Chapter Thirty-Six
Asymmetric Information
不对称信息
Information in Competitive Markets
In purely competitive markets all
agents are fully informed about
traded commodities and other
aspects of the market.
What about markets for medical
services,or insurance,or used cars?
Asymmetric Information in Markets
A doctor knows more about medical
services than does the buyer.
An insurance buyer knows more
about his riskiness than does the
seller,
A used car’s owner knows more about
it than does a potential buyer.
Asymmetric Information in Markets
Markets with one side or the other
imperfectly informed are markets
with imperfect information(不完全信息 ).
Imperfectly informed markets with
one side better informed than the
other are markets with asymmetric
information(不对称信息 ).
Asymmetric Information in Markets
In what ways can asymmetric
information affect the functioning of
a market?
Four applications will be considered:
adverse selection (逆向选择 )
signaling (信号传递 )
moral hazard (道德风险 )
incentives contracting.
Adverse Selection
Consider a used car market.
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.
Adverse Selection
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.
Adverse Selection
Suppose no buyer can tell a peach
from a lemon before buying.
What is the most a buyer will pay for
any car?
Adverse Selection
Let q be the fraction of peaches.
1 - q is the fraction of lemons.
Expected value to a buyer of any car
is at mostEV q q$1200 ( ) $2400,1
Adverse Selection
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.
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 and
only lemons are sold.
Adverse Selection
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 inflicts
an external cost on buyers and
peach owners.
Adverse Selection
How many lemons can be in the
market without crowding out the
peaches?
Buyers will pay $2000 for a car only if
2000$2400$)1(1200$ qqEV
Adverse Selection
How many lemons can be in the
market without crowding out the
peaches?
Buyers will pay $2000 for a car only if
So if over one-third of all cars are
lemons,then only lemons are traded.
.
3
2
2000$2400$)1(1200$
q
qqEV
Adverse Selection
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 a
separating equilibrium.
Adverse Selection
What if there is more than two types
of cars?
Suppose that
car quality is uniformly distributed
between $1000 and $2000
any car that a seller values at $x is
valued by a buyer at $(x+300).
Which cars will be traded?
Adverse Selection
Seller values
1000 2000
Adverse Selection
1000 20001500
Seller values
Adverse Selection
1000 20001500
The expected value of any
car to a buyer is
$1500 + $300 = $1800,
Seller values
Adverse Selection
1000 20001500
The expected value of any
car to a buyer is
$1500 + $300 = $1800,
So sellers who value their cars at
more than $1800 exit the market.
Seller values
Adverse Selection
1000 1800
The distribution of values
of cars remaining on offer
Seller values
Adverse Selection
1000 18001400
Seller values
Adverse Selection
1000 18001400
The expected value of any
remaining car to a buyer is
$1400 + $300 = $1700,
Seller values
Adverse Selection
1000 18001400
The expected value of any
remaining car to a buyer is
$1400 + $300 = $1700,
So now sellers who value their cars
between $1700 and $1800 exit the market.
Seller values
Adverse Selection
Where does this unraveling of the
market end?
Let vH be the highest seller value of
any car remaining in the market,
The expected seller value of a car is1
2 1000
1
2 v H,
Adverse Selection
So a buyer will pay at most1
2 1000
1
2 300v H,
Adverse Selection
So a buyer will pay at most
This must be the price which the
seller of the highest value car
remaining in the market will just
accept; i.e.
1
2 1000
1
2 300v H,
1
2 1000
1
2 300v vH H,
Adverse Selection1
2 1000
1
2 300v vH H
v H $1600,
Adverse selection drives out all cars
valued by sellers at more than $1600.
Adverse Selection with 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?
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.
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.
Adverse Selection with Quality Choice
There is no market equilibrium in
which only high-quality umbrellas
are traded.
Is there a market equilibrium in
which only low-quality umbrellas are
traded?
Adverse Selection with Quality Choice
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.
Adverse Selection with Quality Choice
Now we know there is no market
equilibrium in which only one type of
umbrella is manufactured.
Is there an equilibrium in which both
types of umbrella are manufactured?
