Chapter 3
Topics in Information Economics:
Adverse Selection
1. The adverse selection problem.
2. Akerlof’s application to the second-hand car market.
3. Screening: A price discrimination model.
3.1 Introduction
For a wide range of products (for example, things you buy from a grocery
store or a drug store) the markets are large and decentralized, and the exchanges are anonymous. Usually you do not know who owns the grocery
store when you go in to buy a tube of toothpaste or a zucchini, nor does
the owner bother to keep track of every customer.
There are, however, important exceptions. Consider the market for used
cars. It is difficult to tell how good or bad a used car is unless you use it
for some time. The seller, on the other hand, knows how good the car is.
In such situations, you would care about the identity of the seller. In fact,
in such cases anonymous exchange is often impossible, as that would lead
to a breakdown of the market. The customers are willing to pay a price
based on the average quality. However, this price is not acceptable to the
better than average quality car owner. This leads the owners of better than
average cars to leave the market. But the same phenomenon then applies
to the rest of the market, and so on.
1
The problem is called “lemons problem” or “adverse selection.”
The same problem arises in selling insurance. The insurance company
must know the customer and her past record of illnesses. Anonymous
exchange would, in general, lead to a market price (in this case insurance
premium) that is too high - and only the people who feel that they are very
likely to claim the insurance would buy insurance. This would lead, as in
the case of used cars above, the market to fail.
A different sort of problem arises when you, as the manager of a company,
are trying to hire some salespeople. As the job requires a door to door
sales campaign, you cannot supervise them directly. And if the workers
choose not to work very hard, they can always blame it on the mood of
the customers. If you pay them a market clearing flat wage, they would
(assuming away saintliness) not work hard.
This problem is known as “moral hazard.”
Note the difference between adverse selection and moral hazard. In the
first case, the asymmetry in information exists before you enter into the
exchange (buy used car, sell insurance). In the latter, however, the asymmetry in information arises after the wage contract is signed.
This is why another name for adverse selection is “hidden information”
and another name for moral hazard is “hidden action.”
In the following sections, we will consider certain remedies to adverse
selection and moral hazard. In what follows, attitudes towards risk will
play a role.
First, a fuller description of the lemons problem. This was first noted by
Akerlof (1970). At the time, hardly anyone understood the importance
of his ideas. Five top journals rejected his paper. Today, of course, it is
recognized as a classic. It has spawned a huge literature on information
economics that has significantly advanced our knowledge of economic institutions.
3.2 Akerlof’s Model of the Automobile Market
Suppose there are four kinds of cars — there are new cars and old cars, and
in each of these two categories there may be good cars and bad cars. Buyers of new cars purchase them without knowing whether they are good or
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bad, but believe that with probability x they will get a good car, and with
the residual probability (1 − x ), a bad car.
After using a car for some time the owners can find out whether the car
is good. This leads to an asymmetry: sellers of used cars have more information about the quality of the specific car they offer for sale. But good
cars and bad cars must sell at the same price — since it is impossible for
the buyer to differentiate.
This leads to market failure.
A Generalization to the case with continuous grades of quality Suppose we can index quality by some number q which is uniformly distributed on the interval [0,1]. Hence the average quality of the cars is 1/2.
Suppose that there are a large number of risk neutral buyers who are prepared to pay 3q/2 for a car of quality q, and sellers are prepared to sell a
car of quality q at price q. If quality was observable, any price in this range
would be admissible.
If quality of an individual car cannot be observed by the buyers, they base
their decisions on the expected quality of the cars in the market. If the
expected quality is given by Q, then the buyers would be willing to pay
up to 3Q/2. What is the likely outcome in this market? If the price were
p, all sellers with cars of quality less than p would offer their cars for sale.
Hence, average quality of the cars that appear in the market would be
Q = p/2. But this implies that the reservation price of the buyers would
be 3Q/2 = 3p/4. In other words, there is no price such that the buyers are
prepared to pay the asking price, and the market fails.
Implications This is an instance of market failure owing to adverse selection, and if the welfare gains from trade in the market are sufficiently
great, there is scope for private institutions to evolve to serve as guarantors of quality. Of course, it is costly to set up these institutions, but these
costs may be more than made up by the gains from trade in the relevant
market.
Standard applications of this model include the medical insurance markets (old people cannot buy insurance at any price), credit markets etc. It
is also interesting in this context to think of the specific institutions set up
to counteract these problems.
