Transcript Slide 1

The Economics of Information
Risk
a situation in which there is a probability
that an event will occur.
People tend to prefer greater certainty and
less risk.
Probability
A number between 0 and 1 that measures the
chance that an event will occur.
If probability = 0, the event will definitely not
occur.
If probability = 1, the event will definitely occur.
If probability = 0.5, the event is just as likely to
occur as not.
Example: The probability that a fair (balanced
coin) will land heads is 0.5.
As wealth increases, so does the total utility
of wealth.
But the marginal utility of wealth diminishes.
Total
Utility
TU
In other words,
the slope of the
total utility curve
is positive but
decreasing.
Wealth
(thousands of dollars)
When there is uncertainty, people do
not know the actual utility they will get
from taking a particular action.
They do know the utility they expect
to get.
Expected utility is the average utility
of all possible outcomes.
Expected Value
Suppose you have a generous but forgetful
aunt. There is a 50% probability that she will
remember your birthday and send you a
check for $100. There is also a 50%
probability that she will forget your birthday
and send you nothing.
What is the expected value of the gift (G) you
will receive from your aunt for your birthday?
E(G) = 0.5 (0) + 0.5 (100) = 50.
E(X) = p1X1 + p2X2 + p3X3 + … + pkXk
So to calculate the expected value,
you take the amount of each possible
outcome, multiply it by the probability of that
outcome, and add the products together.
Apart from concerns about your aunt’s
health, would you rather have your aunt
send a $50 check with certainty over the
current situation?
If the answer is yes, you are risk averse.
If you prefer the current situation, you are
risk loving.
If you are indifferent between the two
situations, you are risk neutral.
In general,
A risk-neutral person cares only about
expected wealth and doesn’t care how
much uncertainty there is.
A risk-averse person prefers the expected
wealth with certainty over the risky
situation with the same expected wealth.
A risk-loving person enjoys the thrill of the
gamble, and so prefers the risky situation
over a situation with the same expected
wealth with certainty.
Most people are risk averse, but some
people are more risk averse than others.
The shape of the utility-of-wealth curve tells us
about the person’s degree of risk aversion.
Total
Utility
Person 1
Person 2
Person 3
Wealth
(thousands of dollars)
The more rapidly
the slope of the TU
curve falls, the more
risk averse the
person is.
The slope of the TU
curve of person 3
drops the fastest, so
that person is the
most risk averse.
Example: Alex is considering a
job, which is based on
commission, & pays $3000 with
50% probability & $9000 with
50% probability.
Total Utility
95
85
80
65
3
5
6
9
Wealth
(thousands of dollars)
$3000 is worth 65 units of
utility to Alex, and $9000 is
worth 95 units of utility.
The utility of the job’s
earnings is the average of
65 & 95, or 80 units of
utility.
We can see from the TU
curve that a job paying
$6000 with certainty would
be worth more to Alex (85
units of utility).
A job that paid $5000 with
certainty would be worth
the same level of utility to
Alex as the risky job.
For a risk-neutral
person the TU curve
would be linear,
instead of concave.
For a risk-lover, the
TU curve would be
convex.
Insurance
Insurance works by pooling risks.
It is profitable because people are
risk averse.
Example: Beth’s only wealth is a $10,000 car.
Total Utility
100
85
80
65
0
10
Wealth
(thousands of dollars)
If she doesn’t have
an accident, her
utility is 100 units.
If she has an
accident that totals
her car, her utility is 0
units.
(Assume there are
no other options.)
Suppose the probability that Beth will have an accident
is 0.10.
Without insurance, Beth’s expected wealth is
$10,000  0.9 + $0  0.1 = $9000.
Total Utility
100
Her expected utility is
100  0.9 + 0  0.1 = 90 units.
Beth would also have 90 units
of utility if her wealth was
$7000 with certainty.
90
0
7
9 10
Wealth
(thousands of dollars)
If insurance would pay her the money to replace her
car, and the insurance cost $3000, she would have
$10,000 – $3000 = $7000 with certainty.
Total Utility
100
So she would buy the
insurance if it cost less
than $3000.
90
0
7
9 10
Wealth
(thousands of dollars)
If there are many people like Beth,
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 Beth’s willingness to
pay for insurance.
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.
Optimal Search Rule
• 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.
