:s2 = (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 h
36、ave invested in a new computer company whose profitability depends on (1) whether the U.S. Congress passes a tariff that raises 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 concern
37、ed about?The four mutually exclusive states may be represented as:Congress passes tariffCongress does not pass tariffSlow growth rateState 1:Slow growth with tariffState 2:Slow growth without tariffFast growth rateState 3:Fast growth with tariffState 4:Fast growth without tariff3. Richard is decidin
38、g whether to buy a state lottery ticket. Each ticket costs $1, and the probability of the following winning payoffs is given as follows:ProbabilityReturn0.50$0.000.25$1.000.20$2.000.05$7.50a.What is the expected value of Richards payoff if he buys a lottery ticket? What is the variance?The expected
39、value of the lottery is equal to the sum of the returns weighted by their probabilities:EV = (0.5)(0) + (0.25)($1.00) + (0.2)($2.00) + (0.05)($7.50) = $1.025The variance is the sum of the squared deviation from the mean, $1.025, weighted by their probabilities:s2 = (0.5)(0 - 1.025)2 + (0.25)(1 - 1.0
40、25)2 + (0.2)(2 - 1.025)2 + (0.05)(7.5 - 1.025)2, ors2 = $2.812.b.Richards nickname is “No-risk Rick.” He is an extremely risk-averse individual. Would he buy the ticket?An extremely risk-averse individual will probably not buy the ticket, even though the expected outcome is higher than the price, $1
41、.025 $1.00. The difference in the expected return is not enough to compensate Rick for the risk. For example, if his wealth is $10 and he buys a $1.00 ticket, he would have $9.00, $10.00, $11.00, and $16.50, respectively, under the four possible outcomes. Let us assume that his utility function is U
42、 = W0.5, where W is his wealth. Then his expected utility is:This is less than 3.162, which is the utility associated with not buying the ticket (U(10) = 100.5 = 3.162). He would prefer the sure thing, i.e., $10.c.Suppose Richard was offered insurance against losing any money. If he buys 1,000 lotte
43、ry tickets, how much would he be willing to pay to insure his gamble?If Richard buys 1,000 tickets, it is likely that he will have $1,025 minus the $1,000 he paid, or $25. He would not buy any insurance, as the expected return, $1,025, is greater than the cost, $1,000. He has insured himself by buyi
44、ng a large number of tickets. Given that Richard is risk averse though, he may still want to buy insurance. The amount he would be willing to pay is equal to the risk premium, which is the amount of money that Richard would pay to avoid the risk. See figure 5.4 in the text. To calculate the risk pre
45、mium, you need to know the utility function. If the utility function is U = W0.5, then his expected utility from the 1,000 lottery tickets is This is less than the utility he would get from keeping his $1000 which is U=10000.5=31.62. To find the risk premium, find the level of income that would guar
46、antee him a utility of 21.18, which is $448.59. This means he would pay $1000-$448.59=$551.41 to insure his gamble. d.In the long run, given the price of the lottery ticket and the probability/return table, what do you think the state would do about the lottery?In the long run, the state lottery wil
47、l be bankrupt! Given the price of the ticket and the probabilities, the lottery is a money loser. The state must either raise the price of a ticket or lower the probability of positive payoffs.4. Suppose an investor is concerned about a business choice in which there are three prospects, whose proba
48、bility and returns are given below:ProbabilityReturn0.4$1000.3 300.3 -30What is the expected value of the uncertain investment? What is the variance?The expected value of the return on this investment isEV = (0.4)(100) + (0.3)(30) + (0.3)(-30) = $40.The variance iss2 = (0.4)(100 - 40)2 + (0.3)(30 - 40)2 + (0.3)(-30 - 40)2 = $2,940.5. You are an insurance agent who has to write a policy for a new client named Sam. His company, Society for Creative Alternatives to Mayonnaise (SCAM), is working on a low-fat, low-cholesterol mayonnaise substitute for the sandwich con
