Asymmetric Information

Asymmetric Information

1. Asymmetric Information, Uncertainty, and,
Auctions
Prepared by César R. Sobrino
Universidad del Turabo
August 16, 2018
Prepared by César R. Sobrino
Asymmetric Information, Uncertainty, and, Auctions

2. Outline
1
Asymmetric Information
Moral Hazard
Adverse Selection
2
Uncertainty
Prepared by César R. Sobrino
Asymmetric Information, Uncertainty, and, Auctions

3. Asymmetric Information
In purely competitive markets all agents are fully
informed about traded commodities and other aspects
of the market.
Markets with one side or the other imperfectly
informed are markets withimperfect information.
Imperfectly informed markets with one side better
informed than the other are markets with
asymmetric information.
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Asymmetric Information, Uncertainty, and, Auctions

4. Asymmetric Information: Some examples
A worker knows more than his employer about how
much eort he puts into his job. (example of a hidden
action)
A seller of a used car knows more than the buyer
about the car's condition. (example of a hidden
characteristic).
a customer knows her taste for a good or a service
better than the rm that supplies and prices it.
(example of a hidden characteristic).
a person knows more about his driving habits than the
company that provides his auto insurance (example of
a hidden characteristic)
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5. Asymmetric Information
Hidden actions are actions taken by one side of an
economic relationship (agent) that the other side of the
relationship (principal) cannot observe.
Agent: a person who is performing an act for another
person, called thePrincipal.
Hidden characteristics are things that one side of a
transaction knows about itself that the other side
would like to know but does not.
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6. Asymmetric Information
Moral Hazard
Problems after a contract is written.
The tendency of an imperfectly monitored agent to
engage in dishonest or otherwise undesirable behavior.
Adverse Selection
Problems before a contract is written.
Refers to the tendency for the mix of unobserved
attributes to become undesirable from the standpoint
of an uniformed party.
Imperfect information inuences resource allocation
and the price system.
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7. Moral Hazard
Classic example:employment. The employer is the
principal and the worker is the agent.Moral Hazard
is the temptation of imperfectly monitored workers to
shirk their responsibilities.
Employer's possible responses toMoral Hazard:
better monitoring.
higher wages employer pays above Value Marginal
Product of Labor (VMPL). Then, the worker getting
this wage is less likely to shirk because if caught he
will not be able to nd another high-paying job.
delayed payment the employer can delay part of
worker's compensation so that, if caught shirking and
red, the worker incurs a higher loss.
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8. Moral Hazard
A homeowner buys reinsuranceand then is likely to
buy too few re extinguishers because the homeowners
bears the cost of each extinguisher while the insurance
company receives much of the benet.
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Asymmetric Information, Uncertainty, and, Auctions

