# 19 CHAPTER Uncertainty and Information.

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19 CHAPTER Uncertainty and Information

After studying this chapter you will be able to
Explain how people make decisions when they are uncertain about the consequences Explain why people buy insurance and how insurance companies make a profit Explain why buyers search Explain how markets cope with private information Explain how people use financial markets to lower risk Explain how the presence of uncertainty and incomplete information influence the ability of markets to achieve an efficient allocation of resources

Lotteries and Lemons Life is like a lottery. How do people make a decision when they don’t know what its consequences will be? Markets do a good job in helping people to use scarce resources efficiently. But can markets lead to an efficient outcome when there is uncertainty and incomplete information? How do markets cope when you might be sold a lemon?

Uncertainty and Risk Uncertainty is a situation in which an event might occur but we can’t say how likely it is. Risk is a situation an event might occur and we know the probability that it will occur. A probability is a number between 0 and 1 that measures the chance of some possible event occurring.

Uncertainty and Risk If probability = 0, the event will not happen.
If probability = 1, the event will occur for sure—with certainty. If probability = 0.5, the event is just as likely to occur as not. An example of a probability = 0.5 is that of a tossed coin falling heads.

Uncertainty and Risk Measuring the Cost of Risk
People usually prefer less risk to more risk, other things remaining the same. We measure a person’s 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.

Uncertainty and Risk Figure 19.1 shows that as Tania’s wealth increases, so does her total utility of wealth. But Tania’s marginal utility of wealth diminishes.

Uncertainty and Risk 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 average utility arising from all possible outcomes.

Uncertainty and Risk Figure 19.2 shows how Tania calculates her expected utility from two alternative summer jobs that involve different amounts of risk. One job pays enough for her to save \$5,000 by the end of the summer for sure, which gives her 80 units of utility.

Uncertainty and Risk In a telemarketing job, there is a 50 percent chance that Tania will make \$9,000, which gives her 95 units of utility. There is also a 50 percent chance that she will make \$3,000, which gives her 65 units of utility.

Uncertainty and Risk Tania’s expected utility is the average of these two possible total utilities and is 80 units of utility. Tania expects to earn \$6,000 (the average of \$9,000 and \$3,000) in the telemarketing job.

Uncertainty and Risk The extra \$1,000 is only enough to compensate her for the extra risk. Tania is indifferent between the two jobs.

Uncertainty and Risk Risk Aversion and Risk Neutrality
Attitudes toward risk vary from one person to another. Some people are more risk averse than others. The shape of the utility of wealth curve tells us about the attitude toward risk—about the person’s degree of risk aversion. The more rapidly a person’s marginal utility of wealth diminishes, the more risk averse that person is. A risk neutral person cares only about expected wealth and doesn’t care how much uncertainty there is.

Uncertainty and Risk Figure 19.3 shows that the utility of wealth curve of a risk-neutral person is a straight line. Expected utility does not depend on the range of uncertainty. The cost of risk is zero. Most people are risk averse, and their utility of wealth curves look like Tania’s.

Insurance Insurance Industry in the United States
On the average, we spend 15 percent of our income on private insurance. The four main types of insurance we buy are Health Life Property and casualty Auto

Insurance Figure 19.4 shows the insurance premiums paid in 2004.

Insurance How Insurance Works Insurance works by pooling risks.
Insurance is profitable because people are risk averse.

Insurance Figure 19.5 shows Dan’s utility of wealth curve.
Dan owns a car worth \$10,000, and that is his only wealth. If Dan has no accident, his utility is 100 units. If Dan has an accident that totals his car, his utility is 0 units.

Insurance Suppose that there is a 10 percent chance (a 0.1 probability) that Dan will have an accident. If Dan does not buy insurance, his expected wealth is \$9,000. That is: (\$10,000  0.9) + (\$0  0.1). Dan’s expected utility is 90 units (100   0.1).

Insurance Dan also gets 90 units of utility if he faces no uncertainty and his wealth is \$7,000. Dan would have \$7,000 of wealth and face no risk if he bought \$10,000 of auto insurance for \$3,000.

Insurance If the cost of an insurance policy that pays out in the event of an accident is less than \$3,000 (\$10,000 – \$7,000), Dan will buy the policy.

Insurance 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, which is less than Dan’s willingness to pay for insurance.

