Microeconomic
Theory
AndreuMas-Colell MichaelD. Whinston
and
Jeny R. Green
N e wY o rk Oxfor d OXFORD UNIVERSITY PRESS
r995
C
AdverseSelection,
Signaling,
H
A
P
T
E
R
T3
and Screening
13.4 Introduction
One of the impiicit assumptions
ol the fundamentaiwelfaretheoremsis that the
characteristics
of all commodities
areobservable
to all marketparticipants.
Without
thiscondition,distinctmarketscannotexistfor goodshavingdiffering
characteristics,
and so the completemarketsassumption
cannothold.In reality,however,this kind
of informationis often asymmetrically
held by market participants.Considerthe
foliowingthreeexamples:
(i) When a firm hiresa worker,the firm may know lessthan
the worker does
about the worker'sinnateabilitv.
(ii) Whenan automobileinsuranc..orpunyinsuresan individuai,
theindividual
mayknow morethanthecompanyaboutherinherentdrivingskill
and hence
about her probabilityof havingan accident.
(iii) In the used-car
market,theseilerof a car may havemuchbetterinformation
abouther car'squalitythan a prospective
buyerdoes.
A number of questionsimmediatelyarise about thesesettings
of asynmeîic
information:
How do we characterize
rnu.k., equilibriain thepresence
of asymmetric
information?What are the propertiesof theseequilibria?Are therepossibilities
for
welfare-improving
market intervention?
In this chapter,we study thesequestions,
whichhavebeenamongthe most activeareasof research
in microeconomic
theory
duringthe last twentyyears.
We begin,in Section13.8,by introducingasymmetric
informationinro a simple
competitivemarketmodel.We seethat in the presence
of asymmetricinformation,
marketequilibriaoften fail to be Paretooptimal.The tendency
for inefficiencyin
thesesettingscan be strikinglyexacerbated
by the phenomenon
known as ad.uerse
selection.
Adverseselectionariseswhenan informedindividual'strading decisions
dependon her privately held informationin a manner that adversely
affects
uninformedmarketparticipants.
in the used-car
market,for example,an individual
is morelikelyto decideto sellhercar whensheknowsthat it is not
verygood.When
adverseselectionis present,uninformedtraderswill be wary of any
informedtrader
who wishesto tradewith them,and their willingness
to pay for the productoffered
436
.?{F
A r t v
#+
A 9 v c h 5 t s
will be low' Moreover,this fact may evenfurtherexacerbate
the adverseselection
problem:If thepricethat can be received
by sellinga usedcar is verylow, only sellers
with really bad cars will offer them for sale.As a result,we may see
little trade in
marketsin which adverseselectionis present,evenif a greatdeal of
trade would
occurwereinformationsymmetrically
held by all marketparticipants.
We also introduceand study in Sectionl3.B an important
conceptfor the
analysisof marketinterventionin settingsof asymmetric
information:the notion of
a constrained
Paretooptimalallocation.
Theseareallocationsthat cannotbe pareto
improvedupon by a centralauthoritywho,like marketparticipants,
cannotobserve
individuals'privately
heldinformation.A Pareto-improving
marketinterventioncan
be achievedby suchan authorityonly whenthe equilibriumallocationfails
to be a
constrained
Paretooptimum.In general,the centralauthority'sinabilityto
observe
individuals'privatelyheld informationleadsto a more stringenttest
for paretoimprovingmarketintervention.
"'-In Sections'13.Cand'13.D;
we studyhow mark'eibehaviormay adâpi in response
to theseinformationalasymmetries.
In Section13.C,we considerthe possibilitythat
informedindividualsmay find waysto signalinfot'mationabouttheir unobservable
knowledge
throughobservable
actions.For example,
a sellerof a usedcarcouldoffer
to allow a prospective
buyerto takethe car to a mechanic.
Because
sellerswho have
good carsare more likely to be willing to take suchan action,this
offercan serve
as a signalof quality.In Section13.D,we considerthe possibilitythat
uninformed
partiesmay developmechanisms
to distinguish,
or screen,
informedindividualswho
have differinginformation.For exampie,an insurancecompanymay
ot1ertwo
policies:one with no deductibleat a high premiumand another
with a significant
deductibleat a much lower premium. Potentialinsuredsthen sefse lect,
with
high-abilitydriverschoosingthe policy with a deductibleand low-ability
drivers
choosingtheno-deductible
policy.In both sections,
weconsiderthewelfarecharacteristicsof theresultingmarketequilibriaand thepotentialfor Pareto-improving
market
intervention.