9. Adverse Selection
Market for used cars. The lack of complete
information when purchasing a used car increases the
risk of the purchase and lowers the value of the car.
Automobile Insurance: A rm selling car insurances
cannot identify owners living in high crime areas. If
average cost is charged, it can lead to insurance rm
losing out.
The Market for Credit: Asymmetric information
creates the potential that only high risk borrowers will
seek loans. How can credit histories help make this
market more ecient and reduce the cost of credit?
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10. Adverse Selection
Medical Insurance: Buyers of health insurance know
more about their health problems than do insurance
companies. Because people with greater hidden health
problems are more likely to buy health insurance than
are other people, the price of health insurance reects
the cost of a sicker-than-average person.
Is it possible for insurance companies to separate high
and low risk policy holders? If not, only high risk
people will purchase insurance.
Adverse selection would make medical insurance
unprotable.
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11. Adverse Selection
When markets suer from adverse selection, there are
some problems: Owners of good cars may choose to
keep them rather than sell them at the low price that
skeptical buyers are willing to pay.
In insurance markets, buyers with low risk may choose
to remain uninsured, because the policies they are
oered are too expensive, given their true
characteristics.
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12. Market for used cars:Peaches and Lemons
Akerlof, George A. (1970). The Market for 'Lemons':
Quality Uncertainty and the Market Mechanism.
Quarterly Journal of Economics. The MIT Press. 84
(3): 488500.
Sellers of cars know their vehicles' defects while buyers
often do not. Because owners of the worst cars are
more likely to sell them than are the owners of the best
cars, buyers fear they would get a lemon.
Low quality goods drive high quality goods out of the
market.
The market has failed to produce mutually benecial
trade.
Adverse selection occurs; the only cars on the market
will be low quality cars.
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13. Market for used cars:Peaches and Lemons
Two types of cars: lemons and peaches.
Each lemon seller will accept $1,000; a buyer will pay
at most $1,200.
Each peach seller will accept $2,000; a buyer will pay
at most $2,400.
If every buyer can tell a peach from a lemon, then
lemons sell for between $1,000 and $1,200, and peaches
sell for between $2,000 and $2,400.
Gains-to-trade are generated when buyers are well
informed.
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14. Market for used cars:Peaches and Lemons
Suppose no buyer can tell a peach from a lemon before
buying. What is the most a buyer will pay for any car?
Letbe the fraction of peaches. For all,2]0;1[
(1)is the fraction of lemons.
Expected value (EV) to a buyer of any car is at most
Suppose EV > $2000.
Every seller can negotiate a price between $2000 and
$EV (no matter if the car is a lemon or a peach).
All sellers gain from being in the market.
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15. Market for used cars:Peaches and Lemons
Suppose EV < $2000.
A peach seller cannot negotiate a price below $2000
and will exit the market.
So all buyers know that remaining sellers own lemons
only.
Buyers will pay at most $1200 and only lemons are
sold.
Hence too many lemons crowd out the peaches
from the market.
Gains-to-trade are reduced since no peaches are traded.
The presence of the lemons inicts an external cost on
buyers and peach owners.
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16. Market for used cars:Peaches and Lemons
How many lemons can be in the market without
crowding out the peaches?
Buyers will pay $2000 for a car only if
EV= $1200(1) + $2400$2000