Adverse Selection with Quality Choice
A fraction q of sellers make high-
quality umbrellas; 0 < q < 1.
Buyers’ expected value of an
umbrella is
EV = 14q + 8(1 - q) = 8 + 6q.
High-quality manufacturers must
recover the manufacturing cost,
EV = 8 + 6q? 11? q? 1/2.
Adverse Selection with 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 profit by $1 on each
umbrella sold.
Adverse Selection with Quality Choice
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.
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 equilibrium at
all.
Adverse selection has destroyed the
entire market!
Signaling
Adverse selection is an outcome of an
informational deficiency.
What if information can be improved by
high-quality sellers signaling credibly that
they are high-quality?
E.g,warranties,professional credentials,
references from previous clients etc.
But some form of signaling may be
inefficient …
Signaling
A labor market has two types of
workers; high-ability and low-ability.
A high-ability worker’s marginal
product is aH.
A low-ability worker’s marginal
product is aL.
aL < aH.
Signaling
A fraction h of all workers are high-
ability.
1 - h is the fraction of low-ability
workers.
Signaling
Each worker is paid his expected
marginal product.
If firms knew each worker’s type they
would
pay each high-ability worker wH =
aH
pay each low-ability worker wL = aL.
Signaling
If firms cannot tell workers’ types
then every worker is paid the
(pooling) wage rate; i.e,the expected
marginal product
wP = (1 - h)aL + haH,
Signaling
wP = (1 - h)aL + haH < aH,the wage
rate paid when the firm knows a
worker really is high-ability.
So high-ability workers have an
incentive to find a credible signal.
Signaling
Workers can acquire,education”.
Education costs a high-ability worker
cH per unit
and costs a low-ability worker cL per
unit.
cL > cH.
Signaling
Suppose that education has no effect
on workers’ productivities; i.e.,the
cost of education is a deadweight
loss.
Signaling
High-ability workers will acquire eH
education units if
(i) wH - wL = aH - aL > cHeH,and
(ii) wH - wL = aH - aL < cLeH.
(i) says acquiring eH units of education
benefits high-ability workers.
(ii) says acquiring eH education units
hurts low-ability workers.
Signaling
HHLH ecaa HLLH ecaaand
together require
.
H
LHH
L
LH
c
aae
c
aa
Acquiring such an education level credibly
signals high-ability,allowing high-ability
workers to separate themselves from
low-ability workers.
Signaling
Q,Given that high-ability workers
acquire eH units of education,how
much education should low-ability
workers acquire?
A,Zero,Low-ability workers will be
paid wL = aL so long as they do not
have eH units of education and they
are still worse off if they do.
Signaling
Signaling can improve information in
the market.
But,total output did not change and
education was costly so signaling
worsened the market’s efficiency.
So improved information need not
improve gains-to-trade.
Signaling or Human Capital? The
Debate
Implications of the two theories are different
H.C,theory,government,by subsidizing
education,provides a way out of poverty.
Signaling,the expenditures do not increase
productivity,Socially wasteful.
In the signaling model,education is still
useful:
sorting workers into the right jobs and
increasing productivity
Education could have positive social rate of
return even if it does not increase a
particular worker’s productivity.
Adverse Selection in Insurance
Bike insurance
Some areas have higher risk of theft
than other areas.
Insurance premium is based on
average risk.
Low risk consumers do not buy.
Only sell insurance at high risk areas at
high rates.
Same with health insurance
Solution in the Insurance Market
Screening for health risks
Family history
Disease history
Mandatory insurance
University students
Work-unit sponsored
Universal coverage
Adverse Selection and Moral Hazard
Adverse selection,hidden
information
Moral hazard,hidden action
Moral Hazard
If you have full bike insurance are you
more likely to leave your bike
unlocked?
Moral hazard is a reaction to incentives
to increase the risk of a loss
and is a consequence of asymmetric
information.
Moral Hazard
If an insurer knows the exact risk
from insuring an individual,then a
contract specific to that person can
be written.
If all people look alike to the insurer,
then one contract will be offered to
all insurees; high-risk and low-risk
types are then pooled,causing low-
risks to subsidize high-risks.