For expositional
purposes,
we presentall theanalysisthat followsin termsof the
labormarketexample(i)' we shouldnevertheless
emphasize
thewiderangeof settings
and fieldswithin economics
in which theseissuesarise.Someof theseexamples
are
developed
in the exercises
at the end of the chaoter.
i.B InformationalAsymmetries
and AdverseSelection
Considerthe followingsimplelabor market modeladapredfrom Akerlof's(1970)
pioneeringwork:1 thereare many identicalpotentialfirms that can
hire workers.
Each producesthe same output using an identicalconstantreturns
to scaie
technologyin which labor is the only input. The firms are risk neutral,
seekto
maximizetheir expectedprofits,and act as pricetakers.For simplicity,we
take the
priceof the firms' output to equal 1 (in unitsof a numerairegood).
Workersdifferin the numberof units of output theyproduceif hired by
a firm,
l' Akerlof (1970)usedthe exampreof a used-carmarketin which
only the sellerof a usedcar
knows if the car is a "lemon." For this reason,this type
oi model is sometimesreferredto as a
Iemonsmodel.
L E C T T O N
C H A P T E R 1 4 i
T H E
p R t N C t p A L - A c E N T p R O B L E M
then the managergets exactly the same expectedutility
under w(rc)as under w(n,y)
for any levelof efforthe chooses.
Thus,the manager's
effortchoicewill be unchanged,
and he
will still acceptthe contract.However,because
the managerfaceslessrisk,the expected
wage
paymentsare lower and the owneris betteroff (this
againfollowsfrom Jensen's
inequality:
for all z, u(Elw(n,y)lnl) > Elo(w(n,y))ln), and so w(z)
< Efw(n,y)lzl).
This point can be pushedfurther.Note that we can always
write
(n,
:
yle)
f
fr(nle)fr(yln, e).
rl fz}lz,e) doesnot dependon e, then the
f2(.) termsin condition(14.B.11)
againcancel
out and theoptimalcompensation
package
doesnot dependon y. Thisconditionoi
1rçy1n,e7
is equivalentto the statisticalconceptthat z is a suficient
statisticfory with respectto e. The
converseis also true:As long as n is nota sufticientstatistic
for y, then wagesshouldbe made
to dependon y, at leastto somedegree.
SeeHoimstrom(1979)for furtherdetails.
A numberof extensions
of this basicanalysishavebeenstudiedin the literature.For
example,Hoimsrrom(r9gz), Nalebuffand Stiglitz(19g3),
and Green and Stokey
(1983)examinecasesin whichmanymanagersare
beinghired and considerthe use
of relativeperformance
evaluationin suchsettings;
Bernheimand Whinston(19g6),
on the other hand,extendthe modelin the other direction,
examiningsettingsin
which a single agent is hired simultaneously
by severalprincipals;Dye (19g6)
considers
casesin whicheffortmay be observed
throughcostlymonitoring;Rogerson
(1985a),Allen (1985),and Fudenberg,Holmstrom,
and Milgrom (199b)examine
situationsin which the agencyrelationshipis repeatedover
many periods,with a
particularfocus on the extentto which long-termcontracts
are more effectiveat
resolvingagencyproblemsthan is a sequence
of short-termcontractsof the type we
analyzed
in this section.(Thisiist of extensions
is hardlyexhaustive.)
Many oithese
analysesfocus on the casein which effort is single-dimensional;
Holmstrom and
Milgrom (1991) discusssome interestingaspectsof the
more realisticcase of
multidimensional
effort.
Holmstrom and Miigrom (1987)have pursuedanotherinteresting
extension.
Botheredby the simplicityof real-worldcompensation
schemes
relativeto theoptimal
contractsderivedin modelslike theonewehavestudiedhere,
theyinvestigate
a iodel
in which profits accrueincrementaily
over time and the manageris able to adjust
his effort during the courseof the projectin responseto
eariy profit realizations.
They identifyconditionsunderwhichthe ownercan restrict
himselfwithout lossto
the useof compensationschemes
that arelinearfunctionsof the project'stotal profit.
The optimality of linear compensationschemesarisesbecause
of the need to offer
incentivesthat are "robust" in the sensethat they continue
to provide incentiv.es
regardless
of how earlyprofit reaiizations
turn out. Their analysisillustratesa more
generalidea, namely,that complicatingthe nature
of the incentiveproblem can
actuallylead to simplerformsfor optimalcontracts.For illustrations
of this point,
seeExercises
14.8.5and 14.8.6.
The exercises
at the end of the chapterexploresomeof theseextensions.
l4.c HiddenInformation(andMonopolisticScreening)
In this section,we shift our focus to a setting in which
the postcontractual
informationalasymmetrytakesthe form of hiddeninformation.
S E C T I O N
H l o o E N
T N F O R M A T I O N( A N O
M O N O P O L I S T I C S C R E E N I N G )
Once again,an owner wishesto hire a managerto run a one-timeproject.
