# Uncertainty and Information CHAPTER 19 C H A P T E R C H E C K L I S T When you have completed your study of this chapter, you will be able to 1 Explain.

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Uncertainty and Information CHAPTER 19

C H A P T E R C H E C K L I S T When you have completed your study of this chapter, you will be able to 1 Explain how people make decisions when they are uncertain about the consequences. 2 Explain how markets enable people to buy and sell risk. 3 Explain how markets cope when buyers and sellers have private information.

19.1 DECISIONS IN THE FACE OF UNCERTAINTY Tania, a student, is trying to decide which of two alternative summer jobs to take. 1. She can work as a house painter and have \$2,000 in at the end of the summer and there is no uncertainty about the income from this job. 2.The other job is working as a telemarketer. Tania thinks there is a 50 percent chance that she will earn \$5,000 and a 50 percent chance that she will earn \$1,000. Which job does she prefer?

19.1 DECISIONS IN THE FACE OF UNCERTAINTY Expected Wealth Expected wealth is the money value of what a person expects to own at a given point in time. An expectation is an average calculated by using a formula that weights each possible outcome with the probability (chance) that it will occur. For Tania, the probability that she will have \$5,000 is 0.5 (a 50 percent chance) and the probability that she will have \$1,000 is also 0.5. Expected wealth = (\$5,000 × 0.5) + (\$1,000 × 0.5) = \$3,000.

19.1 DECISIONS IN THE FACE OF UNCERTAINTY Expected Wealth Expected wealth is the money value of what a person expects to own at a given point in time. An expectation is an average calculated by using a formula that weights each possible outcome with the probability (chance) that it will occur. What is Tanias expected wealth from the telemarketing job?

19.1 DECISIONS IN THE FACE OF UNCERTAINTY The probability that Tania will have \$5,000 is 0.5 (a 50 percent chance). The probability that she will have \$1,000 is also 0.5. Expected wealth = (\$5,000 × 0.5) + (\$1,000 × 0.5) = \$3,000. Tania can now compare the expected wealth from two jobs: \$2,000 for non-risky painting job \$3,000 for the risky telemarketing job

19.1 DECISIONS IN THE FACE OF UNCERTAINTY Will Tania take the risky job? It will depend on how much Tania dislikes risk. Risk Aversion Risk aversion is the dislike of risk. We measure a persons attitude toward risk by using a utility of wealth schedule and curve. Greater wealth brings greater total utility, but the marginal utility of wealth diminishes as wealth increases.

Utility of Wealth Figure 19.1 shows that as Tanias utility of wealth curve. 1. If Tanias wealth is \$2,000 2. She gets 70 units of utility. 19.1 DECISIONS IN THE FACE OF UNCERTAINTY

Tanias total utility increases when her wealth increases. But the marginal utility of wealth diminishes. Each additional dollar of wealth brings successively smaller increments in total utility. 19.1 DECISIONS IN THE FACE OF UNCERTAINTY

Because of diminishing marginal utility, for a loss of wealth or a gain of wealth of equal size, 3. Tanias pain from the loss exceeds her pleasure from the gain. 19.1 DECISIONS IN THE FACE OF UNCERTAINTY

Expected Utility When there is uncertainty, people do not know the actual utility they will get from taking a particular action. But they know the utility they expect to get. Expected utility is the utility value of what a person expects to own at a given point in time. 19.1 DECISIONS IN THE FACE OF UNCERTAINTY

Figure 19.2 shows how Tania calculates her expected utility. 1. Tania has a 50 percent chance of having \$5,000 of wealth and total utility of 95 units. 19.1 DECISIONS IN THE FACE OF UNCERTAINTY

2. Tania has a 50 percent chance of having \$1,000 of wealth and a total utility of 45 units. 3. Tanias expected wealth is \$3,000 and 4. Her expected utility is 70 units. 19.1 DECISIONS IN THE FACE OF UNCERTAINTY

5. With \$3,000 wealth and no uncertainty, utility is 83 units. For a given expected wealth, the greater the range of uncertainty, the smaller is expected utility. 19.1 DECISIONS IN THE FACE OF UNCERTAINTY