Moral Hazard
Examples of efforts to avoid moral
hazard by using signals are:
higher life and medical insurance
premiums for smokers or heavy
drinkers of alcohol
lower car insurance premiums for
contracts with higher deductibles
or for drivers with histories of safe
driving.
Incentives Contracting
A worker is hired by a principal to do
a task.
Only the worker knows the effort she
exerts (asymmetric information).
The effort exerted affects the
principal’s payoff.
Incentives Contracting
The principal’s problem,design an
incentives contract (激励和约 ) that
induces the worker to exert the
amount of effort that maximizes the
principal’s payoff.
Incentives Contracting
e is the agent’s effort.
Principal’s reward is
An incentive contract is a function
s(y) specifying the worker’s payment
when the principal’s reward is y,The
principal’s profit is thus
)).(()()( efsefysyp
).(efy?
Incentives Contracting
Let be the worker’s (reservation)
utility of not working.
To get the worker’s participation,the
contract must offer the worker a
utility of at least
The worker’s utility cost of an effort
level e is c(e).
u~
.~u
Incentives Contracting
So the principal’s problem is choose e to
))(()(m a x efsefp
subject to,~)())(( uecefs(participationconstraint)
To maximize his profit the principal
designs the contract to provide the
worker with her reservation utility level,
That is,...
Incentives Contracting
the principal’s problem is to
))(()(m a x efsefp
subject to,~)())(( uecefs(participationconstraint)
Incentives Contracting
the principal’s problem is to
subject to (participationconstraint)
Substitute for and solve
))(()(m a x efsefp
.~)())(( uecefs
.~)()(m a x uecefp
))(( efs
Incentives Contracting
the principal’s problem is to
subject to (participationconstraint)
The principal’s profit is maximized when
).()( ecef
))(()(m a x efsefp
.~)())(( uecefs
.~)()(m a x uecefp
Substitute for and solve))(( efs
Incentives Contracting
.*)()( eeecef
The contract that maximizes the
principal’s profit insists upon the
worker effort level e* that equalizes
the worker’s marginal effort cost to
the principal’s marginal payoff from
worker effort.
Incentives Contracting
How can the principal induce the
worker to choose e = e*?
.*)()( eeecef
The contract that maximizes the
principal’s profit insists upon the
worker effort level e* that equalizes
the worker’s marginal effort cost to
the principal’s marginal payoff from
worker effort.
Incentives Contracting
e = e* must be most preferred by the
worker.
Incentives Contracting
e = e* must be most preferred by the
worker.
So the contract s(y) must satisfy the
incentive-compatibility (激励相容 )
constraint;
.0al lf o r),())((*)(*) )(( eecefsecefs
Rental Contracting
Examples of incentives contracts:
(i) Rental contracts,The principal
keeps a lump-sum R for himself and
the worker gets all profit above R; i.e,
Why does this contract maximize the
principal’s profit?
.)())(( Refefs
Rental Contracting
Given the contract
the worker’s payoff is
and to maximize this the worker
should choose the effort level for
which
)()()())(( ecRefecefs
.*,ist h a t);()( eeecef
Refefs )())((
Rental Contracting
How large should be the principal’s
rental fee R?
The principal should extract as much
rent as possible without causing the
worker not to participate,so R
should satisfy
i.e.;~*)(*) )(( uRecefs
.~*)(*) )(( uecefsR
Other Incentives Contracts
(ii) Wages contracts,In a wages
contract the payment to the worker is
w is the wage per unit of effort.
K is a lump-sum payment.
and K makes the worker
just indifferent between participating
and not participating.
.)( Kwees
*)( efw
Other Incentives Contracts
(iii) Take-it-or-leave-it,Choose e = e*
and be paid a lump-sum L,or choose
e? e* and be paid zero.
The worker’s utility from choosing
e? e* is - c(e),so the worker will
choose e = e*.
L is chosen to make the worker
indifferent between participating and
not participating.
Incentives Contracts in General
The common feature of all efficient
incentive contracts is that they make
the worker the full residual claimant
(剩余索取者 ) on profits.
I.e,the last part of profit earned must
accrue entirely to the worker.