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3.3 Price Discrimination under Asymmetric information
This section is adapted from Salanie, The Economics of Contracts, MIT
Press, Chapter 2.
3.3.1 The Model
There is a seller and a buyer. The seller sells a unit of quality q at price t.
Cost of producing quality q is c(q), where c′ (q) > 0, and c′′ (q) > 0.
The profit of the seller is given by
π (t, q) = t − c(q)
and the utility of the buyer is given by
u(t, q, θ ) = θq − t.
θ is a parameter that reflects how much the buyer cares about quality. θ
is usually referred to as the buyer’s “type.” This is the buyer’s private
information.
Suppose θ can take two values, θ1 and θ2 , where θ2 > θ1 .
A contract is a pair (q, t) offered by the seller.
The buyer gets 0 utility if he does not buy. Thus any contract must give
the buyer at least 0.
Assume, for simplicity, that the seller has all the bargaining power.
The indifference curve of a buyer of type θi , i ∈ {1, 2} is given by θi q − t =
constant. Thus the slope of the indifference curve is given by
dq = θi .
dt utility constant
Figure 3.1 shows the indifference curves of type θ2 .
Next, an iso-profit curve for the seller is given by t − c(q) = constant. The
slope of the iso-profit curve is given by
dq = c ′ ( q ).
dt profit constant
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θ 2q - t < 0
t
θ 2q - t = 0
t
θ 2q - t > 0
θ 1q - t < 0
θ 1q - t = 0
θ q-t>0
1
q
q
Figure 3.1: Indifference maps of types θ2 and θ1 . The arrows show the direction
of improvement.
Note that all iso-profit curves have the same slope at points along any
vertical line.
t
t
A
B
q
~
q
q
Figure 3.2: Iso-profit map of the seller. The arrow shows the direction of improvement. Iso-profit curves have the same slope at points along any vertical
line. At points A and B the slope of the iso profit curves is c′ (q̃).
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3.3.2 The Full Information Benchmark
Under full information, the seller offers a contract (q1∗ , t1∗ ) to type θ1 and
another contract (q2∗ , t2∗ ) to type θ2 .
To determine the optimal contract for each type θi , i ∈ {1, 2}, the seller
solves
max ti − c(qi ) subject to θi qi − ti ≥ 0.
q i ,ti
However, since the seller has all the bargaining power, there is no reason
to give the buyer any more than 0, and thus the constraint holds with
equality. Thus the seller solves:
max ti − c(qi ) subject to θi qi − ti = 0,
q i ,ti
which can be rewritten as
max θi qi − c(qi ).
qi
Thus qi∗ is such that c′ (qi∗ ) = θi , and ti∗ = θi qi∗ . Figure 3.3 shows the
optimal contracts under full information.
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!h
t
θ2 q - t = 0
t*2
iso-profit
θ1 q - t = 0
t*
1
q*
1
q*
2
q
Figure 3.3: The full information solution. The optimal contract for type θi is obtained at the point of tangency between the iso-profit curve and the indifference
curve of type θi at the reservation utility level (here the reservation utility is 0).
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3.3.3 Contracts Under Asymmetric Information
Under asymmetric information, the full information contracts are not incentive compatible. To see this, note that θ2 q2∗ − t2∗ = 0, but θ2 q1∗ − t1∗ >
θ1 q1∗ − t1∗ = 0. Thus type θ2 prefer contract (q1∗ , t1∗ ) to contract (q2∗ , t2∗ ).
To preserve incentive compatibility, the seller must offer contracts (q̂1 , t̂1 )
and (q̂2 , t̂2 ) such that
θ2 q̂2 − t̂2 ≥ θ2 q̂1 − t̂1 .
Given any (q1 , t1 ), the best that the seller can do is to offer a contract (q2 , t2 )
such that the above is satisfied with equality. In other words, given any
contract (q1 , t1 ), the incentive compatible contract (q2 , t2 ) lies somewhere
on the indifference curve of type θ2 passing through the contract (q1 , t1 ).
The best contract for the seller on this indifference curve is of course the
point at which an iso-profit curve is tangent to the indifference curve.
Since the slope of all indifference curves of type θ2 is θ2 , the tangency occurs exactly at the quantity q2∗ . Thus under asymmetric information, the
optimal contract for type θ2 involves q̂2 = q2∗ . What about t̂2 ? Given any
(q̂1 , t̂1 ), this is determined by the incentive compatibility condition
θ2 q2∗ − t̂2 = θ2 q̂1 − t̂1 .