Information We spend a huge amount of our scare resources on economic information. Economic information includes data on the prices, quantities, and qualities of goods and services and factors of production, is scarce. People are willing to incur costs to access information. The opportunity cost of economic information is called information cost.

Information Searching for Price Information
When many firms sell the same item, there is a range of prices and buyers try to find the lowest price. But searching for a lower price is costly. Buyers balance the expected gain from further search against the cost of further search. To perform this balancing act, buyers use a decision rule called the optimal-search rule—or optimal-stopping rule.

Information The optimal-search rule is
Search for a lower price until the expected marginal benefit of additional search equals the marginal cost of search. When the expected marginal benefit from additional search is less than or equal to the marginal cost, stop searching and buy.

Information Figure 19.6 illustrates the optimal-search rule.
Suppose you’ve decided to buy a used car. Your marginal cost of search is \$C per dealer visited and is shown by the horizontal red line.

Information The blue curve shows the expected marginal benefit of visiting one more dealer. The lower the price you’ve already found, the lower is your expected marginal benefit of visiting one more dealer.

Information The price at which expected marginal benefit equals marginal cost is your reservation price. This price is \$8,000. If you find a price equal to or below your reservation price, you stop searching and buy.

Information If you find a price that exceeds your reservation price, you continue to search for a lower price.

Private Information Private information is information that is available to one person but is too costly for others to obtain. Examples are your knowledge about: The quality of your driving Your work effort The quality of your car Whether you intend to repay a loan

Private Information Private information creates two problems:
1. Moral hazard 2. Adverse selection

Private Information 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. 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.

Private Information Moral hazard and adverse selection operate in many markets, but they are especially important in the markets for: Used cars Loans Insurance

Private Information The Market for Used Cars A car might be a lemon.
A lemon is worth less than a car with no defects. But only the seller knows whether a car is a lemon. How does a market work when a product might be a lemon?

Private Information Used Cars Without Warranties
A lemon is worth \$1,000. A car without defects is worth \$5,000. Only the current owner knows whether a car is a lemon. A buyer discovers a lemon only after buying it. Because buyers can’t tell the difference between a lemon and a good car, the price they are willing to pay for a used car reflects the fact that the car might be a lemon. What is that price?

Private Information The highest price that a buyer will pay must be less than \$5,000 because the car might be a lemon. But if the price is less than \$5,000, only lemons will be offered for sale. So the price is \$1,000, and all the cars traded are lemons. Moral hazard exist because the sellers have an incentive to claim that lemons are good cars. Adverse selection exists, which results in only lemons actually being traded. The market in good used cars fails.

Private Information Used Cars with Warranties
Buyers of used cars can’t tell a lemon from a good car, but car dealers sometimes can. To convince a buyer that it is worth paying \$5,000 for what might be a lemon, the dealer offers a warranty. The dealer signals which cars are good ones and which are lemons. A signal is an action taken outside a market that conveys information that can be used by that market. Warranties enable the market to trade good used cars.

Private Information The Market for Loans
The lower the interest rate, the greater is the quantity of loans demanded— the demand curve for loans is downward-sloping. The supply of loans by banks depends on the cost of lending.

Private Information One cost of lending is interest, which is determined in the market for bank deposits—the market in which the banks borrow the funds that they lend. Another cost of lending is the loan default cost. The interest cost of a loan is the same for all borrowers.

Private Information The loan default cost depends on the quality of the borrower. Low-risk borrowers always repay. High-risk borrowers frequently default on their loans. Banks cannot tell whether they are lending to a low-risk or a high-risk borrower so everyone pays the same interest rate.

Private Information If banks offered loans to everyone at the low-risk interest rate, borrowers would face moral hazard and the banks would attract a lot of high-risk borrowers—adverse selection. Most borrowers would default, and the banks would incur losses. If the banks offered loans to everyone at the high-risk interest rate, low-risk borrowers would be unwilling to borrow.

Private Information Faced with moral hazard and adverse selection, banks use signals to discriminate between borrowers and ration or limit loans to amounts below that demanded. To restrict the amounts they are willing to lend to borrowers, banks use signals such as length of time in a job, ownership of a home, marital status, age, and business record.

Private Information Figure 19.7 shows how the market for loans works in the face of moral hazard and adverse selection. The demand for loans is D. The supply of loans is S.

