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Chapter Thirty-Six
Asymmetric Information
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Information in Competitive Markets
In purely competitive markets allagents are fully informed abouttraded commodities and other
aspects of the market.What about markets for medical
services, or insurance, or used cars?
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Asymmetric Information in Markets
A doctor knows more about medicalservices than does the buyer.
An insurance buyer knows more
about his riskiness than does theseller.
A used cars owner knows more about
it than does a potential buyer.
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Asymmetric Information in Markets
Markets with one side or the otherimperfectly informed are marketswith imperfect information.
Imperfectly informed markets withone side better informed than theother are markets with asymmetric
information.
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Asymmetric Information in Markets
In what ways can asymmetricinformation affect the functioning ofa market?
Four applications will be considered:
adverse selection
signaling
moral hazard
incentives contracting.
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Adverse Selection
Consider a used car market.
Two types of cars; lemons andpeaches.
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.
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Adverse Selection
If every buyer can tell a peach from alemon, 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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Adverse Selection
Suppose no buyer can tell a peachfrom a lemon before buying.
What is the most a buyer will pay for
any car?
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Adverse Selection
Let qbe the fraction of peaches.
1 - qis the fraction of lemons.
Expected value to a buyer of any caris at most
EV q q$1200( ) $2400 .1
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Adverse Selection
Suppose EV > $2000.
Every seller can negotiate a pricebetween $2000 and $EV (no matter if
the car is a lemon or a peach).
All sellers gain from being in themarket.
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Adverse Selection
Suppose EV < $2000.A peach seller cannot negotiate a
price above $2000 and will exit the
market.So all buyers know that remaining
sellers own lemons only.
Buyers will pay at most $1200 andonly lemons are sold.
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Adverse Selection
Hence too many lemons crowdout the peaches from the market.
Gains-to-trade are reduced since no
peaches are traded.
The presence of the lemons inflictsan external cost on buyers and
peach owners.
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Adverse Selection
How many lemons can be in themarket without crowding out thepeaches?
Buyers will pay $2000 for a car only if2000$2400$)1(1200$ qqEV
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Adverse Selection
How many lemons can be in themarket without crowding out thepeaches?
Buyers will pay $2000 for a car only if
So if over one-third of all cars arelemons, then only lemons are traded.
.3
2
2000$2400$)1(1200$
q
qqEV
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Adverse Selection
A market equilibrium in which bothtypes of cars are traded and cannotbe 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 bedistinguished by the buyers, is aseparating equilibrium.
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Adverse Selection
What if there is more than two typesof cars?
Suppose that
car quality is Uniformlydistributed between $1000 and$2000
any car that a seller values at $x isvalued by a buyer at $(x+300).
Which cars will be traded?
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Adverse Selection
Seller values1000 2000
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Adverse Selection
1000 20001500Seller values
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Adverse Selection
1000 20001500
The expected value of any
car to a buyer is$1500 + $300 = $1800.
Seller values
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Adverse Selection
1000 20001500
The expected value of any
car to a buyer is$1500 + $300 = $1800.
So sellers who value their cars atmore than $1800 exit the market.
Seller values
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Adverse Selection
1000 1800
The distribution of values
of cars remaining on offer
Seller values
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Adverse Selection
1000 18001400Seller values
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Adverse Selection
1000 18001400
The expected value of any
remaining car to a buyer is$1400 + $300 = $1700.
Seller values
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Adverse Selection
1000 18001400
The expected value of any
remaining car to a buyer is$1400 + $300 = $1700.
So now sellers who value their carsbetween $1700 and $1800 exit the market.
Seller values
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Adverse Selection
Where does this unraveling of themarket end?
Let vHbe the highest seller value of
any car remaining in the market.
The expected seller value of a car is1
21000
1
2 v
H
.
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Adverse Selection
So a buyer will pay at most1
21000
1
2300 vH .
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Adverse Selection
So a buyer will pay at most
This must be the price which theseller of the highest value carremaining in the market will just
accept; i.e.
1
21000
1
2300 vH .
1
21000
1
2300 v vH H .
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Adverse Selection1
2 1000
1
2 300
v vH H
vH $1600.
Adverse selection drives out all carsvalued by sellers at more than $1600.
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Adverse Selection with Quality Choice
Now each seller can choose thequality, or value, of her product.
Two umbrellas; high-quality and low-
quality.Which will be manufactured and sold?
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Adverse Selection with Quality Choice
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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Adverse Selection with Quality Choice
Suppose every seller makes only high-quality umbrellas.