Asymmetric Information
不对称信息
Information in Competitive Markets
In purely competitive markets all
agents are fully informed about
traded commodities and other
aspects of the market.
What about markets for medical
services,or insurance,or used cars?
Asymmetric Information in Markets
A doctor knows more about medical
services than does the buyer.
An insurance buyer knows more
about his riskiness than does the
seller,
A used car’s owner knows more about
it than does a potential buyer.
Asymmetric Information in Markets
Markets with one side or the other
imperfectly informed are markets
with imperfect information(不完全信息 ).
Imperfectly informed markets with
one side better informed than the
other are markets with asymmetric
information(不对称信息 ).
Asymmetric Information in Markets
In what ways can asymmetric
information affect the functioning of
a market?
Four applications will be considered:
adverse selection (逆向选择 )
signaling (信号传递 )
moral hazard (道德风险 )
incentives contracting.
Adverse Selection
Consider a used car market.
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.
Adverse Selection
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.
Adverse Selection
Suppose no buyer can tell a peach
from a lemon before buying.
What is the most a buyer will pay for
any car?
Adverse Selection
Let q be the fraction of peaches.
1 - q is the fraction of lemons.
Expected value to a buyer of any car
is at mostEV q q$1200 ( ) $2400,1
Adverse Selection
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.
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 and
only lemons are sold.
Adverse Selection
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 inflicts
an external cost on buyers and
peach owners.
Adverse Selection
How many lemons can be in the
market without crowding out the
peaches?
Buyers will pay $2000 for a car only if
2000$2400$)1(1200$ qqEV
Adverse Selection
How many lemons can be in the
market without crowding out the
peaches?
Buyers will pay $2000 for a car only if
So if over one-third of all cars are
lemons,then only lemons are traded.
.
3
2
2000$2400$)1(1200$
q
qqEV
Adverse Selection
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 a
separating equilibrium.
Adverse Selection
What if there is more than two types
of cars?
Suppose that
car quality is uniformly distributed
between $1000 and $2000
any car that a seller values at $x is
valued by a buyer at $(x+300).
Which cars will be traded?
Adverse Selection
Seller values
1000 2000
Adverse Selection
1000 20001500
Seller values
Adverse Selection
1000 20001500
The expected value of any
car to a buyer is
$1500 + $300 = $1800,
Seller values
Adverse Selection
1000 20001500
The expected value of any
car to a buyer is
$1500 + $300 = $1800,
So sellers who value their cars at
more than $1800 exit the market.
Seller values
Adverse Selection
1000 1800
The distribution of values
of cars remaining on offer
Seller values
Adverse Selection
1000 18001400
Seller values
Adverse Selection
1000 18001400
The expected value of any
remaining car to a buyer is
$1400 + $300 = $1700,
Seller values
Adverse Selection
1000 18001400
The expected value of any
remaining car to a buyer is
$1400 + $300 = $1700,
So now sellers who value their cars
between $1700 and $1800 exit the market.
Seller values
Adverse Selection
Where does this unraveling of the
market end?
Let vH be the highest seller value of
any car remaining in the market,
The expected seller value of a car is1
2 1000
1
2 v H,
Adverse Selection
So a buyer will pay at most1
2 1000
1
2 300v H,
Adverse Selection
So a buyer will pay at most
This must be the price which the
seller of the highest value car
remaining in the market will just
accept; i.e.
1
2 1000
1
2 300v H,
1
2 1000
1
2 300v vH H,
Adverse Selection1
2 1000
1
2 300v vH H
v H $1600,
Adverse selection drives out all cars
valued by sellers at more than $1600.
Adverse Selection with 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?
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.
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.
Adverse Selection with Quality Choice
There is no market equilibrium in
which only high-quality umbrellas
are traded.
Is there a market equilibrium in
which only low-quality umbrellas are
traded?
Adverse Selection with Quality Choice
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.
Adverse Selection with Quality Choice
Now we know there is no market
equilibrium in which only one type of
umbrella is manufactured.
Is there an equilibrium in which both
types of umbrella are manufactured?
