asymmetric information snyder and nicholson, copyright ©2008 by thomson south-western. all rights...
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Asymmetric Information
Snyder and Nicholson, Copyright ©2008 by Thomson South-Western. All rights reserved.
Asymmetric Information• Transactions can involve a considerable
amount of uncertainty– can lead to inefficiency when one side has
better information
• The side with better information is said to have private information or asymmetric information
The Value of Contracts• Contractual provisions can be added in
order to circumvent some of the inefficiencies associated with asymmetric information– rarely do they eliminate them
Principal-Agent Model• The party who proposes the contract is
called the principal
• The party who decides whether or not to accept the contract and then performs under the terms of the contract is the agent– typically the party with asymmetric
information
Leading Models• Two models of asymmetric information
– the agent’s actions affect the principal, but the principal does not observe the actions directly
• called a hidden-action model or a moral hazard model
– the agent has private information before signing the contract (his type)
• called a hidden-type model or an adverse selection model
First, Second, and Third Best• In a full-information environment, the
principal could propose a contract that maximizes joint surplus– could capture all of the surplus for himself,
leaving the agent just enough to make him indifferent between agreeing to the contract or not
• This is called a first-best contract
First, Second, and Third Best• The contract that maximizes the
principal’s surplus subject to the constraint that he is less well informed than the agent is called a second-best contract
• Adding further constraints leads to the third best, fourth best, etc.
Hidden Actions• The principal would like the agent to take
an action that maximizes their joint surplus
• But, the agent’s actions may be unobservable to the principal– the agent will prefer to shirk
• Contracts can mitigate shirking by tying compensation to observable outcomes
Hidden Actions• Often, the principal is more concerned
with outcomes than actions anyway– may as well condition the contract on
outcomes
Hidden Actions• The problem is that the outcome may
depend in part on random factors outside of the agent’s control– tying the agent’s compensation to
outcomes exposes the agent to risk– if the agent is risk averse, he may require
the payment of a risk premium before he will accept the contract
Owner-Manager Relationship• Suppose a firm has one representative
owner and one manager– the owner offers a contract to the manager– the manager decides whether to accept the
contract and what action e 0 to take• an increase in e increases the firm’s gross
profit but is personally costly to the manager
Owner-Manager Relationship• The firm’s gross profit is
g = e + – where represents demand, cost, and
other economic factors outside of the agent’s control
• assume ~ (0,2)
– c(e) is the manager’s personal disutility from effort
• assume c’(e) > 0 and c’’(e) < 0
Owner-Manager Relationship• If s is the manager’s salary, the firm’s
net profit isn = n – s
• The risk-neutral owner wishes to maximize the expected value of profit
E(n) = E(e + – s) = e – E(s)
Owner-Manager Relationship• We will assume the manager is risk
averse with a constant risk aversion parameter of A > 0
• The manager’s expected utility will be
ecsA
sEuE Var2
First-Best• With full information, it is relatively easy
to design an optimal salary contract– the owner can pay the manager a salary if
he exerts a first-best level of effort and nothing otherwise
– for the manager to accept the contract
E(u) = s* - c(e*) 0
First-Best• The owner will pay the lowest salary
possible [s* = c(e*)]
• The owner’s net profit will be
E(n) = e* - E(s*) = e* - c(e*)
– at the optimum, the marginal cost of effort equals the marginal benefit
Second Best• If the owner cannot observe effort, the
contract cannot be conditioned on e– the owner may still induce effort if some of
the manager’s salary depends on gross profit
– suppose the owner offers a salary such as
s(g) = a + bg
– a is the fixed salary and b is the power of the incentive scheme
Second Best• This relationship can be viewed as a
three-stage game– owner sets the salary (choosing a and b)– the manager decides whether or not to
accept the contract– the manager decides how much effort to
put forth (conditional on accepting the contract)
Second Best• Because the owner cannot observe e
directly and the manager is risk-averse, the second-best effort will be less than the first-best effort– the risk premium adds to the owner’s cost
of inducing effort
First- versus Second-Best Effort
ee**
MB1
e*
MC in first bestc’(e)
The owner’s MC is higher in the second best, leading to lower effort by the manager
MC in second bestc’(e) + risk term
Moral Hazard in Insurance• If a person is fully insured, he will have
a reduced incentive to undertake precautions– may increase the likelihood of a loss
occurring
Moral Hazard in Insurance• The effect of insurance coverage on an
individual’s precautions, which may change the likelihood or size of losses, is known as moral hazard
Mathematical Model• Suppose a risk-averse individual faces
the possibility of a loss (l) that will reduce his initial wealth (W0)
– the probability of loss is – an individual can reduce this probability by
spending more on preventive measures (e)
Mathematical Model• An insurance company offers a contract
involving a payment of x to the individual if a loss occurs– the premium is p
• If the individual takes the coverage, his expected utility is
E[u(W)] = (1-)u(W0-e-p) + ()u(W0-e-p-l+x)
First-Best Insurance Contract