2
3
So if over one-third of all cars are lemons, then only
lemons are traded.
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17. Market for used cars:Peaches and Lemons
A market equilibrium in which both types of cars are
traded and cannot be distinguished by the buyers is a
pooling equilibrium.
A market equilibrium in which only one of the two
types of cars is traded, or both are traded but can be
distinguished by the buyers, is aseparating
equilibrium.
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18. Quality Choice
Now each seller can choose the quality, or value, of her
product.
Two umbrellas; high-quality and low-quality.
Which will be manufactured and sold?
Buyers value a high-quality umbrella at $14 and a
low-quality umbrella at $8.
Before buying, no buyer can tell quality.
Marginal production cost of a high-quality umbrella is
$11.
Marginal production cost of a low-quality umbrella is
$10.
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19. Quality Choice
Suppose every seller makes only high-quality umbrellas.
Every buyer pays $14 and sellers' prot per umbrella is
$14 - $11 = $3.
But then a seller can make low-quality umbrellas for
which buyers still pay $14, so increasing prot to $14 -
$10 = $4.
There is no market equilibrium in which only
high-quality umbrellas are traded.
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20. Quality Choice
Is there a market equilibrium in which only low-quality
umbrellas are traded?
All sellers make only low-quality umbrellas.
Buyers pay at most $8 for an umbrella, while marginal
production cost is $10.
There is no market equilibrium in which only
low-quality umbrellas are traded.
Now we know there is no market equilibrium in which
only one type of umbrella is manufactured.
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21. Quality Choice
Is there an equilibrium in which both types of umbrella
are manufactured?
A fractionof sellers make high-quality umbrellas;
0< <1
Buyers' expected value of an umbrella is
EV= 14+ 8(1) = 8 + 6
High-quality manufacturers must recover the
manufacturing cost
EV= 8 + 611)
1
2
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22. Quality Choice
So at least half of the sellers must make high-quality
umbrellas for there to be a pooling market equilibrium.
But then a high-quality seller can switch to making
low-quality and increase prot by $1 on each umbrella
sold.
Since all sellers reason this way, the fraction of
high-quality sellers will shrink towards zero but then
buyers will pay only $8.
So there is no equilibrium in which both umbrella
types are traded.
The market has no equilibrium
with just one umbrella type traded
with both umbrella types traded
so the market has no equilibrium at all.
Adverse selection has destroyed the entire market!
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23. Mechanisms that reduce adverse selection
There is a number of mechanisms that may reduce adverse
selection, and, increase the volume of trade and the total
welfare. These mechanisms include:
Regulation: for instance, the government regulates
the markets for food and drugs, so you can be sure
that even at a very low price you will not buy a
lemon that will poison you.
Reputation: well-established businesses, such as big
car dealerships, cannot aord to sell lemons because
it hurts their reputation and future prots.
Assurance: the less-informed party can pay for an
expert opinion, e.g. ,it is common to hire a mechanic to
inspect a used car, and to check the history of the car.
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24. Mechanisms that reduce adverse selection
Warranty: The seller of a used car who claims it to
have a top quality may commit to pay a compensation
to the buyer if the car needs a repair within a certain
time period. In order for warranty to work, it must
incur dierent costs for owners of cars of dierent
qualities.
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25. Signalling and Screening
Signalling. The better-informed party takes the lead
Often the better informed party would benet from
communicating this information.
High-quality seller must do something costly and
veriable to signal quality convincingly. E.g.
reputation, warranty, job market, etc.
Informed individuals may nd ways to signal
information about their unobservable knowledge
through observable actions.
ScreeningThe less-informed party takes the lead.
Uninformed parties may develop mechanism to
distinguish , or screen , informed individuals who have
dierent information.
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26. Signalling: Examples
Looking Busy: Ever known someone whose desk was
always a mess of papers and who always looked
frazzled? You could argue that looking busy is a way
of signaling that your role is important and keeping
the boss o your back.
Seller of a used car could oer to allow a prospective
buyer to take the car to a mechanic.
Firms may spend money on advertising to signal to
potential buyers.
Students earning college and postgraduate degrees
signal to potential employers that they are high-ability
individuals.
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27. Signalling: Labor Market
Michael Spence (1973). Job Market Signalling.
Quarterly Journal of Economics. 87 (3): 355374.
Two types of workers; high-ability and low-ability.
A high-ability worker's marginal product isaH= 80
A low-ability worker's marginal product isaL= 40
The workers' eort is xed (say 40 Hrs. a week) and
plays no role in signalling. The employers are perfectly
competitive (rather than being a monopoly).
50% (=) of all workers are high-ability, and, 50%
(=(1)) is the fraction of low-ability workers.
Each worker is paid his expected marginal product.
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28. Signalling: Labor Market
If rms knew each worker's type they would
pay each high-ability workerwH=aH.
pay each low-ability workerwL=aL.
In the perfect information case when the productivity
of each worker is known to the employers, the able
workers will receive the wage 80 and the unable the
wage 40.
Pooling equilibrium: if rms cannot tell workers'
types then every worker is paid the wage rate; i.e. the
expected marginal product
wP= (1)aL+aH
wP=
1
=240 +
1
=280 = 60
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29. Signalling: Labor Market
Separating equilibrium
wP= (1)aL+aH< aH, the wage rate paid when
the rm knows a worker really is high-ability.
High-ability workers have an incentive to nd a
credible signal.