Making a Choice with Uncertainty Faced with uncertainty, a person chooses the action that maximizes expected utility. To select the job that gives her the maximum expected utility, Tania must calculate 1. The expected utility from the risky telemarketing job. 2. The expected utility from the safe painting job. 3. Compare the two expected utilities. 19.1 DECISIONS IN THE FACE OF UNCERTAINTY

Figure 19.3 shows the choice under uncertainty. 1. In a telemarketing job, there is a 50 percent chance that Tania will make \$5,000 and a 50 percent chance that she will make \$1,000. Her expected wealth is \$3,000. 19.1 DECISIONS IN THE FACE OF UNCERTAINTY

2. Tania expected utility is 70 units. Tania would have the same 70 units utility with wealth of \$2,000 and no risk, so 3. Tanias cost of bearing this risk is \$1,000. 19.1 DECISIONS IN THE FACE OF UNCERTAINTY

Tania is indifferent between The job that pays \$2,000 with no risk and The job that offers an equal chance of \$5,000 and \$1,000. 19.1 DECISIONS IN THE FACE OF UNCERTAINTY

19.2 BUYING AND SELLING RISK Just as buyers and sellers gain from trading goods and services, they can also gain from trading risk. Risk is a bad, not a good, so the good that is traded is risk avoidance. A buyer of risk avoidance can gain because the value of avoiding risk is greater than the price that must be paid to get someone else to bear that risk. The seller of risk avoidance faces a lower cost of risk than the price that people are willing to pay to avoid that risk.

Insurance Markets Insurance reduces the risk that people face by sharing or pooling risks. When people buy insurance against the risk of an unwanted event, they pay an insurance company a premium. If the unwanted event occurs, the insurance company pays out the amount of the insured loss. 19.2 BUYING AND SELLING RISK

Why People Buy Insurance 19.2 BUYING AND SELLING RISK Figure 19.4 illustrates. Dan owns a car worth \$10,000, and that is his only wealth. There is a 10 percent chance that Dan will have a serious accident that makes his car worth nothing.

19.2 BUYING AND SELLING RISK 1. Dans wealth (the value of his car) is \$10,000. 2. His utility is 100 units. With no insurance, if Dan has a crash, 3. He has no wealth and 4. No utility.

19.2 BUYING AND SELLING RISK With a 10 percent chance of a crash, 5. Dans expected wealth is \$9,000. (\$10,000 × 0.1) 6. His expected utility is 90 units. So with no insurance, Dans expected utility is 90 units.

19.2 BUYING AND SELLING RISK Figure 19.5 shows the situation when Dan buys insurance. If Dan had \$7,000 of wealth with no risk, he would have the same utility as has with \$10,000 of wealth and 10 percent risk of loss.

19.2 BUYING AND SELLING RISK 1. If Dan pays \$3,000 for insurance, his wealth is \$7,000 and 2. His utility is 90 units. 3. So \$3,000 is the value of insurance for Dan.

19.2 BUYING AND SELLING RISK If there are lots of people like Dan, each with a \$10,000 car and each with a 10 percent chance of having an accident, an insurance company pays out \$1,000 per person on the average.

19.2 BUYING AND SELLING RISK The insurance company can provide coverage for people like Dan for \$1,000. 4. If Dan pays \$1,000 for insurance, 5. His expected wealth is \$9,000 and 6. His expected utility is 98 units.

19.2 BUYING AND SELLING RISK 7. Dan gains from insurance. Dan is willing to pay up to \$3,000 for insurance that costs the insurance company \$1,000, so there is a gain from trading risk of \$2,000 per person.

19.3 PRIVATE INFORMATION Private information is information possessed by either buyers or sellers about the value of the item being traded that is not available to the persons on the other side of a transaction. Examples are your knowledge about the quality of your driving, your work effort, the quality of your car, and whether you intend to repay a loan. When either buyers or sellers have private information, the market has asymmetric information.

19.3 PRIVATE INFORMATION Asymmetric Information: Examples and Problems Asymmetric information creates two problems: 1. Adverse selection 2. Moral hazard

19.3 PRIVATE INFORMATION Adverse Selection Adverse selection is the tendency for people to enter into agreements in which they can use their private information to their own advantage and to the disadvantage of the less informed party. For example, if Jackie advertises jobs for salespeople at a fixed wage, she will attract lazy salespeople. Hardworking salespeople will prefer to work for someone who pays by results, rather than a fixed wage. The fixed-wage contract adversely selects those with private information about their work effort.