• In the first-best case, the insurance company can perfectly monitor e– should set the terms to maximize its expected
profit subject to the participation constraint• the expected utility with insurance must be at least
as large as the utility without the insurance
– will result in full insurance with x = l– the individual will choose the socially efficient
level of precaution
Second-Best Insurance Contract
• Assume the insurance company cannot monitor e at all– an incentive compatibility constraint must be
added
• The second-best contract will typically not involve full insurance– exposing the individual to some risk induces
him to take some precaution
Hidden Types• In the hidden-type model, the individual
has private information about an innate characteristic he cannot choose– the agent’s private information at the time
of signing the contract puts him in a better position
Hidden Types• The principal will try to extract as much
surplus as possible from agents through clever contract design– include options targeted to every agent
type
Nonlinear Pricing• Consider a monopolist who sells to a
consumer with private information about his own valuation for the good
• The monopolist offers a nonlinear price schedule– menu of different-sized bundles at different
prices– larger bundles sell for lower per-unit price
Mathematical Model• Suppose a single consumer obtains surplus
from consuming a bundle of q units for which he pays a total tariff of T
u = v(q) – T– assume that v’(q) > 0 and v’’(q) < 0– the consumer’s type is
H is the “high” type (with probability of )
L is the “low” type (with probability of 1-)
• 0 < L < H
Mathematical Model• Suppose the monopolist has a constant
average and marginal cost of c
• The monopolist’s profit from selling q units is
= T – cq
First-Best Nonlinear Pricing• In the first-best case, the monopolist
observes • At the optimum
v’(q) = c– the marginal social benefit of increased
quantity is equal to the marginal social cost
First-Best Nonlinear Pricing
q
T
U0L
This graph shows the consumers’ indifference curves (by type) and the firm’s isoprofit curves
U0H
First-Best Nonlinear Pricing
q
T
A
U0L
A is the first-best contract offered to the “high” type and B is the first-best offer to the “low” type
U0H
B
Second-Best Nonlinear Pricing• Suppose the monopolist cannot observe
– knows the distribution
• Choosing A is no longer incentive compatible for the high type– the monopolist must reduce the high-type’s
tariff
Second-Best Nonlinear Pricing
q
T
A
U0L
The “high” type can reach a higher indifference curve by choosing B
U0H
B
U2H
To keep him from choosing B, the monopolist must reduce the “high” type’s tariff by offering a point like C
C
Second-Best Nonlinear Pricing
q
T
A
U0L
The monopolist can also alter the “low” type’s bundle to make it less attractive to the high type
U0H
B
U2H
C
D
E
q**Hq**L
Monopoly Coffee Shop• The college has a single coffee shop
– faces a marginal cost of 5 cents per ounce
• The representative customer faces an equal probability of being one of two types– a coffee hound (H = 20)
– a regular Joe (L = 15)
• Assume v(q) = 2q0.5
First Best• Substituting such that marginal cost =
marginal benefit, we get
q = (/c)2
q*L = 9 q*H = 16
T*L = 90 T*H = 160
E() = 62.5
Incentive Compatibility when Types Are Hidden
• The first-best pricing scheme is not incentive compatible if the monopolist cannot observe type– keeping the cup sizes the same, the price
for the large cup would have to be reduced by 30 cents
– the shop’s expected profit falls to 47.5
Second Best
• The shop can do better by reducing the size of the small cup
• The size that is second best would be
LqL-0.5 = c + (H - L)qL
-0.5
q**L = 4
T**L = 60
E() = 50
Adverse Selection in Insurance• Adverse selection is a problem facing
insurers where the risky types are more likely to accept an insurance policy and are more expensive to serve– assume policy holders may be one of two
typesH = high risk
L = low risk
First Best• The insurer can observe the individual’s
risk type
• First best involves full insurance– different premiums are charged to each
type to extract all surplus
First Best
certainty line
W1
W2
U0L
Without insurance each type finds himself at E
U0H
A
B
E
A and B represent full insurance
Second Best• If the insurer cannot observe type, first-
best contracts will not be incentive compatible– if the insurer offered A and B, the high-risk
type would choose B– the insurer must change the coverage
offered to low-risk individuals to make it unattractive to high-risk individuals
First Best
certainty line
W1
W2
U0L
U0H
A
B
E
U1H
The high-risk type is fully insured, but his premium is higher (than it would be at B)
C
The low-risk type is only partially insured
D
Market Signaling• If the informed player moves first, he
can “signal” his type to the other party– the low-risk individual would benefit from
providing his type to insurers• he should be willing to pay the difference
between his equilibrium and his first-best surplus to issue such a signal
Market for Lemons• Sellers of used cars have more
information on the condition of the car– but the act of offering the car for sale can
serve as a signal of car quality• it must be below some threshold that would
have induced the owner to keep it
Market for Lemons• Suppose there is a continuum of
qualities from low-quality lemons to high-quality gems– only the owner knows a car’s type
• Because buyers cannot determine the quality, all used cars sell for the same price– function of average car quality
Market for Lemons• A car’s owner will choose to keep a car
that is in the upper end of the spectrum– reduces the average quality– reduces the market price– leads sellers of the high end of the
remaining cars to keep their cars• reduces average quality and market price
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.
