Download Uncertainty and Risk

UNCERTAINTY AND
INFORMATION
19
CHAPTER
Objectives
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 invisible hand
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
In Figure 19.1, 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
In Figure 19.3, the utility of
wealth curve of a riskneutral person is a straight
line.
The marginal utility of
wealth is constant.
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
 Life
 Health
 Auto
 Property and casualty
Insurance
Figure 19.4 shows the
insurance premiums paid
in 2000.
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 there is a 10
percent chance (a
probability of 0.1) 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  0.9 + 0  0.1).
Insurance
With no uncertainty in his
life, Dan gets 90 units of
utility if his wealth is
$7,000.
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
Economic information, which includes data on the prices,
is scarce.
People are willing to incur cost to access information.
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 orange line in
the figure.
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 in the
figure.
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 are especially important in three markets:
 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 until 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.
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.
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 at the low-risk interest rate, they
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 they
ration or limit loans to amounts below the amounts
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 of moral hazard
and adverse selection, the
banks 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:
Both promise 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:
 Lose $12,500 on each project, a loss of $25,000.
 Earn $25,000 on Project 1 and lose $12,500 on Project
2, a return of $12,500.
 Lose $12,500 on Project 1 and earn $25,000 on Project
2, again, a return of $12,500.
 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
Volatility in Stock Prices
Stock prices are volatile because expectations change as
information changes
New information arrives at random, so prices change
randomly.
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.
THE END