19.3 PRIVATE INFORMATION Moral Hazard Moral hazard exists when one of the parties to an agreement has an incentive after the agreement is made to act in a manner that brings additional benefits to himself or herself at the expense of the other party. For example, Jackie hires Mitch as a salesperson and pays him a fixed wage regardless of how much he sells. Mitch faces a moral hazard. He has an incentive to put in the least possible effort, benefiting himself and lowering Jackies profits.

19.3 PRIVATE INFORMATION A variety of devices have evolved that enable markets to function in the face of adverse selection and moral hazard. Weve just seen one, the use of incentive payments for salespeople. Were going to look at how three markets cope with adverse selection and moral hazard. They are The market for used cars The market for loans The market for insurance

19.3 PRIVATE INFORMATION The Market for Used Cars A used car might be a lemona car that is worth less than a car with no defects. But only the seller knows whether a car is a lemon. Lemon problem is the problem that in a market in which it is not possible to distinguish reliable products from lemons, too many lemons and too few reliable products traded. How does a market work when it has a lemon problem?

19.3 PRIVATE INFORMATION The Lemon Problem in a Used Car Market The market has two types of cars: Lemons worth \$5,000 each. Cars without defects worth \$25,000 each. Whether the car is a lemon or not is private information of the current owner. A buyer discovers a lemon only after buying it.

19.3 PRIVATE INFORMATION Because buyers cant tell the difference between a lemon and a good car, the price they are willing to pay reflects the fact that the car might be a lemon. The highest price that a buyer will pay must be less than \$25,000 because the car might be a lemon. Some people with low incomes and time to fix a car are willing to buy lemons as long as they know what they are buying and paying for. What is the price of a used car?

19.3 PRIVATE INFORMATION So the most that the buyer knows is the probability of buying a lemon. If half of the used cars sold turn out to be lemons, the buyer know that he has a 50 percent chance of getting a good car and a 50 percent chance of getting a lemon. The price that a buyer is willing to pay for a car of unknown quality is more than the value of a lemon because the car might be a good one. But the price is less than the value of a good car because it might turn out to be a lemon.

19.3 PRIVATE INFORMATION Sellers of used cars know the quality of their cars. Someone who owns a good car is going to be offered a price that is less than the value of that car to the buyer. Many owners will be reluctant to sell, so fewer good cars will be supplied than if the price reflected its value. But someone who owns a lemon is going to be offered more than the value of that car to the buyer. Owners of lemons will be eager to sell, so more lemons will be supplied than if the price reflected its value.

In the used car market: Adverse selection exists because there is a greater incentive to offer a lemon for sale. Moral hazard exist because the owner of a lemon has little incentive to take good care of the car, so it is likely to become even worse. The market for used cars is not working well. 19.3 PRIVATE INFORMATION

Figure 19.6 illustrates the used car market. Part (a) shows the used car market. 1. Equilibrium price is \$10,000 a car and 2. 400 cars traded.

19.3 PRIVATE INFORMATION Part (b) shows the demand for good cars and the supply of good cars. 3. At \$10,000 a car, 200 good cars are traded.

19.3 PRIVATE INFORMATION 4. Buyers are willing to pay \$25,000 for a good car. 5. Too few good cars are traded and a deadweight loss is created.

19.3 PRIVATE INFORMATION Part (c) shows the demand for and the supply of lemons. 6. At \$10,000 a car, 200 lemons are traded.

19.3 PRIVATE INFORMATION 7. Buyers are willing to pay \$5,000 for a lemon. 8. Too many lemons are traded and a deadweight loss is created.

19.3 PRIVATE INFORMATION A Used Car Market with Dealers Warranties Buyers of used cars cant tell a lemon from a good car, but car dealers sometimes can. To convince a buyer that it is worth paying \$10,000 for what might be a lemon, the dealer offers a warranty. The dealer signals which cars are good ones and which are lemons. Signaling occurs when an informed person takes actions that send information to less-informed persons. Warranties enable the market to trade good used cars.

19.3 PRIVATE INFORMATION Figure 19.7 shows how warranties solve the lemon problem. Part (a) shows the market for good cars. 1. With warranties, the price of a good car is \$20,000. 2. 400 good cars are traded. 3. The market for good cars is efficient.