Every buyer pays $14 and sellers
profit per umbrella is $14 - $11 = $3.But then a seller can make low-quality
umbrellas for which buyers still pay
$14, so increasing profit to$14 - $10 = $4.
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Adverse Selection with Quality Choice
There is no market equilibrium inwhich only high-quality umbrellasare traded.
Is there a market equilibrium inwhich only low-quality umbrellas aretraded?
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Adverse Selection with Quality Choice
All sellers make only low-qualityumbrellas.
Buyers pay at most $8 for an
umbrella, while marginal productioncost is $10.
There is no market equilibrium in
which only low-quality umbrellas aretraded.
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Adverse Selection with Quality Choice
Now we know there is no marketequilibrium in which only one type ofumbrella is manufactured.
Is there an equilibrium in which bothtypes of umbrella are manufactured?
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Adverse Selection with Quality Choice
A fraction qof sellers make high-quality umbrellas; 0 < q< 1.
Buyers expected value of an
umbrella isEV = 14q+ 8(1 - q) = 8 + 6q.
High-quality manufacturers must
recover the manufacturing cost,EV = 8 + 6q 11 q 1/2.
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Adverse Selection with Quality Choice
So at least half of the sellers mustmake high-quality umbrellas for thereto be a pooling market equilibrium.
But then a high-quality seller canswitch to making low-quality andincrease profit by $1 on each
umbrella sold.
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Adverse Selection with Quality Choice
Since all sellers reason this way, thefraction of high-quality sellers willshrink towards zero -- but then
buyers will pay only $8.So there is no equilibrium in which
both umbrella types are traded.
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Adverse Selection with Quality Choice
The market has no equilibrium
with just one umbrella type traded
with both umbrella types traded
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Adverse Selection with Quality Choice
The market has no equilibrium
with just one umbrella type traded
with both umbrella types traded
so the market has no equilibriumatall.
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Adverse Selection with Quality Choice
The market has no equilibrium
with just one umbrella type traded
with both umbrella types traded
so the market has no equilibriumatall.
Adverse selection has destroyed theentire market!
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Signaling
Adverse selection is an outcome of aninformational deficiency.
What if information can be improved
by high-quality sellers signalingcredibly that they are high-quality?
E.g. warranties, professional
credentials, references from previousclients etc.
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Signaling
A labor market has two types ofworkers; high-ability and low-ability.
A high-ability workers marginal
product is aH.A low-ability workers marginal
product is aL.
aL< aH.
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Signaling
A fraction hof all workers are high-ability.
1 - his the fraction of low-ability
workers.
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Signaling
Each worker is paid his expectedmarginal product.
If firms knew each workers type they
wouldpay each high-ability worker wH=aH
pay each low-ability worker wL= aL.
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Signaling
If firms cannot tell workers typesthen every worker is paid the(pooling) wage rate; i.e. the expected
marginal productwP= (1 - h)aL+ haH.
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Signaling
wP= (1 - h)aL+ haH< aH, the wagerate paid when the firm knows aworker really is high-ability.
So high-ability workers have anincentive to find a credible signal.
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Signaling
Workers can acquire education.
Education costs a high-ability workercHper unit
and costs a low-ability worker cLperunit.
cL> cH.
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Signaling
High-ability workers will acquire eHeducation units if(i) wH- wL= aH- aL> cHeH, and(ii) w
H
- wL
= aH
- aL
< cL
eH
.
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Signaling
High-ability workers will acquire eHeducation units if(i) wH- wL= aH- aL> cHeH, and(ii) w
H
- wL
= aH
- aL
< cL
eH
.
(i) says acquiring eHunits of educationbenefits high-ability workers.
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Signaling
High-ability workers will acquire eHeducation units if(i) wH- wL= aH- aL> cHeH, and(ii) w
H
- wL
= aH
- aL
< cL
eH
.
(i) says acquiring eHunits of educationbenefits high-ability workers.
(ii) says acquiringe
Heducation unitshurts low-ability workers.
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Si li
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Signaling
Q: Given that high-ability workersacquire eHunits of education, howmuch education should low-ability
workers acquire?
Si li
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Signaling
Q: Given that high-ability workersacquire eHunits of education, howmuch education should low-ability
workers acquire?A: Zero. Low-ability workers will be
paid wL= aLso long as they do not
have eHunits of education and theyare still worse off if they do.
Si li
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Signaling
Signaling can improve information inthe market.
But, total output did not change and
education was costly so signalingworsened the markets efficiency.
So improved information need notimprove gains-to-trade.