What is
effortlevel,denotedby e, is lully observable.
Now,however,the manager's
afterthecontractis signedis therandomrealizationoi the manager's
not observable
the managermaycometo find himselfwellsuited
disutilityfrom effort.For example,
low disutility
to thetasksrequiredat thefrrm,in whichcasehighefforthasa relatively
with it, or the oppositemay be true.However,only the managercomes
associated
to knowwhichcaseobtains.ro
we develophere can also be
we note that the techniques
Beforeproceeding,
by
where,in a settingcharacterized
screening
appliedto modelsof monopolistic
a singleuninformedindividual offers a
p'rrrortrnrtualinformational asymmetries,
m.nu of contractsin order to distinguish,or screen,informedagentswho have
differinginformationat the time ol contracting(seeSection13.Dfor an analysisof
:1'::j
;H*,#iïilî1,îili#,i?,1.T11,ru'.,*:ï::,'n:"':1'-':l::,i'.1:il!,',:,:.'.:"
model,we supposethat
To formulateour hidden informationprincipal-agent
variablee e [0, .o). Gross profits
effort can be measuredby a one-dimensional
function
any wagepaymentsto the manager)are a simpledeterministic
(excluding
of effort,z(e),with z(0):0,n'(e) > 0, and n"(e)< 0 for all e'
The manageris an expectedutility maximizerwhoseBernoulliutility function
overwagesand effort,u(w,e,g),dependson a stateof nature'0that is realizedafter
We assumethat 0 e R,
the contractis signedand that only the managerobserves.
and we focuson a specialform of u(w,e,0)that is widely usedin the literature:Ir
u(w,e,0) = u(w- g(e,0))'
the disutilityof effortin monetaryunits.We assume
The functiong(e,g) measures
g
that
denotepartialderivatives,
that g(0,0) : 0 for all and,lettingsubscripts
g " ( ' , ù { ' ?ff oo rr ee >: 00
L : U
9""(e,0) > 0
for all e
ge@,0) < 0
for all e
fore>0
, ^ . f. 0
o"ele,a)\:g fore:0.
in effort,and this aversionis larger the greater
Thus,the manageris averseto increases
the current ievel of effort. In addition, higher valuesof 0 are more productive states
in the sensethat both the manager's total disutility irom effort, g(e,0), and his
marginal disutiiity from effort at any current effort level,g"(e,0), are lower when 0
10. A seeminglymore importantsourceof hiddeninformationbetweenmanagersand owners
is that the managerof a firm oftencomesto know more aboutthe potentialprofitabilityof various
actionsthan does the owner. In Section 14.D, we discussone hybrid hidden action-hidden
its formalanalysis
informationmodelthat capturesthisalternative
sort of informationalasymmetry;
reduces
to that oi the modelstudiedhere.
utility function.
form for the manager's
ll. Exercise14.C.3asksyou to consideran alternative
4 9 0
c H A p r E R 1 4 : T H E
-
p R t N c t p A L - A G E N Tp R o B L E M
is greater.we also assumethat the manageris strictlyrisk averse,with u"(.) < 0.t,
As in Section14.8,the manager's
reservation
utility level,the levelof expected
utiiity
he must receiveif he is to acceptthe owner'scontractoffer,is denotedby u. Note
that our assumptions
aboutg(e,0) imply that the manager's
indifference
curveshave
the singie-crossing
propertydiscussed
in Section13.C.
Finally,for expositionalpurposes,
we focuson the simplecasein which g can
t a k eo n i y o n e o f t w o v a l u e s0, " a n d 0 r , w i t h 0 r > 0 " a n d P r o b( g r ) : , l e ( 0 , 1 ) .
(Exercise14.C.1asksyou to considerthecaseof an arbitraryfinite numberof states.)
A contractmust try to accomplishtwo objectives
here:frrst,as in Section14.8,
the risk-neutralownershouldinsurethe manageragainstfluctuationsin his income;
second,
althoughthereis no problemherein insuringthat the managerputs in effort
(because
the contractcan explicitlystatethe effort levelrequired),a contractthat
maximizesthe surpiusavailablein the relationship(and hence,the owner'spayoff)
mustmakethe levelof manageriaieffortresponsive
to the disutilityincurredby the
manager,that is, to the state0. To fix ideas,we first iliustratehow thesegoalsare
accomplished
when0 is observable;
we thenturn to an analysisof the problemsthat
arisewhen0 is observedonly by the manager.