19.3 PRIVATE INFORMATION Part (b) shows the market for lemons. Because buyers can now spot a lemon (a car without a warranty) 4. The price of a lemon is \$6,667. 5. 150 lemons are traded. 6. The market for lemons is efficient.

19.3 PRIVATE INFORMATION Pooling Equilibrium and Separating Equilibrium Without warranties, only one message is visible to the buyer: All cars look the same. The market equilibrium when only one message is available and a less-informed person cannot determine quality is a pooling equilibrium.

19.3 PRIVATE INFORMATION In a market with warranties, there are two messages: Cars with warranties are good cars and cars without warranties are lemons. The market equilibrium when signaling provides full information to a previously less-informed person is a separating equilibrium.

19.3 PRIVATE INFORMATION The Market for Loans Borrowers demand loans. The lower the interest rate, the greater is the quantity of loans demanded the demand curve for loans is downward-sloping. Banks and other lenders supply loans. For a given credit risk, the higher the interest rate the greater is the quantity of loans supplied.

19.3 PRIVATE INFORMATION The risk that a borrower, also called a creditor, might not repay a loan is called credit risk or default risk. The credit risk depends on the quality of the borrower. Low-risk borrowers always repay. High-risk borrowers frequently default on their loans. The market for loans determines the interest rate and the price of credit risk.

19.3 PRIVATE INFORMATION A Pooling Equilibrium Suppose that banks cannot tell whether they are lending to a low-risk or a high-risk customer. In this situation, all borrowers pay the same interest rate and the market is a pooling equilibrium. The market for loans has the same problems as the used car market without warranties.

19.3 PRIVATE INFORMATION If all borrowers pay the same interest rate, low-risk customers borrow less than they would if they were offered the low interest rate appropriate for their low credit risk. High-risk customers borrow more than they would if they faced the high interest rate appropriate for their high credit risk. So banks face an adverse selection problem. Too many borrowers are high risk and too few are low risk.

19.3 PRIVATE INFORMATION Signaling and Screening in the Market for Loans Lenders dont know how likely it is that a given loan will be repaid, but the borrower does know. Low-risk borrowers have an incentive to signal their risk by providing lenders with relevant information. Signals might include information about a persons employment, home ownership, marital status, and age.

19.3 PRIVATE INFORMATION High-risk borrowers might be identified simply as those who have failed to signal low risk. These borrowers have an incentive to mislead lenders; and lenders have an incentive to induce high-risk borrowers to reveal their risk level. Inducing an informed party to reveal private information is called screening. Figure 19.8 shows the gains from separating borrowers.

19.3 PRIVATE INFORMATION Part (a) shows the pooling equilibrium in the market for loans. 1.The equilibrium interest rate is 8 percent a year. 2. The equilibrium quantity of loans is \$16 million.

19.3 PRIVATE INFORMATION Part (b) shows the demand for loans and the supply of loans to low-risk borrowers. 3. At 8 percent a year, the quantity of loans is \$8 million.

19.3 PRIVATE INFORMATION 4. If low-risk borrowers can signal their low risk, the interest rate for these borrowers would fall to 4 percent a year. 5. The equilibrium quantity of loans increases to \$12 million. 6. The deadweight loss from too few low-risk loans is avoided.

19.3 PRIVATE INFORMATION Part (c) shows the demand for loans and the supply of loans to high-risk borrowers. 7. At 8 percent a year, the quantity of loans is \$8 million.

19.3 PRIVATE INFORMATION 8. If lenders can screen high-risk borrowers, the interest rate for these borrowers would rise to 12 percent a year. 9. The equilibrium quantity of loans decreases to \$4 million. 10. Deadweight loss from too many high-risk loans is avoided.

The Market for Insurance People who buy insurance face moral hazard, and insurance companies face adverse selection. Moral hazard arises because a person with insurance against a loss has less incentive than an uninsured person to avoid the loss. Adverse selection arises because people who create greater risks are more likely to buy insurance. 19.3 PRIVATE INFORMATION

Insurance companies have an incentive to find ways around the moral hazard and adverse selection problems. By doing so, they can lower premiums for low-risk people and raise premiums for high-risk people. Insurance companies use two devices to avoid moral hazard and adverse selection: The no-claim bonus A deductible 19.3 PRIVATE INFORMATION

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