Workers can acquire education.
Education costs:
For a high-ability workercHper unit.cH= 10
For a low-ability workercLper unit.cL= 20
Crucial assumption: Signaling costs are negatively
correlated with productive ability.
It could simply be eort (Hrs. of study necessary to
learn a particular thing).
Or the more able students usually receive more
nancial support.
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30. Signalling: Labor Market
For simplicity, assume that the education does not
aect productivity at all and serves only the signalling
purpose.
High-ability workers will acquireeHeducation units if
wHwL=aHaL> cHeH, and
wHwL=aHaL< cLeH
AcquiringeHunits of education benets high-ability
workers.
AcquiringeHeducation units hurts low-ability workers.
ifcHeH< aHaL< cLeH, so
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31. Signalling: Labor Market
aHaL
cL
< eH<
aHaL
cH
8040
20
< eH<
8040
10
2< eH<4
Note:
if4< eHthe able will not want to get the education
eHbecause it is not worth it: the cost of such
education is above 40, and hence is greater than the
wage dierential.
if2> eHthen both able and unable will chooseeH
units of education because the cost is below 40 hence,
is less than the wage dierential.
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32. Signalling: Labor Market
Acquiring such an education level credibly signals
high-ability, allowing high-ability workers to separate
themselves from low-ability workers.
Given that high-ability workers acquireeHunits of
education, how much education should low-ability
workers acquire?
Zero. Low-ability workers will be paidwL=aL. so
long as they do not haveeHunits of education and
they are still worse o if they do.
Signalling can improve information in the market.
But, total output did not change and education was
costly so signalling worsened the market's eciency.
So improved information need not improve
gains-to-trade.
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33. Screening: Examples
Insurance
Insuree knows her risk, insurer does not
Insurer oers several packages with dierent premiums
and deductibles. Search for historical Records,
demographic characteristics, etc
Finance
Borrower knows the risk of project, lender does not
Lender oers several packages with dierent interest
rates and collateral requirements
Hiring
Applicants know their ability, employer does not
Employers give aptitude tests, check letters of
recommendation, school aliations, GPA. Give
bonuses, etc.
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34. Screening: Examples
Pricing
Buyer knows her valuation of the product, seller does
not
Seller oers dierent qualities at dierent prices, or
quantity discounts
Selling used cars
Sellers of cars know their vehicles' defects while buyers
often do not.
Buyer may ask that car may be checked by a
mechanic before the sale. If seller refuses, he reveals
his private information that the car is a lemon.
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35. Screening: Insurance
A rm sells car insurance. Desirable: charge a low
premium to safe drivers and a high premium to risky
drivers.
How can the rm separate the drivers?. Firm separates
drivers by oering dierent insurance policies.
Policy 1: high premium and covers all costs (no
deductible). Policy 2: lower premium but the driver is
responsible for the rst $1000 of damage ($1000
deductible).
Policy 2 is more of a burden for risky drivers because
they are more likely to have an accident. With a large
enough deductible, risky drivers will choose Policy 1
while safe drivers choose Policy 2.
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36. Screening: Credit Market
J. E. Stiglitz and A. Weiss (1981) Credit Rationing in
Markets with Imperfect Information The American
Economic Review, 71 (3): 393-410.
If markets worked perfectly, supply and demand for
credit would x the interest rate at which lenders' d
assume the risk, and borrowers'd accept it in order to
fund their projects.
If the project succeeds, the loan is repaid to the bank;
if it fails, the investor declares bankruptcy and the
bank gets nothing. The possibilities are:
acquiring the loan in good will but despite your best
eorts you'll probably default anyway
simply do not care about the interest rate because you
have no intention of paying the loan back in the rst
place.
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37. Screening: Credit Market
Banks do not know dierent kinds of investors.
Each of several potential liquidity constrained investors
has access to a project.
The project's protability is private information.
The bank might be reluctant to raise the interest rates
to a level that clears the loan market. Thus, credit
might be rationed and investment curtailed.
Credit rationing implies that credit is not available for
all those who want it, at any interest rate.
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38. Screening: Credit Market
An increase in the bank's interest rate.
Its prots increase in the event that the project is
successful.
Signal 1: if we have a good credit rating and are not
desperately in need of funds, we probably won't
accept excessively high interest rates, we will simply
put o our projects or purchases.
Signal 2: When interest rates rise above a certain
level, nancial agents can assume that you are a
lemon, and that the risk of you defaulting on your
credit is too high.
It attracts riskier investors at the margin because the
greater amount that needs to be repaid can only be
generated through riskier projects.
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39. Screening: Credit Market
Suppose two types of borrowers,AsandBs.
Both want to invest in similar projects with a dierent
level of risk.
SupposeAsinvest in safer projects thanBsalthough
the mean return is the same, 110.
AsROIs between 90 and 120 for their investment.
If they invest 100, then for interest rates over 20%
their prot will be 0 even if their project is successful.
BsROIs between 70 and 180 for their investment.
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40. Screening: Credit Market
IfBsare really optimistic (as riskier investors tend to
be), they can potentially accept interest rates of up to
80% and still break even.
Suppose bothAsandBsdefault on their credit if their
ROI is negative (below 100).
Suppose that all those willing to accept rates of over
20% are therefore risky investors,Bs.
When interest rates approachBs, credit will simply
dry up as all those willing to accept higher rates and