The State 0 is Obseruable
If 0 is observable,a contract can directly specifythe effort level and remuneration
of the managercontingenton eachrealizationof 0 (note that thesevariablesfully
determinethe economicoutcomesfor the two parties).Thus,a completeinformation
contract consistsof two wage-effortpairs: (w",err)e R x R* for state 0" and
(*t,er) e R x R* for state0.. The owneroptimallychoosesthesepairsto solvethe
foiiowingproblem:
Max
)"ln(eu)- wrl + (1 - )")ln(e")- wrl
(14.C.1)
w2,e1lO
wg,exlO
s . t . i u ( w u - g ( e n , 0 " ) )+ ( l - ) , ) u ( w 1 -g ( e u 0 ) ) > A .
In any solutionl(*T,eT),(rTr,efr))to problem(14.C.1)the reservation
utility
constraintmust bind; otherwise,the owner could lower the level of wagesoffered
and stiil havethe manageracceptthe contract.In addition,lettingI à 0 denotethe
multiplier on this constraint, the solution must satisfy the following first-order
conditions:
-0.
- )"+ ylu'(wf,- g(efi,0H))
-(1 - 1) + y(r - l)u'(wf - g(eT,0t))- 0 .
<0,
i n ' (e fr)- y i u(w
' fi- g (eh,0r ) ) g"( efi
, 0r ) { - 0
t
(
(r4.c.2)
(14.C.3)
ifefr>0.
<0,
- y(l - 1)u'(wT- s@T,
( 1 - l ) n '(eT)
0r))s"(eT.,
0,-)l
t :0
ifef>0.
(14.C.4)
(14.C.s)
12. As with the caseof hidden actionsstudiedin Section14.8, nonobservaùilitycausesno
welfareloss in the caseof managerialrisk neutrality.As there,a "sellout" contract that facesthe
managerwith the full marginal returnsfrom his actionscan generatethe first-bestoutcome.(See
Exercise14.C.2.)
S E C T I O N
1 4 . C :
H I O D E N
I N F O R M A T I O I I ( A N D
M O N O P O L I S T T C S C R E Ê N t N c )
4 9 1
Theseconditionsindicatehow the two objectives
of insuringthe managerand
and combining
makingeffort sensitiveto the stateare handled.First, rearranging
(14.C.2)
(14.C.3),
and
we seethat
conditions
- g(efi,
u'(wfr
0,)) : u'(wt- g@T.,
0")),
(14.C.6)
so the manager'smarginalutility of incomeis equalizedacrossstates.This is the
individual.
usualconditionfor a risk-neutralparty optimallyinsuringa risk-averse
C o n d i t i o n( 1 4 . C . 6i)m p l i e st h a t w f g ( e f r , ? o ) : w T - g @ T , 0 1 )w, h i c h i n t u r n
i m p l i e st h a t u ( w f - g ( e f i , ? r ) ) = u ( w T . - g ( e T , $ ) ) ; t h a t i s , t h e m a n a g e r u' st i l i t y i s
equalizedacrossstates.Given the reservationutility constraintin (14.C.1),the
managerthereforehasutility levelu in eachstate.
Now considerthe optimaleffort levelsin the two states.Sinceg"(0,0): 0 and
must hold with equalityand ef > 0 for
ft'(O)> 0, conditions(la.C.a)and (14.C.5)
:1,2.
(14.C.2)
Combining condition
with (14.C.4),and condition (14.C.3)with
iF*,, i
(14.C.5),we seethat the optimal level of effort in state9i, ef, satisfies
(14.C.7)
n'(ef) : g"(ef,0)
lor i : L, H.
This conditionsaysthat the optimal levelof effortin state0, equatesthe marginal
beneûtof effort in termsof increasedprofit with its marginaldisutilitycost.
The pair (rI, eI) is illustratedin Figure 14.C.1(note that the wageis depicted
on theverticalaxisand theeffortlevelon thehorizontalaxis).As shown,themanager
is betteroff as we move to the northwest(higherwagesand lesseffort),and the
the managerreceives
Because
owneris betteroff as we movetoward the southeast.
utility levelù in state9,, the owner seeksto find the most profitablepoint on the
state9, indifference
curvewith utility levelri. This is a point ol tangency
manager's
indifference
curveand oneof the owner'sisoprofitcurves.At
betweenthe manager's
profit is
this point, the marginalbenefitto additionaleffort in termsof increased
exactlyequaito the marginalcostborneby the manager.
The owner'sprofitlevelin state0, is flf : n(ei) - u-'(u) - g(ef,0'). As shown
in Figure 14.C.1,this profit is exactlyequalto the distancefrom the origin to the
point at which the owner'sisoprofitcurvethroughpoint (rI, eI) hits the vertical
Figure14.C.1
= 71
{(w,e):u(w- g(e,O,))
The optimal
wage-effort pair for
state 0' lvhen statesare
observable.
