Uncertainty and Information

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19
Uncertainty and Information
CHAPTER
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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.

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19.1 DECISIONS IN THE FACE OF UNCERTAINTY

• Tania, a student, is trying to decide which of
  two alternative summer jobs to take.
• 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?

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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.

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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?

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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

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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.

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19.1 DECISIONS IN THE FACE OF UNCERTAINTY

• Utility of Wealth
• Figure 19.1 shows that as Tanias utility of
  wealth curve.
• If Tanias wealth is 2,000
• She gets 70 units of utility.

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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.

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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.

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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.

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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.

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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.

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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.

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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
• The expected utility from the risky
  telemarketing job.
• 2. The expected utility from the safe painting
  job.
• 3. Compare the two expected utilities.

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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.

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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.

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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.

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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.

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19.2 BUYING AND SELLING 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.

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19.2 BUYING AND SELLING RISK

• Why People Buy Insurance

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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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19.3 PRIVATE INFORMATION

• In the markets that youve studied so far, the
  buyer and the seller are well informed about the
  features and value of the good, service, or
  factor of production being traded.
• But in some markets, either the buyers or the
  sellers are better informed about the value of
  the items being traded than the person on the
  other side of the market.
• These buyers or sellers have private information.
• 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

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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.

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19.3 PRIVATE INFORMATION

• Asymmetric Information Examples and Problems
• Asymmetric information creates two problems
• 1. Adverse selection
• 2. Moral hazard

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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.

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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.

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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

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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?

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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.

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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?

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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.

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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.

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19.3 PRIVATE INFORMATION

• 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.

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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.
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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.
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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.
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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.
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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.
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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.

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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.
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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.
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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.
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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.
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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.
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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.
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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.
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19.3 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.

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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