M l H d
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Moral Hazard
If you have full car insurance are youmore likely to leave your car unlocked?
Moral hazardis a reaction to incentives
to increase the risk of a lossand is a consequence of asymmetric
information.
M l H d
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Moral Hazard
If an insurer knows the exact riskfrom insuring an individual, then acontract specific to that person can
be written. If all people look alike to the insurer,
then one contract will be offered toall insurees; high-risk and low-risktypes are then pooled, causing low-risks to subsidize high-risks.
M l H d
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Moral Hazard
Examples of efforts to avoid moralhazard by using signals are:
higher life and medical insurance
premiums for smokers or heavydrinkers of alcohol
lower car insurance premiums for
contracts with higher deductiblesor for drivers with histories of safedriving.
I ti C t ti
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Incentives Contracting
A worker is hired by a principal to doa task.
Only the worker knows the effort she
exerts (asymmetric information).The effort exerted affects the
principals payoff.
I ti C t ti
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Incentives Contracting
The principals problem: design anincentives contractthat induces theworker to exert the amount of effort
that maximizes the principals payoff.
I ti C t ti
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Incentives Contracting
eis the agents effort.Principals reward is
An incentive contract is a functions(y) specifying the workers paymentwhen the principals reward is y. Theprincipals profit is thus
)).(()()( efsefysyp
).(efy
I ti C t ti
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Incentives Contracting
Let be the workers (reservation)utility of not working.
To get the workers participation, the
contract must offer the worker autility of at least
The workers utility cost of an effort
level eis c(e).
u~
.~u
I ti C t ti
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Incentives Contracting
So the principals problem is choose eto))(()(max efsefp
subject to .~)())(( uecefs (participationconstraint)
To maximize his profit the principaldesigns the contract to provide the
worker with her reservation utility level.That is, ...
I ti C t ti
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Incentives Contracting
the principals problem is to))(()(max efsefp
subject to .~)())(( uecefs (participationconstraint)
I ti C t ti
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Incentives Contracting
the principals problem is to
subject to (participation
constraint)Substitute for and solve
))(()(max efsefp .~)())(( uecefs
.~)()(max uecefp ))(( efs
I ti C t ti
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Incentives Contracting
the principals problem is to
subject to (participation
constraint)
The principals profit is maximized when).()( ecef
))(()(max efsefp .~)())(( uecefs
.~)()(max uecefp Substitute for and solve))(( efs
Incenti es Contracting
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Incentives Contracting
.*)()( eeecef The contract that maximizes theprincipals profit insists upon theworker effort level e* that equalizesthe workers marginal effort cost tothe principals marginal payoff fromworker effort.
Incentives Contracting
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Incentives Contracting
How can the principal induce theworker to choose e = e*?
.*)()( eeecef The contract that maximizes theprincipals profit insists upon theworker effort level e* that equalizesthe workers marginal effort cost tothe principals marginal payoff fromworker effort.
Incentives Contracting
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Incentives Contracting
e= e* must be most preferred by theworker.
Incentives Contracting
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Incentives Contracting
e= e* must be most preferred by theworker.
So the contract s(y) must satisfy the
incentive-compatibilityconstraint;
.0allfor),())((*)(*))(( eecefsecefs
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Rental Contracting
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Rental Contracting
Given the contractthe workers payoff is
and to maximize this the workershould choose the effort level forwhich
)()()())(( ecRefecefs
.*,isthat);()( eeecef
Refefs )())((
Rental Contracting
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Rental Contracting
How large should be the principalsrental fee R?
The principal should extract as much
rent as possible without causing theworker not to participate, so Rshould satisfy
i.e.
;~*)(*))(( uRecefs .~*)(*))(( uecefsR
Other Incentives Contracts
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Other Incentives Contracts
(ii) Wages contracts: In a wagescontract the payment to the worker is
wis the wage per unit of effort.Kis a lump-sum payment.
and Kmakes the worker
just indifferent between participatingand not participating.
.)( Kwees
*)(efw
Other Incentives Contracts
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Other Incentives Contracts
(iii) Take-it-or-leave-it: Choose e= e*and be paid a lump-sum L , or choosee e* and be paid zero.
The workers utility from choosinge e* is - c(e), so the worker willchoose e= e*.
L is chosen to make the workerindifferent between participating andnot participating.
Incentives Contracts in General
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Incentives Contracts in General
The common feature of all efficientincentive contracts is that they makethe worker the full residual claimant
on profits. I.e. the last part of profit earned must
accrue entirelyto the worker.