The Economics of Information

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The Economics of Information
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Risk
a situation in which there is a probability that
an event will occur. People tend to prefer
greater certainty and less risk.
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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.
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As wealth increases, so does the total utility of
wealth. But the marginal utility of wealth
diminishes.
Total Utility
In other words, the slope of the total utility
curve is positive but decreasing.
TU
Wealth(thousands of dollars)
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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.
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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 you 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.
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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.
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Apart from concerns about your aunts 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.

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In general,
A risk-neutral person cares only about expected
wealth and doesnt 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.
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The shape of the utility-of-wealth curve tells us
about the persons degree of risk aversion.
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.
Person 1
Total Utility
Person 2
Person 3
Wealth(thousands of dollars)
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Example Alex is considering a job, which is
based on commission, pays 3000 with 50
probability 9000 with 50 probability.
3000 is worth 65 units of utility to Alex, and
9000 is worth 95 units of utility. The utility
of the jobs 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.
Total Utility
95
85
80
65
9
6
3
5
Wealth(thousands of dollars)
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For a risk-neutral person the TU curve would be
linear, instead of concave.

• For a risk-lover, the TU curve would be convex.

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Insurance
Insurance works by pooling risks. It is
profitable because people are risk averse.
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Example Beths only wealth is a 10,000 car.
If she doesnt 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.)
Total Utility
100
85
80
65
10
0
Wealth(thousands of dollars)
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Suppose the probability that Beth will have an
accident is 0.10. Without insurance, Beths
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
10
9
0
7
Wealth(thousands of dollars)
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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
10
9
0
7
Wealth(thousands of dollars)
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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 Beths willingness to pay for insurance.
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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.

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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.

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Benefits Costs of Search
The red line is the marginal cost of visiting one
more dealer. The green line is the expected
marginal benefit of visiting one more dealer. The
MB is declining because the lower the best price
youve found so far, the lower the expected
marginal benefit of visiting one more dealer.
Benefits Costs of Search
MB
MC
0
10
15
35 30 25 20
Lowest price found(thousands of dollars)
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The price at which expected marginal benefit
equals marginal cost is your reservation price.
If you find a price that is greater than your
reservation wage, 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.
Benefits Costs of Search
MB
MC
0
10
15
35 30 25 20
Lowest price found(thousands of dollars)
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Two Types of Information Problems

• 1. Moral hazard
• 2. Adverse selection

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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.

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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.

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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.

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A case of adverse selectionThe 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 its a lemon after buying it.
• Because buyers cant 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.

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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.

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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.

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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 may be
  more likely to default on a loan.

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Managing Risk in Financial Markets

• To cope with risky investments such as stocks
  bonds, people diversify their asset holdings.
• How does diversification reduce risk?

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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.

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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.

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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.

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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.