The remaining problem is to determine the optimal (q̂1 , t̂1 ). We will not
derive this here (for a full derivation, see Salanie, ch 2)- but simply note
the following:
First, there is no reason for the seller to give any surplus to type θ1 . Thus
(q̂1 , t̂1 ) is such that t̂1 = θ1 q̂1 .
Second, it must be that 0 ≤ q̂1 < q1∗ . To see this, note that under full
information, q1∗ is derived by equating marginal revenue (given by θ1 )
to marginal cost (given by c′ (q1 )). Under asymmetric information, the
marginal revenue is the same, but marginal cost is greater than c′ (q1 ).
This is because, for any additional q1 , in addition to the direct production cost there is an indirect cost arising through incentive compatibility.
To maintain incentive compatibility, t2 must be lowered. This is shown in
figure 3.5.
Thus new marginal cost of q1 is equal to c′ (q1 ) + ∆ where ∆ > 0 and
denotes the information cost (revenue lost through lower t2 ). Thus the
optimal choice of q1 must be lower than q1∗ .
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t
θ2 q - t = 0
θ q-t>0
2
θ1 q - t = 0
t
1
q
q
1
Figure 3.4: Given (q1 , t1 ), incentive compatibility requires that (q2 , t2 ) must be
on the dotted indifference curve of type θ2 .
θ 2q-t=0
t
θ 2q-t = K 1>0
a
t2
θ 2q-t = K2 >0
iso-profit
t b2
c
t
2
θ1 q-t=0
0
q1
1
q2
1
q2
q
Figure 3.5: If no other contract is offered, (q2 , t2a ) is incentive compatible (note
that q2 = q2∗ , and t2a = t2∗ ). If a low quality-low price contract is offered so that
q1 = q11 (with corresponding change in t1 to keep the contract on the 0 utility
indifference curve of type θ1 ), to preserve incentive compatibility, (q2 , t2 ) must
lie on θ2 q2 − t2 = K1 . The best such contract for the seller is (q2 , t2b ). Thus t2
is reduced. As q1 increases from q11 to q21 , to preserve incentive compatibility, t2
must be further reduced to t2c . Thus under asymmetric information, there is an
additional indirect marginal cost (or marginal information cost) of increasing q1 .
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Figure 3.6 shows the contracts under asymmetric information.
θ 2q-t=0
t
Information
Rent of type
θ2
t *2
{ ^t
θ 2q-t>0
iso-profit
2
θ1 q-t=0
^
t1
q^1
q*1
^
q*=q
2 2
q
Figure 3.6: Contracts under asymmetric information.
Note that type θ1 gets a 0 utility under both full and asymmetric information. Type θ2 gets a 0 utility under full information, but positive utility
under asymmetric information whenever q̂1 > 0. The information rent of
type θ2 is given by
(θ2 q̂2 − t̂2 ) − (θ2 q2∗ − t2∗ ).
Since q̂2 = q2∗ , the information rent is given simply by
t̂2 − t2∗ .
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Chapter 4
Topics in Information Economics:
Moral Hazard
1. The principal-agent problem, moral hazard.
2. Risk neutral agents.
3. Risk averse agents and agency costs.
4.1 Introduction
Suppose a risk-averse individual has purchased an insurance policy that
promises to compensate her fully in case his bike is stolen. Once insured,
the individual has no incentive to be careful about securing the bike because if it is stolen, the insurance company, and not he, will bear the loss.
(Assume, for the sake of argument, that he does not mind the bother of
reporting the loss to the police, filling claim-forms, etc.). Indeed, if being security-minded causes disutility, he might choose to be downright
careless, and so expose the insurance company to an especially high level
of risk. Of course, the insurance contract may require that he take ‘due
care’ to prevent theft, but then it may be hard to observe carelessness, or
to prove it in a court of law. This phenomenon – that the very act of insurance blunts the incentives of the insured party to be careful, and so
increases the overall risk to the insurer – is described as moral hazard in the
insurance literature.
We know how insurance companies react to this hazard. To preserve the
right incentives, they may provide only partial insurance. This exposes the
11
insured party to at least some residual risk, and thus prompts more careful behavior. This feature of insurance contracts, namely that the risk is
effectively shared between the insurance company and the insured party
is known as co-insurance. Note that the consequence of the moral hazard
problem is to reduce the amount of insurance that is available to individuals.