still borrow will be singled out as probable defaulters.
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41. Expected Utility Theory: Utility Theory
Can we even measure satisfaction or happiness?
Suppose that everyone likes to eat gourmet food at
ve-star hotels, drink French wine, vacation in exotic
places, and drive luxury cars.
All these goods are assumed to provide satisfaction,
some more than others.
Utility Theory
bases its beliefs upon individuals' preferences.
rests upon the idea that people behave as if they make
decisions by assigning imaginary utility values to the
original monetary values
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42. Expected Utility Theory: Utility Theory
It explains behavior of individuals based on the
premise people can consistently rank order their
choices depending upon their preferences.
Placing certain restrictions, preferences can be
represented using autility function
It is a mathematical formulation that ranks the
preferences of the individual in terms of satisfaction
dierent consumption bundles provide.
Under the assumptions of utility theory, we can
assume that people behaved as if they had a utility
function and acted according to it.
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43. Expected Utility Theory: Uncertainty
WhileUtility Theorydeals with situations in which
there is no uncertainty, theExpected Utility
Theorydeals with choices individuals make when the
outcomes they face are uncertain.
If individuals maximize utility under certainty, they
will also attempt to maximizeexpected utilityunder
uncertainty.
Using Expected Utility Theory, we will nd that even
if governments did not make purchase of insurance
mandatory, the product would still have existed.
Risk-averse individuals would always demand
insurance for the peace of mind it confers.
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44. Expected Utility Theory: Uncertainty
What is uncertain in economic systems?
tomorrow's prices
future wealth
future availability of commodities
present and future actions of other people.
What are rational responses to uncertainty?
buying insurance (health, life, auto)
a portfolio of contingent consumption goods.
States of Nature: Car accident and no car
accident. Each one occurs with a certain probability.
Contingencies: A contract implemented only when a
particular state of nature occurs is state-contingent.
E.g. the insurer pays only if there is an accident.
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45. Expected Utility Theory: Uncertainty
Expected value(EV) computed as a weighted
average of the events, and the weights are the
probabilities those events will take place with.
Expected utilityallows people to compare gambles
Given two gambles, we assume people prefer the
situation that generates the greatest expected utility.
People maximize expected utility.
Many people are risk averse and prefer certainty to the
uncertain gamble.
For example
Job A: certain income of $50K and Job B: 50% chance
of $10K and 50% chance of $90K
Expected income is the same ($50K) but Job A
implies a certain income. Which one is preferred?
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46. Expected Utility Theory: Uncertainty
Risk-averse individuals: Utility functionU(X) =
p
X
EUa=
p
50000 = $223:61and
EUb= 0:5
p
10000 + 0:5
p
90000 = $200
Job (a) is preferred
Risk-neutral individuals: Utility functionU(X) =X
EUa= 50000 = $50000and
EUb= 0:510000 + 0:590000 = $50000
Individuals are indierent toward risk
Risk-seeking individuals: Utility functionU(X) =X
2
EUa= 50000
2
= 25(10000)
2
and
EUb= 0:5(10000)
2
+ 0:5(90000)
2
= 41(10000)
2
Job (b) is preferred
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47. Insurance: Risk Aversion
Ty is a student who gets a monthly allowance of $200
(initial wealthW0) from his parents.
He might lose $100 on any given day with a probability
0.5 or not lose any amount with 50% chance.
His expected loss (E[L]) is 0.5($0) + 0.5($100) = $50.
His expected nal wealth is
E(FW) = 0:5($200$0) + 0:5($200$100) =
W0E(L) = $150.
How much Ty would be willing to pay to hedge his
expected loss of $50?
Assume that Ty's utility function isU(W) =
p
W, a
risk averter's utility function
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48. Insurance: Risk Aversion
Expected utility, no insurance
He retains all the uncertainty.
His expected nal wealth of $150 as calculated above.
What is his expected utility?
The expected utility is calculated as a weighted sum of
the utilities in the two states, loss and no loss.
EU= 0:5
p
($200$0)+0:5
p
($200$100) = $12:07
What is the actuarially fair premium (AFP) for Ty?
The AFP is the expected loss ($50).
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49. Insurance: Risk Aversion
Expected Utility with insurance at AFP(=$50)
With no loss, his nal wealth is $150 (($200)-AFP
($50)).
With a loss, his nal wealth = $200-AFP ($50)-Loss
($100)+Indemnity ($100)= $150.
Ty has purchased a certain wealth of $150, by paying
an AFP of $50. His expected utility is $12.25 .
Ty will always purchase full insurance at AFP.
A risk-averse person will always hedge the risk
completely at a cost (AFP) that equals the expected
loss.
A risk-averse person always prefers certainty to
uncertainty, if uncertainty can be hedged away at its
actuarially fair price.
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50. Insurance: Risk Aversion
Expected Utility with insurance at a price greater
than AFP
What is the maximum premium Ty would be willing
to pay?
We should equate the utility when Ty purchases
insurance atPto the expected utility in the
no-insurance case ($12.07).
Now, Ty's certain utility is
p
200P, and the
expected utility is:
EU= 0:5
p
($200$P)+0:5
p
($200$P) = 12:07
P = $54.29.
The risk premiun is $54.29-$50= $4.29
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51. Insurance: Risk Aversion
Risk Premium: The premium above the AFP that a
risk-averse person is willing to pay to get rid of the
risk.
Any insurance company that charges a premium
greater than $54.29 will not be able to sell insurance to
Ty.
Individuals' risk aversion is a key component in
insurance pricing.
The greater the degree of risk aversion, the higher the
risk premium an individual will be willing to pay.
The premium has to be less than or equal to the
maximum premium the person is willing to pay.
Otherwise, the individual will never buy full insurance.
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Asymmetric Information, Uncertainty, and, Auctions