\Managrr
Off
Yetter
{(w,e):r(e)-w=IIf}
w!
,
I
u '\u)
- l l - \
Profitsof 0
'.
uwnerln J
State0, I
(nl)
4 9 2
c H A p r E R
1 4 :
p R t N c t p A L - A c E N TP R O B L E M
T H E
u(w-g(e,0))=ù
u(w-gle,0r))=t
z(e)-w=lll
z(e)-w=flf
wl.
wi
u '\u)
- l l - \
I n';{
n;]
t
axis [sincen(0) : 0, if the wagepaymentat this point on the verticalaxis is ]a
< 0,
the owner'sprofit at (wf, ef) is exactiy-f,].
From condition (I4.C.7),we see that g"r(e,0)< 0, rc,,(e)
< 0, and g,"(e,0)> 0
impiy rhatefi > ef. Figure 14.C.2
depicrsthe optimalconrract,l@fr,eîr),(wi,ei)].
Theseobservations
are summanzed
in proposition14.c.1.
P r o p o s i t i o1n4 . C ' 1 :I n t h e p r i n c i p a l - a g em
n to d e lw i t ha n o b s e r v a b l set a t ev a r i a b l e0 ,
theoptimalcontractinvolvesan effortlevele,ïin stateg,suchthatæ,(ef : g
)
"(eî , 0i)
and fully insuresthe manager,settinghis wage in each state g, at the ièvet razî
s u c ht h a t v ( w I - O @ 1 , 0 , 1
: 1s .
Thus,with a strictlyrisk-averse
manager,the first-bestcontractis characterized
by two basicfeatures:
first,the ownerfully insuresthe manageragainstrisk; second,
he requiresthe managerto work to the point at whichthe marginalbenefitof effort
exactlyequalsits marginaicost.Because
the marginalcostof effortis lower in state
0uthan in stategr, the contractcallsfor more effortin statego.
The State 0 is ObseruedOnly by the Manager
As in Section14.8,the desireboth to insurethe risk-averse
managerand to eiicit
the proper levelsof effort comeinto conflictwhen informationalasymmetries
are
present.Suppose,for exampie,that the owner offersa risk-aversemanager
the
contractdepictedin Figure 14.C.2and relieson the managerto revealthe
state
voluntarily.If so,the ownerwill run into problems.As is evidentin the figure,in
state
0o, the managerpreferspoint (wf, ef) to point (wfi,e[). consequently,in state
0,
he will /ie to the owner,claimingthat it is actuallystate0r. As is alsoevidentin
the
figure,this misrepresentation
lowersthe owner'sprofit.
Giventhisproblem,whatis theoptimalcontractfor theownerto offer?To answer
this question,it is necessary
to start by identifyingthe set of possiblecontractsthat
the owner can offer.One can imaginemany differentforms that a contractcould
conceivably
take.For example,the ownermight offera compensation
functionw(z)
that pays the manageras a functionof realizedprofit and that leavesthe effort
Figure 14.C.2
The optimalcontn.
with full obsqvebll,
of 0.
S E C T I O N
HtooEN tNFORMATIoN(ANO MONOPoLlsTlc ScREENING) 493
the ownercouldoffer
Alternatively,
discretion.
in eachstateto the manager's
;u.,,.,
"^-^-nensation
effortchoicesby the manager
w(z) but restrictthe possible
schedule
Bvv"'r
^ rL - ^----^^^-.tl
^ç1^^^-^^-^^ri^
as a
Anotherpossibilityis that the ownercould offercompensation
i^"."r. degree.
with
possibly
again
manager,
effort levelchosenby the
l,i*io" of the observable
arrangements
choices.Finally,more complicated
the
allowable
on
.-or, ,rrrrittion
make an
i'rn, U. imagined.For example,the managermight be requiredto
about what the stateis and then be free to choosehis effort levei
,nioun...n.nt
9.
lunctionw(n| Ô that dependson his announcement
whileiacinga compensation
mayseem
possibilities
Althoughfindingan optimalcontractfrom amongall these
result known as the reuelationprinciplegreatly
n dauntingtask, an important
of contractingproblems:t3
limplifiesthe analysisof thesetypes
14.C.2:(TheRevetationPrinciple)Denotethe set of possiblestatesby @
.- g'eposition
c,o1!fa!!
I"e"igi.-clliTSgl!
lbegwleli3l*yiln9ït,i9:!
lËil;""rchins r9fa1.o9ti1al
form:
!pT='ontracts of the following
{
e hich
( i ) A f t e rt h e s t a t eg i s r e a l i z e dt,h e m a n a g e irs r e q u i r e dt o a n n o u n c w
:
statehas occurred.