Benefits & Costs
of Search
The green line is the
expected marginal
benefit of visiting one
more dealer.
Benefits & Costs
of Search
MB
MC
0
35
30
25
The red line is the
marginal cost of visiting
one more dealer.
20 15 10
Lowest price found
(thousands of dollars)
The MB is declining
because the lower the
best price you’ve found
so far, the lower the
expected marginal
benefit of visiting one
more dealer.
The price at which expected marginal benefit
equals marginal cost is your reservation price.
Benefits & Costs
of Search
MB
MC
0
35
30
25
20 15 10
Lowest price found
(thousands of dollars)
If you find a price that
is greater than your
reservation price, you
keep searching.
If you find a price
equal to or below your
reservation price, you
stop searching and
buy.
In this example, the
reservation price is
$15,000.
Two Types of Information Problems
–1. Moral hazard
–2. Adverse selection
Moral hazard
• 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.
• Example: As a result of having
insurance, an individual may be more
likely to engage in risky behavior.
A market response
to moral hazard
• The insured person is required to pay part
of the costs.
• This is coinsurance.
• In addition to lowering the costs of
insurance directly, coinsurance gives the
insured person the incentive to be
economical.
Adverse selection
• the tendency for people to enter into
agreements in which they can use their
private information to their advantage and
to the disadvantage of the less informed
party.
• Example 1: Sellers may be more likely to
sell low-quality goods.
• Example 2: Higher-risk customers may be
more likely to purchase.
A case of adverse selection:
The Lemon Problem
• Suppose a defective used car (lemon) is worth
$2,000.
• A used car without defects is worth $8,000.
• Only the current owner or dealer knows if a car is a
lemon.
• A buyer only knows it’s a lemon 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.
Suppose 25% of the used cars are lemons.
• Then a buyer would only be willing to purchase a
car for 0.75 x 8000 + 0.25 x 2000 = $6500.
• At this price, fewer cars are supplied to the
market.
• Furthermore, the number of good cars is likely to
drop more than the number of lemons, so the
proportion of defective cars will probably be
higher.
• The buyers would then adjust the price they are
willing to pay downward.
• This process could continue until the good cars
are driven out of the market.
A Market Response to the
Lemon Problem: Warranties
– To convince a buyer that it is worth paying
$8000, the dealer offers a warranty.
– The dealer signals which cars are good ones
and which are lemons.
Another way that the market deals with
adverse selection is that companies
sometimes use indirect measures to help
identify high-risk customers.
• For example, young men have more accidents
than women and older men, so insurance
companies charge them a higher rate.
• In making loans, banks use signals such as
length of time in a job, ownership of a home,
marital status, and age as indicators of people
who may be more likely to default on a loan.
Managing Risk in Financial Markets
–To cope with risky investments
such as stocks & bonds, people
diversify their asset holdings.
–How does diversification reduce
risk?
Example
• Suppose you can invest $100,000 in one of two
projects.
• Suppose also that the 2 projects are
independent, so the outcome of one project is
unrelated to the outcome of the other.
• Both investments have a 50% probability of a
$50,000 profit & a 50% probability of a $25,000
loss.
• So the expected return on each project is
($50,000  0.5) + (–$25,000  0.5) = $12,500.
Undiversified
• Invest $100,000 in either project.
• 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.
Diversified
•
Invest 50% of your money in Project 1 & 50% in Project 2.
•
$50,000 invested in a project results in a 50% chance of a 25,000 profit &
a 50% chance of a 12,500 loss from that project.
•
•
•
•
You now have 4 possible returns with a 25% chance each:
(1) Lose $12,500 on each project, a loss of $25,000.
(2) Make a profit of $25,000 on Project 1 and lose $12,500 on Project 2,
a return of $12,500.
(3) Lose $12,500 on Project 1 and make a profit of $25,000 on Project 2,
again a return of $12,500.
(4) Make a profit of $25,000 on each project, and your return is $50,000.
•
•
•
•
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.
•
You still have an expected return of $12,500.
•
But…
• You have lowered the chance that you will
earn $50,000 from 0.50 to 0.25.
• You have lowered the chance that you will
lose $25,000 from 0.50 to 0.25.
• And you have increased the chance that
you will earn your expected return of
$12,500 from 0 to 0.50.