52. Risk Aversion
Most individuals with average wealth and good
education tend to be risk neutral over small gambles.
Over larger gambles individuals tend to be risk averse.
(Except when buying lottery tickets.)
Large organizations: banks, insurance companies, rms
tend to be risk neutral.Two reasons:
The risks are small relative to the organization's size.
They have so many risky things that they on average
tend to cancel each other out diversied risk.
A risk averse individual will always be better o
buying actuarially fair insurance.
As insurance becomes less fair (administration costs,
deductibles, copays etc), risk averse individuals will
buy less insurance.
Prepared by César R. Sobrino
Asymmetric Information, Uncertainty, and, Auctions

53. Insurance: Moral Hazard
An insurance company has to decide whether to sell an
auto insurance policy to Luke.
Luke is a risk-averse person whose utility function is
U(W) =
p
W.
Luke claims to be a good risk because Luke's driving
record is excellent.
Luke can also choose to be either a careful driver or a
not-so-careful driver.
Luke drives a car carrying a market value of $10,000.
The only other asset he owns is the $3,000 in his
checking account.
His total initial wealth of $13,000
If he drives carefully, he incurs a cost of $3,000.
Prepared by César R. Sobrino
Asymmetric Information, Uncertainty, and, Auctions

54. Insurance: Moral Hazard
Luke faces the following loss distribution
Drives with Care without Care
Prob.LossProb.Loss
accident0.25$10,0000.75$10,000
no accident0.75 0 0.25 0
When he has an accident, his car is a total loss.
The probabilities of loss and no loss are reversed
when he decides to drive without care.
EV[loss]= $2,500 and EV[loss]= $7,500.
Luke's problem has 4 parts: whether to drive with or
without care, (I) when he has no insurance and (II)
when he has insurance.
Prepared by César R. Sobrino
Asymmetric Information, Uncertainty, and, Auctions