(ii) Thecontractspecifiesan outcomelwtù, e(â)ltor eachpossibleannouncem e n t0 e @ .
(iii) ln every state g e @, the managerfinds it optimalto report the state
truthf ullY.
outcomes
thestateI andassociates
A contractthat asksthemanagerto announce
The
mechani.sm.
is known as a reuelation
with the variouspossibleannouncements
a
revelation
using
to
principletellsus that the ownercan restricthimself
revelation
mechanisms
truthfully;revelation
for whichthemanageralwaysresponds
mechanism
(or
with this truthfulnessproperty are known as incentiuecompatible truthful)
The revelationprincipleholds in an extremelywide array
revelationmechanisms.
of incentiveproblems.Aithough we deferits formal (and very generai)proof to
Chapter23 (seeSections23.Cand 23.D),its basicideais relativelystraightforward.
For example,imaginethat the owneris offeringa contractwith a compensation
w(z) that leavesthe choiceof effortup to the manager.Let the resulting
schedule
We cannow showthat
leveisof effortin Statesg, and 0rbe erand es, respectively.
exactlythe sameoutcomeas
that generates
thereis a truthful revelationmechanism
that
that theownerusesa revelationmechanism
thiscontract.In particular,suppose
that the stateis 9, and
assignsoutcomelw(n(e1)),ey)tf.the managerannounces
that the stateis 0o. Considerthe
outcome[w(z(es)),e)if the managerannounces
Suppose,
mechanism.
for truth tellingwhenlacingthisrevelation
manager's
incentives
w(z),
schedule
firsr rharrhestateis 9,. Underthe initial contractwith compensation
outcomelw(n(es)),es)in state0r by choosing
the managercould haveachieved
effort level es. Sincehe insteadchosee', it must be that in state 91 outcome
Thus.
lw(n(e)),er] is at leastas good for the manageras outcome[w(z(er)),e11].
the managerwill find tellingthe truth to
underthe proposedrevelationmechanism,
whenthe stateis 9.. A similarargumentappiieslor state0"'
be an optimalresponse
resultsin truthful announcements
We seethereforethat this revelationmechanism
(1979)and Dasgupta,
13. Two early discussionsof the revelationprinciple are Myerson
Hammond,and Maskin (1979).
4 9 4
c H A p r E R 1 4 :
T H E
p R t N c t p A L - A c E N Tp R o B L E M
by the managerand yieldsexactlythe sameoutcomeas the initial
contract.In fact,
a similar argumentcan be constructedlor any initial contract(see
Chapter 23),
and so the owner can restrict his attention without loss to
truthful revelation
Io
mechanisms.
To simplify the characterization
of the optimal contract,we restrict attention
from this point on to a specificand extremecaseof managerial
risk aversion:infnite
risk aversion.In particular,we take the expected
utility of the managerto equalthe
manager's
lowestutility levelacrossthe two states.Thus,for the manager
to accept
the owner'scontract,it must be that the managerreceives
a utility of at leastu in
eachstate'15As above,efficientrisk sharingrequiresthat an
infinitely risk-averse
managerhavea utility levelequalto u in eachstate.If, for example,
his utility is ,
in onestateand u' > û in the other,thenthe owner'sexpected
wagepaymentis larger
than necessary
for givingthe manageran expected
utility of ù.
Giventhis assumptionaboutmanagerial
risk preferences,
the revelationprincipie
allowsus to write the owner,sproblemas foliows:
Max
w H , e H> O , w L , e L > Q
)"ln(er) - wul + (1 - À)ln(e")_ wt)
s.t. (i) ,r - g@1,0) > ,-t(t)]
(ii) w, - g(eu,g") > u-rfu))
( 14.c.8)
reseruationutility
(or indiuidualr arionality)
constraint
atibitit
v
(iii)w" - g(en, 0n) 2 w, - s(er, 0,)
\'ër"i::i:r-i"rirp
(iv) w. - g(eu 0r) > w, - g(er, g))
or self-s.election)
constramts.
The pairs (wo,eu) and (w",er) that the contractspecifies
are now the wage and
effortleveisthat resultfrom differe
nl announcemefis
or the stateby the manager;that
is, the outcomeif the managerannounces
that the stateis g, is (*,,e,). constraints
(i) and (ii) make up the reseruationutility (or indiuidualrationality)
constrainrfor the
infinitelyrisk-averse
manager;if he is to acceptthe contract,he must be guaranteed
a utility of at least n in eachstate.Hence,we must have u(w,_
g(ei,g,))> u for
i : L , r l o r , e q u i v a l e n t lw
! , i - g k i , 0 ) > n - ' ( u ) f o r i : z , Ë 1 .c o n s t r a i n t s( i i i )
and
(iv) are the incentiuecompatibility(or truth-tellingor self-selection)
constrajnrsfor the
managerin states0u andgr, respectively.
consider,for example,constraint(iii). The
14' one restrictionthat we haveimposedherefor expositionalpurposes
is to lirnit the outcomes
specifiedfollowing the manager'sannouncementto being
nonstochastic(in fact, much of the
literaturedoesso as well). Randomizationcan sometimes
be desirablein thesesettingsbecauseit
can aid in satisfyingthe incentivecompatibilityconstraints
that we introducein problem (14.C.g).