.32
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 SelectionThe expected value of anycar to a buyer is $1500 + $300 = $1800.
1000 20001500Seller values
So sellers who value their cars atmore than $1800 exit the market.
Adverse Selection
1000 18001400
The expected value of anyremaining car to a buyer is $1400 + $300 = $1700.
So now sellers who value their carsbetween $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 is121000
12
vH .
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.
121000
12
300 vH .
121000
12
300 v vH H .
Adverse Selection
121000
12
300 v vH H
vH $1600.
Adverse selection drives out all carsvalued by sellers at more than $1600.
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.
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.
• 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.• 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.
SignalingHHLH ecaa HLLH ecaa and
together require
.H
LHH
L
LH
caa
ecaa
Acquiring such an education level crediblysignals high-ability, allowing high-abilityworkers to separate themselves fromlow-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.
Auctions• A seller can often do better if several
buyers compete against each other– high-value consumers are pushed to bid
high
• Different formats may lead to different outcomes– sellers should think carefully about how to
design the auction
First-Price Sealed Auction Bid• All bidders simultaneously submit secret
bids
• The auctioneer unseals the bids and awards the object to the highest bidder
• The highest bidder pays his own bid
First-Price Sealed Auction Bid• In equilibrium, it is a weakly dominated
strategy to submit a bid b greater than or equal to the buyer’s valuation v– a strategy is weakly dominated if there is
another strategy that does at least as well against all rivals’ strategies and strictly better against at least one
First-Price Sealed Auction Bid• A buyer receives no surplus if he bids
b=v no matter what his rivals bid– by bidding b < v, there is a chance for
some positive surplus
• Since players likely avoid weakly dominated strategies, we can expect bids to be lower then buyers’ valuations
Second-Price Sealed Auction Bid• The highest bidder pays the next
highest bid rather than his own
• All bidding strategies are weakly dominated by the strategy of bidding exactly one’s valuation– second-price auctions induce bidders to
reveal their valuations
Second-Price Sealed Auction Bid• The reason that bidding one’s valuation
is weakly dominant is that the winner’s bid does not affect the amount he has to pay– that depends on someone else’s bid
Common Values Auctions• In complicated economic environments,
different auction formats do not necessarily yield the same revenue
• Suppose the good has the same value to all bidders, but they do ot know exactly what that value is– common values auction
Common Values Auctions• The winning bidder realizes that every
other bidder probably though the object was worth less– means that he probably overestimated the
value when bidding
• This is often referred to as the winner’s curse
Important Points to Note:• Asymmetric information is often studied
using a principal-agent model in which a principal offers a contract to an agent who has private information– the two main variants of the model are the
models of hidden actions and hidden types
Important Points to Note:• In a hidden-action model (called a moral
hazard model), the principal tries to induce the agent to take appropriate actions by tying the agent’s payments to observable outcomes– doing so exposes the agent to random
fluctuations, which is costly for a risk-averse agent
Important Points to Note:• In a hidden-type model (called an
adverse selection model), the principal cannot extract all of the surplus from high types because they can always gain positive surplus by pretending to be a low type– the principal will offer a menu of contracts
from which different types of agents can select
Important Points to Note:• In a hidden-type model, the principal will
offer a menu of contracts from which different types of agents can select– the principal distorts the quantity offered to
low types in order to make the contract less attractive to high types
Important Points to Note:• Most of the insights gained from the
basic form of a principal-agent model, in which the principal is a monopolist, carry over to the case of competing principals– the main change is that agents obtain more
surplus
Important Points to Note:• The lemons problem arises when
sellers have private information about the quality of their goods– sellers whose goods are higher than
average quality may refrain from selling– the market may collapse, with goods of
only the lowest quality being offered for sale
Important Points to Note:
• The principal can extract more surplus from agents if several of them are pitted against one another in an auction setting– in a simple economic environment, a variety of
common auction formats generate the same revenue
– differences in auction format may generate different levels of revenue in more complicated settings