Adverse Selection with Quality Choice
A fraction q of sellers make high-
quality umbrellas; 0 < q < 1.
Buyers’ expected value of an
umbrella is
EV = 14q + 8(1 - q) = 8 + 6q.
High-quality manufacturers must
recover the manufacturing cost,
EV = 8 + 6q? 11? q? 1/2.
Adverse Selection with 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 profit by $1 on each
umbrella sold.
Adverse Selection with Quality Choice
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.
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 equilibrium at
all.
Adverse selection has destroyed the
entire market!
Signaling
Adverse selection is an outcome of an
informational deficiency.
What if information can be improved by
high-quality sellers signaling credibly that
they are high-quality?
E.g,warranties,professional credentials,
references from previous clients etc.
But some form of signaling may be
inefficient …
Signaling
A labor market has two types of
workers; high-ability and low-ability.
A high-ability worker’s marginal
product is aH.
A low-ability worker’s marginal
product is aL.
aL < aH.
Signaling
A fraction h of all workers are high-
ability.
1 - h is the fraction of low-ability
workers.
Signaling
Each worker is paid his expected
marginal product.
If firms knew each worker’s type they
would
pay each high-ability worker wH =
aH
pay each low-ability worker wL = aL.
Signaling
If firms cannot tell workers’ types
then every worker is paid the
(pooling) wage rate; i.e,the expected
marginal product
wP = (1 - h)aL + haH,
Signaling
wP = (1 - h)aL + haH < aH,the wage
rate paid when the firm knows a
worker really is high-ability.
So high-ability workers have an
incentive to find a credible signal.
Signaling
Workers can acquire,education”.
Education costs a high-ability worker
cH per unit
and costs a low-ability worker cL per
unit.
cL > cH.
Signaling
Suppose that education has no effect
on workers’ productivities; i.e.,the
cost of education is a deadweight
loss.
Signaling
High-ability workers will acquire eH
education units if
(i) wH - wL = aH - aL > cHeH,and
(ii) wH - wL = aH - aL < cLeH.
(i) says acquiring eH units of education
benefits high-ability workers.
(ii) says acquiring eH education units
hurts low-ability workers.
Signaling
HHLH ecaa HLLH ecaaand
together require
.
H
LHH
L
LH
c
aae
c
aa
Acquiring such an education level credibly
signals high-ability,allowing high-ability
workers to separate themselves from
low-ability workers.
Signaling
Q,Given that high-ability workers
acquire eH units of education,how
much education should low-ability
workers acquire?
A,Zero,Low-ability workers will be
paid wL = aL so long as they do not
have eH units of education and they
are still worse off if they do.
Signaling
Signaling can improve information in
the market.
But,total output did not change and
education was costly so signaling
worsened the market’s efficiency.
So improved information need not
improve gains-to-trade.
Signaling or Human Capital? The
Debate
Implications of the two theories are different
H.C,theory,government,by subsidizing
education,provides a way out of poverty.
Signaling,the expenditures do not increase
productivity,Socially wasteful.
In the signaling model,education is still
useful:
sorting workers into the right jobs and
increasing productivity
Education could have positive social rate of
return even if it does not increase a
particular worker’s productivity.
Adverse Selection in Insurance
Bike insurance
Some areas have higher risk of theft
than other areas.
Insurance premium is based on
average risk.
Low risk consumers do not buy.
Only sell insurance at high risk areas at
high rates.
Same with health insurance
Solution in the Insurance Market
Screening for health risks
Family history
Disease history
Mandatory insurance
University students
Work-unit sponsored
Universal coverage
Adverse Selection and Moral Hazard
Adverse selection,hidden
information
Moral hazard,hidden action
Moral Hazard
If you have full bike insurance are you
more likely to leave your bike
unlocked?
Moral hazard is a reaction to incentives
to increase the risk of a loss
and is a consequence of asymmetric
information.
Moral Hazard
If an insurer knows the exact risk
from insuring an individual,then a
contract specific to that person can
be written.
If all people look alike to the insurer,
then one contract will be offered to
all insurees; high-risk and low-risk
types are then pooled,causing low-
risks to subsidize high-risks.
