Ch36 Asymmetric Information

8/13/2019 Ch36 Asymmetric Information

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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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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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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


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


remaining car to a buyer is$1400 + $300 = $1700.

Seller values


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Adverse Selection

1000 18001400


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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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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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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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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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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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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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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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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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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The market has no equilibrium

with just one umbrella type traded

with both umbrella types traded


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so the market has no equilibriumatall.


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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


H

- wL

= aH

- aL

< cL

eH

.

(i) says acquiring eHunits of educationbenefits high-ability workers.


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Signaling


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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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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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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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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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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the principals problem is to))(()(max efsefp

subject to .~)())(( uecefs (participationconstraint)

I ti C t ti


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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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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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.*)()( 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.



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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.



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e= e* must be most preferred by theworker.



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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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(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



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(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.

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Ch36 Asymmetric Information