Private Information The supply curve is horizontal—perfectly elastic supply—because banks have access to a large quantity of funds that have a constant marginal cost of r. With no loan limits, the interest rate is r and the quantity of loans is Q.

Private Information Because banks face moral hazard and adverse selection, they set loan limits based on signals and restrict the total loans to L. At the interest rate r, there is an excess demand for loans.

Private Information A bank cannot increase its profit by making more loans because lending more means taking on more high-risk borrowers.

Private Information 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.

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

Managing Risk in Financial Markets
Stocks and bonds are risky investments. To cope with risky investments, people diversify their asset holdings. Diversification to lower risk is not putting all one’s eggs into the same basket. How does diversification reduce risk?

Managing Risk in Financial Markets
Diversification to Lower Risk Suppose you can invest \$100,000 in one of two projects. Each project promises you an equal chance of \$50,000 profit or a \$25,000 loss. The expected return on each project is (\$50,000  0.5) + (–\$25,000  0.5), which is \$12,500. Suppose the two projects are independent, which means that the outcome of one project in no way influences the outcome of the other.

Managing Risk in Financial Markets
Undiversified Invest \$100,000 in either Project 1 or Project 2. Your expected return is \$12,500. But there is no chance that you will actually make a return of \$12,500. You either earn \$50,000 or lose \$25,000.

Managing Risk in Financial Markets
Diversified Invest 50 percent of your money in Project 1 and 50 percent in Project 2. (Someone else put up the other 50 percent in each project.) You now have four possible returns. And each of the four possible outcomes has a 25 percent chance of occurring.

Managing Risk in Financial Markets
The four possibilities are 1. Lose \$12,500 on each project and your return is a loss of \$25,000. 2. Earn \$25,000 on Project 1 and lose \$12,500 on Project 2 and your return is \$12,500. 3. Lose \$12,500 on Project 1 and earn \$25,000 on Project 2, and your return is \$12,500. 4. Earn \$25,000 on each project, and your return is \$50,000.

Managing Risk in Financial Markets
Your expected return is now –(\$25,000  0.25) + (\$12,500  0.25) + (\$12,500  0.25) + (\$50,000  0.25) = –\$6,250 + \$3,125 + \$3,125 + \$12,500 = \$12,500. By diversifying your portfolio of assets, you have maintained an expected return of \$12,500.

Managing Risk in Financial Markets
But you have lowered the chance that you will earn \$50,000 from 0.5 to 0.25. You have also lowered the chance that you will lose \$25,000 from 0.5 to 0.25. And you have increased the chance that you will earn your expected return of \$12,500 from 0 to 0.5.

Managing Risk in Financial Markets
The Stock Market The prices of the stocks are determined by demand and supply. Demand and supply in the stock market are dominated by the expected future price. If the price of a stock today is higher than the expected price tomorrow, people will sell the stock today. If the price of a stock today is less than its expected price tomorrow, people will buy the stock today.

Managing Risk in Financial Markets
Today’s price equals tomorrow’s expected price. Today’s price embodies all the information that is available about the stock. A market in which the actual price embodies all currently available relevant information is called an efficient market. In an efficient market, it is impossible to forecast changes in price.

Managing Risk in Financial Markets

Managing Risk in Financial Markets
So an efficient market has two features: 1. Its price equals the expected future price and embodies all the available information. 2. No forecastable profit opportunities are available. The key thing to understand about an efficient market is that: If something can be anticipated, it will be, and the anticipation of a future event will affect the current price.

Uncertainty, Information, and the Invisible Hand
Do uncertainty and incomplete information mean that markets fail and that government intervention is required to achieve efficiency?

Uncertainty, Information, and the Invisible Hand
Information as a Good We face a tradeoff between information and all other goods and services. Information can be produced only at an increasing opportunity cost—an increasing marginal cost. The principle of decreasing marginal benefit also applies to information.

Uncertainty, Information, and the Invisible Hand
Information as a Good Because the marginal cost of information is increasing and the marginal benefit is decreasing, there is an efficient amount of information. Perfect competition in markets for information might deliver the efficient quantity of information.

Uncertainty, Information, and the Invisible Hand
Monopoly in Markets that Cope with Uncertainty Economies of scale in providing services that cope with uncertainty and incomplete information mean that some markets for information are highly concentrated. So in some information markets, including insurance markets, there might be underproduction and deadweight loss.

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