The moral hazard problem is a direct consequence of an informational
asymmetry: in the example, the true level of care (or effort) is hidden from
the firm. The asymmetry in information here is described as hidden action,
as distinct from that of hidden type.
The issue can be studied more generally as a principal-agent problem. Many
economic transactions have the feature that unobservable actions of one
individual have direct consequences for another, and the affected party
may seek to influence behavior through a contract with the right incentives. In the above example, the insurance company (the principal) is affected by the unobservable carelessness of the insured (the agent): it then
chooses a contract with only partial insurance to preserve the right incentives. Other economic relationships of this type include, shareholders and
managers, manager and salespersons, landlord and tenants, patient and
doctors, etc. We consider the principal-agent problem a bit more generally.
4.2 A formalization
A principal (or just P) hires an agent (A) to carry out a particular project.
Once hired, A chooses an effort level, and his choice affects the outcome
of the project in a probabilistic sense: higher effort leads to a probability of
success, and that translates into higher expected profit for P. If the choice
of effort was observable P could stipulate, as part of the contract, the level
of effort that is optimal for her (that is, for P). When effort cannot be monitored, P may yet be able to induce a desired effort level, by using a wage
contract with the right incentive structure. What should these contracts
look like? The formal structure can be set up as follows:
1. Let e denote the effort exerted by the agent on the project. Assume,
for the moment, that A can either work hard (choose e = e H ) or take
it easy (choose e = e L ); the story can later be generalized for more
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than two, but finite number of, effort choices. The choice of e cannot
be monitored by P: this feature – hidden action – characterizes the
informational asymmetry in the problem.
2. Let the random variable π denote the (observable) profit of the project.
Profit is affected by the effort level chosen, but is not fully determined by it. (If it was fully determined, the principal can infer the
true effort choices by observing the realization of π: we would no
longer be in a situation of hidden actions.) Higher effort leads to
higher profit in a probabilistic sense. Assume that π can take a value
in some finite set, {πi }. Let f (π |e) be the conditional probability of π
under effort e, and F(π |e) be the associated cumulative distribution.
We assume that the distribution of π conditional on e H dominates
(in the first order stochastic sense) the distribution conditional on e L :
we have F(π |e H ) ≤ F(π |e L ), with strict inequality for some π.
3. The principal is risk neutral: she maximizes expected profit net of
any wage payments to the agent.
4. The agent is (weakly) risk-averse in wage-income, and dislikes effort.
His utility function takes the form
u(w, e) = v(w) − g(e),
where w is wage received from the principal, and g(e) is the disutility
of effort. Assume v′ > 0, v′′ ≤ 0, and g(e H ) > g(e L ).
Note the central conflict of interest here. The principal would like the
agent to choose higher effort, since this leads to higher expected profits.
But, other things being the same, the agent prefers low effort. However,
(to anticipate our conclusion), if the compensation w package is carefully
designed, their interests could be more closely aligned. For instance, if
the agent’s compensation increases with profitability (say, by means of
a profit-related bonus), the agent would be tempted to work hard (because high effort will increase the relative likelihood of more profitable
outcomes). However, this will also make the agent’s compensation variable (risky), and that is not so efficient from a risk-sharing perspective. The
inefficiency in risk-sharing will be an unavoidable consequence of asymmetric information.
5. The principal chooses a wage schedule w(π ) that depends on π.
Note this is a (variable) payment schedule rather than a constant
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payment, precisely because the principal may wish to influence the
effort choices of the agent. (More generally, the wage schedule could
condition payments jointly on π and any other observable signal m
that is correlated with the effort choice.
With the right wage schedule, it may be possible to induce a particular
effort choice. To persuade the agent to accept the contract and to induce
e H , for instance, the wage contract must satisfy the following constraints:
• The contract should be acceptable to the agent. Let u0 be the reservation utility (the expected utility the agent gets from alternative occupations). The compensation package should be such that its expected
utility under e H is at least as large as u0 . This is the participation constraint (PC), or the individual rationality constraint.
• The compensation package should be such that the agent prefers to
exert e H rather than any other effort level. In other words, w(π) must
create the right incentives for choosing e H over e L . This is called
the incentive compatibility(IC), or relative incentive constraint. (NB:
If there are K possible effort choices, there would be K − 1 (IC) constraints to satisfy.)