SeeMaskin and Riley (198aa)for an example.
15' This can be thought of as the limiting casein which,
starting from the concaveutilrty
function u(x), we take the concavetransformationur(u): -u(x)o
îor p <0 as the manager,s
Bernoulliutility functionand let p - - a. To seethis,notethat
the manager'sexpectedutility over the
random outcomegiving (wn - g@a,0n))with probabilityÀ
and,(w,I S@r,d.)) with probability
(1 - l') is then EU = -Uufr + (t - zi)ufll,where
u,: u(wr- gk,,O.S1fori: Z, 11.ff,L expected
u t i l i t y i s c o r r e c t l y o r d e br eyd( n g y r r o : l h u f i + ( 1 - S , 1 u g 1 t r o . N o w a s - _ * , L À u f r + ( L _
) . ) u f l t r ci
Min {un, ur} (seeExercise3.C.6).Hence,â contractgivesthe manager
an expectedutility greater
t h a n h i s ( c e r t a i n r) e s e r v a t i o u
ntilityif and only ii Min
{u(w,_ S@r,0)),u(wr_ g(et,0r)t} >ù.
( A N D M O N O P O L t s T I cS c R E E N I N G ) 4 9 5
s E C T t o N 1 4 . C : H T O O E NT N F O R M A T T O N
f"j,
S.
S'
Ïi
1',
I
:
in state gr is u(wr - g(es,oH) if he tells the truth, but it is
*anager'sutility
Thus,he will tell the truth if
;;: " -1 s@r,g')) if he insteadclaimsrhat it is state0r.
g ( e u g " ) . C o n s t r a i n(ti v ) f o l l o w ss i m i l a r l y '
:"n o k , , 0 r ) 2 w r contractdepictedin Figure14.C.2does
NJù inui ,tt. first-best(full observability)
it violatesconstraint(iii).
not sarisfythe constraintsof problem(14.C.8)because
""'W.
o[lemmas.Our argumentsfor
aÂalyreproblem(14.C.8)througha sequence
useof graphicalanalysisto build intuition.An analysis
th.r. resultsmakeextensive
in AppendixB.
conditionsis presented
oirnt, problemusingKuhn-Tucker
is a solutionto
1 4 . C . 1 :W e c a n i g n o r e c o n s t r a i n t ( i i ) . T h a t i s , a . c o n t r a c t
L
ue
" "m
' oi rl ao 6 ' " r
(14.C'8)
( 1 4 . C . 8i)f a n d o n l y i f i t i s t h e s o l u t i o nt o t h e p r o b l e md e r i v e df r o m
c o n s t r a i n(ti i ) .
dropPing
''' -' '
F.Frtr*
Proof, Whenever both constraints
fl' ula (iii)
"are
tAtn.jd'it mustbe that
>- u- 1(u),and so constraint(ii) is
w 1' 1 g ( e n , 0 r )> w t g ( e u 0 r ) 2 w t g(eu0r)
This impliesthat the set ol feasiblecontractsin the problem derived
alsosatisfied.
(ii)
sameas the set of feasible
from (14.C.8)by droppingconstraint is exactlythe
in Problem(1a.C.8)'r
contracts
By constraint(i), (wr,e.) must lie
Lemma14.C.1is illustratedin Figure 14.C.3.
(iii), (w", e") must lie on or
in the shadedregion oi the figure.But by constraint
point (wr, e1)' As can be seen,
;i abovethe state 0r, indifferencecurve through
stateg" utility is at leastù, the utility he getsat point
,r, thisimpliesthat the manager's
i(t),
0).
(*, e) : (ui'
from this point on we can ignoreconstraint(ii).
Therefore,
tl.rr"
) u s t h a v ew 2 - g @ L , 0 1 ) :
1 4 . c . 2A
: n o p t i m a tc o n t r a c itn p r o b l e m( 1 4 . c . 8m
v tut.
i'i'
"'',
-
1 ?