Moral Hazard
Examples of efforts to avoid moral
hazard by using signals are:
higher life and medical insurance
premiums for smokers or heavy
drinkers of alcohol
lower car insurance premiums for
contracts with higher deductibles
or for drivers with histories of safe
driving.
Incentives Contracting
A worker is hired by a principal to do
a task.
Only the worker knows the effort she
exerts (asymmetric information).
The effort exerted affects the
principal’s payoff.
Incentives Contracting
The principal’s problem,design an
incentives contract (激励和约 ) that
induces the worker to exert the
amount of effort that maximizes the
principal’s payoff.
Incentives Contracting
e is the agent’s effort.
Principal’s reward is
An incentive contract is a function
s(y) specifying the worker’s payment
when the principal’s reward is y,The
principal’s profit is thus
)).(()()( efsefysyp
).(efy?
Incentives Contracting
Let be the worker’s (reservation)
utility of not working.
To get the worker’s participation,the
contract must offer the worker a
utility of at least
The worker’s utility cost of an effort
level e is c(e).
u~
.~u
Incentives Contracting
So the principal’s problem is choose e to
))(()(m a x efsefp
subject to,~)())(( uecefs(participationconstraint)
To maximize his profit the principal
designs the contract to provide the
worker with her reservation utility level,
That is,...
Incentives Contracting
the principal’s problem is to
))(()(m a x efsefp
subject to,~)())(( uecefs(participationconstraint)
Incentives Contracting
the principal’s problem is to
subject to (participationconstraint)
Substitute for and solve
))(()(m a x efsefp
.~)())(( uecefs
.~)()(m a x uecefp
))(( efs
Incentives Contracting
the principal’s problem is to
subject to (participationconstraint)
The principal’s profit is maximized when
).()( ecef
))(()(m a x efsefp
.~)())(( uecefs
.~)()(m a x uecefp
Substitute for and solve))(( efs
Incentives Contracting
.*)()( eeecef
The contract that maximizes the
principal’s profit insists upon the
worker effort level e* that equalizes
the worker’s marginal effort cost to
the principal’s marginal payoff from
worker effort.
Incentives Contracting
How can the principal induce the
worker to choose e = e*?
.*)()( eeecef
The contract that maximizes the
principal’s profit insists upon the
worker effort level e* that equalizes
the worker’s marginal effort cost to
the principal’s marginal payoff from
worker effort.
Incentives Contracting
e = e* must be most preferred by the
worker.
Incentives Contracting
e = e* must be most preferred by the
worker.
So the contract s(y) must satisfy the
incentive-compatibility (激励相容 )
constraint;
.0al lf o r),())((*)(*) )(( eecefsecefs
Rental Contracting
Examples of incentives contracts:
(i) Rental contracts,The principal
keeps a lump-sum R for himself and
the worker gets all profit above R; i.e,
Why does this contract maximize the
principal’s profit?
.)())(( Refefs
Rental Contracting
Given the contract
the worker’s payoff is
and to maximize this the worker
should choose the effort level for
which
)()()())(( ecRefecefs
.*,ist h a t);()( eeecef
Refefs )())((
Rental Contracting
How large should be the principal’s
rental fee R?
The principal should extract as much
rent as possible without causing the
worker not to participate,so R
should satisfy
i.e.;~*)(*) )(( uRecefs
.~*)(*) )(( uecefsR
Other Incentives Contracts
(ii) Wages contracts,In a wages
contract the payment to the worker is
w is the wage per unit of effort.
K is a lump-sum payment.
and K makes the worker
just indifferent between participating
and not participating.
.)( Kwees
*)( efw
Other Incentives Contracts
(iii) Take-it-or-leave-it,Choose e = e*
and be paid a lump-sum L,or choose
e? e* and be paid zero.
The worker’s utility from choosing
e? e* is - c(e),so the worker will
choose e = e*.
L is chosen to make the worker
indifferent between participating and
not participating.
Incentives Contracts in General
The common feature of all efficient
incentive contracts is that they make
the worker the full residual claimant
(剩余索取者 ) on profits.
I.e,the last part of profit earned must
accrue entirely to the worker.