55. Insurance: Moral Hazard
Case I when he carries no insurance.
Drives with Care without Care
Prob.U(W)Prob.U(W)
accident0.25 0 0.75$54.77
no accident0.75$1000.25$114.02
Drives with care and has an accident:
W= $13000$3000$10000 = 0)U(0) = 0
Drives with care and has not an accident:
W= $13000$30000 = $10000)U($10000) = $100
Drives without care and has an accident:W=
$130000$10000 = $3000)U($3000) = $54:77
Drives without care and has not an accident:
W= $1300000 = $13000)U($13000) = $114:02
Prepared by César R. Sobrino
Asymmetric Information, Uncertainty, and, Auctions

56. Insurance: Moral Hazard
The expected utility of driving with care:
EU= 0:250 + 0:75100 = $75
The expected utility of driving without care:
EU= 0:7554:77 + 0:25114:02 = $69:58
Luke will drive carefully since his expected utility is
higher when he exercises due care. His utility is $75
versus $69.58.
Prepared by César R. Sobrino
Asymmetric Information, Uncertainty, and, Auctions

57. Insurance: Moral Hazard
Case II when he carries insurance. Insurance
premiun=$2750 = $2500(1 + 0:1)
Drives with Care without Care
Prob.U(W)Prob.U(W)
accident0.25$85.150.75$101.24
no accident0.75$85.150.25$101.24
With an insurance, Luke has eliminated the
uncertainty.
If he has an accident, the insurance company
indemnies him with $10,000.
Drives with care and has an accident:
W= $10250$3000$10000 + $10000 = $7250)
U(7250) = $85:15
Drives with care and has not an accident:
W= $10250$3000 = $7250)U(7250) = $85:15
Prepared by César R. Sobrino
Asymmetric Information, Uncertainty, and, Auctions

58. Insurance: Moral Hazard
Drives without care and has an accident:
W= $102500$10000 + $10000 = $10250)
U(10250) = $101:24
Drives without care and has not an accident:
W= $102500 = $10250)U(10250) = $101:24
The expected utility of driving with care:
EU= 0:2585:15 + 0:7585:15 = $85:15
The expected utility of driving without care:
EU= 0:75101:24 + 0:25101:242 = $101:24
The net result is he switches to driving with no care
Prepared by César R. Sobrino
Asymmetric Information, Uncertainty, and, Auctions

59. Insurance: Moral Hazard
Why do we get this result?
The cost of insurance is cheaper than the cost of care.
Insurance companies can charge a price greater than
the cost of care up to a maximum of what Luke is
willing to pay.
In the event of asymmetric information, the insurance
company will not know the cost of care.
Inexpensive insurance distorts the incentives and
individuals switch to riskier behavior ex post.
Prepared by César R. Sobrino
Asymmetric Information, Uncertainty, and, Auctions

60. References
Varian, Hal R. 2010. Intermediate microeconomics: a
modern approach. New York: W.W. Norton & Co.
Prepared by César R. Sobrino
Asymmetric Information, Uncertainty, and, Auctions