4.3 The principal’s problem
Given the wage schedule w(π ), the principal gets the surplus π − w(π )
for outcome π. Define w(πi ) = wi . So the choice of a wage schedule boils
down to the choice of a set of numbers {wi }, one wi for each πi , in order to
maximize
∑ ( π i − w i ) f ( π i | e ).
i
This expected surplus depends on {wi }, and on the agent’s choice of e. If
effort was observable, it could be stipulated in the contract: the principal
then needs to worry about satisfying only the participation constraint. If
effort is not observable, the agent’s choice of e will depend on the {wi }
offered, and to induce any level of effort, the principal must try to satisfy
both the participation and incentive compatibility constraints. The principal’s problem is solved in two steps.
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Step 1: For each effort level, e H or e L , determine the wage schedule that
would implement that effort level most cheaply. That is, for given e j , minimize ∑i wi f (πi |e j ), subject to the relevant constraints. (If effort is observable, only (PC) is relevant; if not observable both (PC) and (IC) are relevant). Let C(e j ) be the minimized cost of implementing e j . If e j can never
be implemented, define C(e j ) to be infinite.
Step 2: Choose to implement the effort level that yields the highest expected surplus. That is, choose e j , to maximize
∑ π i f ( π i | e j ) − C ( e j ).
i
4.4 Observable effort
Suppose effort is observable. The principal can then implement any level
of effort subject only to the participation constraint. To implement e j , she
must choose {wi } to minimize
∑ w i f ( π i | e j ),
i
subject to
∑ f ( π i | e j ) v ( w i ) − g ( e j ) ≥ u0 .
(PC)
i
Proposition 1. With observable effort, a constant wage level would implement
e j most cheaply.
Having solved the above problem for both e H or e L , she must choose to
implement that level of effort which yields a higher net surplus.
4.5 Unobservable effort
If effort is unobservable, to implement any e j the principal must choose a
wage that satisfies both the participation constrain and incentive compatibility constraint. To implement e j , she must choose w(.) to minimize
∑ w i f ( π i | e j ),
i
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subject to
∑ f ( π i | e j ) v ( w i ) − g ( e j ) ≥ u0 ,
(PC)
i
∑ f ( π i | e j ) v ( w i ) − g ( e j ) ≥ ∑ f ( π i | e k ) v ( w i ) − g ( e k ),
i
i
k 6= j
(IC)
Note: as stated earlier, if there were K possible effort levels, we would
have K − 1 (IC) constraints. We now consider two cases
Case 1: Risk neutral agent
Proposition 2. If the agent is risk neutral, and effort is unobservable, the optimal
contract leads to the same outcome as when effort is observable.
Why? Choose a wage schedule of the form wi = πi − α, where α is
fixed, and so chosen that the participation constraint is just satisfied. This
amounts to selling the project to the agent for a price α: then the agent then
has all the incentive to maximize profits.
Case 2: Risk averse agent
When effort is not observable, and the agent is risk averse, to implement e L
is easy: offer a constant wage that just satisfies the participation constraint.
Given a constant wage, the agent will have no incentive to work hard and
will choose e L .
To implement e H is harder: we demonstrate this with an example.
Example:
Consider the following principal-agent model. A principal hires an agent
to work on a project in return for wage payment w > 0. The agent’s utility
function is separable in the effort and wage received: we have u(w, ei ) =
v(w) − g(ei ), where v(·) is his von-Neumann Morgenstern utility function
for money, and g(ei ) is the disutility associated with effort level ei exerted
on the project.
Assume that the agent can choose one of two possible effort levels, e1 or e2 ,
with associated disutility levels g(e1 ) = 53 , and g(e2 ) = 43 . The value of the
project’s output depends on the agent’s chosen effort level in a probabilistic fashion: If the agent chooses effort level e1 , the project yields output
π H = 10 with probability p( H |e1 ) = 23 , and π L = 0 with the residual
probability. If the agent chooses effort level e2 , the project yields π H = 10
with probability p( H |e2 ) = 13 , and π L = 0 with the residual probability.
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The principal is risk neutral: she aims to maximize the expected value
of the output, net of any wage payments to the agent. The agent is risk1
averse, with v(w) = w 2 , and his reservation utility equals 0.
(a) Suppose, first, that the effort level chosen by the agent is observable
by the principal. A wage contract then specifies an effort level e, and
an output-contingent wage schedule {w H , w L }. Here w H is the wage
paid if π = π H , and w L the wage if π = π L . Show that if effort
is observable, it is optimal for the principal to choose a fixed wage
contract (that is, w H = w L = w). Provide brief intuition for this
result.
(b) If effort is observable, which wage w should the principal offer if she
wants to implement e1 ? Which wage implements e2 ? Which induced
effort level provides a higher expected return to the principal, net of
wage costs?
(c) Suppose, next, that the agent’s choice of effort level is not observable. In this circumstance, a contract consists of an output-contingent
wage schedule {w H , w L }. Which wage schedule will implement e1
in this case? Which expected net return does the principal get in this
case? How does this compare with the value in part (b), where effort
was observable?
(d) If effort is not observable, which contract is best for the principal?
Should she implement e1 or e2 ?
Answer:
(a) Since the agent is risk-averse and the principal is risk-neutral, an optimal risk-sharing result is for the principal to take all risk. If the
agent were to carry unwanted risk, he would have to be given a
higher expected wage than in the optimal case. Since this is not necessary for incentive reasons because effort is observable, the first best
solution is for the principal to take all risk and completely insure the
agent.
The principal’s problem is to minimize the agent’s expected wages.
Suppose the principal offers state dependent wages {w H , w L }. Let pi
denote the probability of π H under effort ei , i ∈ {1, 2}.
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Formally, the principal’s problem when offering state dependent wages
{w H , w L } is, for a particular ei , to
min pi w H + (1 − pi )w L
w H ,w L
s.t.( IRi )
pi v(w H ) + (1 − pi )v(w L ) − g(ei ) = 0.
We solve this using the Lagrangian
L = pi w H + (1 − pi )w L − λ [ pi v(w H ) + (1 − pi )v(w L ) − g(ei )]
which has the foc
∂L
1
= 0 ⇒ = v ′ (w L )
∂w L
λ
and
∂L
1
= 0 ⇒ = v ′ ( w H ).
∂w H
λ
Therefore
1
= v ′ (w H )
λ
′
Since v > 0, this implies that w L = w H = w as required. Further,
given that v is concave, the second order condition for a maximum
is satisfied.
v ′ (w L ) =
(b) Because of (a), we know that in the first best contracts the wage depends on the observable effort ei ∈ {1, 2} and not on the state of the
world j ∈ { L, H }. To implement ei at minimum cost, the principal
simply needs to pay a wage wi to satisfy the participation constraint
for that effort level, given by
v(wi ) − g(ei ) = u0 = 0.
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(4.5.1)
We get
1. (high effort) e1 :
agent’s participation:
principal’s profit:
√
w1 = 53 ⇒ w1 = 25
9,
20
25
35
3 − 9 ⇒ π (e1 ) = 9 .
2. (low effort) e2 :
agent’s participation:
principal’s profit:
√
w2 = 43 ⇒ w2 = 16
9,
10
16
14
3 − 9 ⇒ π (e2 ) = 9 .
Since π (e1 ) > π (e2 ), the principal will implement e1 .
(c) State dependent contracts are {w H , w L }. Implementing e1 at minimum expected wage cost requires minimizing 23 w H + 13 w L subject
to the participation constraint as well as incentive constraint of the
agent. Solving the two constraints completely determine w H and w L ,
so that there is no further minimization to be done.
√
√
( IR1 ) 23 w H + 13 w L − 53 ≥ 0, and
√
√
√
√
( IC1 ) 23 w H + 13 w L − 53 ≥ 13 w H + 23 w L − 43 .
Since there are two variables to be determined, and two inequalities,
it is possible to find w H and w L so that both bind. ( IC1 ) implies
√
√
w H = 1 + w L . We can use this in ( IR1 ) and obtain
2 (1 +
√
wL ) +
√
w L = 5 ⇒ (w L = 1, w H = 4)
with an associated profit of
π (e1 ) =
2
1
11
(10 − 4) + (0 − 1) ⇒ π (e1 ) = .
3
3
3
(d) Implementing e2 : Any flat wage that satisfies the agent’s participation constraint implements e2 . The cheapest way for the principal to
do this is to offer the first best flat wage w1 = 16/9.
As before, π (e2 ) = 14
9 . Since π (e1 ) > π (e2 ), the principal’s optimal
choice under asymmetric information is e1 .
Birkbeck College 2006
MSc Finance
page 19 of 19