- \
not, that is, that thereis an optimalsolutionl(*",er),(w",et)] in
Proof:Suppose
contract
whichw. - g(et,0r)> r- 1(ù).Now, consideran alterationto the owner'S
u(w-s(e,0))=a
u ( w- g ( e ,ù0) = û
u ( w- g ( e , 0 n )=) u n > û
u '(u)
("r, er)
Figure 14.C.3
Constraint(ii) in
is
problem(1a.C.8)
satisfiedby any
contractsatisfying
(i) and (iii).
constraints
496
cHAprER
u(w-
.l
T H E
P R I N C I P A L . A G E N TP R O B L E M
=
s(e,0,.))
( w u ,e n )
u(w-g(e,0r))=u
s k ' 0 B Du
=n )ù
u '(ù)
State0"
Indifference
çuçveThrough
({,,,1,
$t, êt)
Isoprofit
Curves
(fru êt)
u-tQ)
in which the owner pays wagesin the two statesof û,1: wr-
E and lô,n: wH _ E,
wheree > 0 (i.e.,the owneriowersthe wagepaymentsin both statesby e).This new
contractstill satisfies
constraint(i) as long as e is chosensmallenough.In addition,
the incentivecompatibilityconstraintsare still satisfiedbecausethis changejust
subtractsa constant,e, from eachsideof theseconstraints.
But if this new contract
satisfies
all theconstraints,
the originalcontractcouldnot havebeenoptimalbecause
the ownernow has higherprofits,whichis a contradiction.r
L e m m a1 4 . C . 3 I: n a n y o p t i m a lc o n t r a c t :
( i ) e r < e I ; t h a t i s , t h e m a n a g e r ' se f f o r tl e v e li n s t a t eg . i s n o m o r et h a nt h e
l e v e lt h a t w o u l d a r i s e i f 0 w e r e o b s e r v a b l e .
(ii) er: eâ; that is, the manager'seffortrevelin stateg, is exacilyequatto
t h e l e v e lt h a t w o u l da r i s ei { 6 w e r e o b s e r v a b l e .
Proof: Lemma 14.c.3can bestbe seengraphically.By Lemma 14.c.2,(w.,e.) iies
on the locus {(w,e): u(w- g(e,7r)): ù} in any optimal contracr.Figure 14.C.4
depictsonepossiblepair (frr, êr).In addition,the truth-tellingconstraints
imply that
the outcomefor state0r, (*r,e"), must lie in the shadedregionof Figure 14.C.4.
To seethis, note that by constraint(iv), (w", e") must lie on or belowthe stateg,
indifferencecurvethrough (ûr, êr). in addition,by constraint(iii), (*r, er) must lie
on or abovethe state0" indifference
curvethrough(frr,ê,.).
To seepart (i),supposethat wehavea contractwith ê" > ef. Figure14.C.5depicts
sucha contractoffer:(r0r,êr) lieson the manager'sstatef. indifference
curvewith
utility level r7,and (w", er) lies in the shadedregion detned by the rruth-telling
constraints.
The state0" indifference
curvefor the managerand the isoprofitcurve
for the owner which go through point (rôr,êr) havethe relationdepictedat point
(ôu ê) because
êr > eT.
As can be seenin the figure,the ownercan raisehis profit levelin stateg, by
moving the state0. wage-effortpair down the manager'sindifference
curvefrom
(fruê) to its first-bestpoint (wf,ei). This changecontinuesro satisfyall the
constraints
in problem(1a.C.8):
The manager's
utility in.eachstateis unchanged,
Figure 14.C.4(tett)
In a feasiblecontract
offering (vn", ê,) îor
state 0., the pair
( w r , e r ) m u s tl i ei n
the shadedregion.
Figure14.C.5(righl)
An optimal contracl
has e, < ef.
u(w- 9(e,0r.))= ri
u ( w- s ( e , 0 ) ) :a
u ( w- g ( e , 0 " ) )= u ( r ô-, g ( ê t ,0r ) )
r(e)-w=f1,,
(frt,êt)
(wi,ei)
u(w-g(e,0n))=un>ù
(mo'ei)
Isoprofit
Curves
i*", efi)
u '(u)
éL YL
6 State6
S t a t el g , I
oH i prontl
Profit
I
Thus, Figure14.C.6(left)
arestillsatisfied.
thetruth-tellingconstraints
and,asis evidentin Figure14.C.5,
An optimal contract
a contractwith ê1> el cannotbe optimal.
has e, : g;.
(
such
ef,
êr
Now considerpart (ii). Given any wage-effortpair (frr,ê") with
asthat shownin Figurel4.C.6,theowner'sproblemis to find thelocationfor (wr' e")
gH.The solutionoccursat a Figure14.C.7(right)
in the shadedregionthat maximizeshis profit in state
best contract with
curvethroughpoint The
point of tangencybetweenthe manager'sstate9s indifference
e- : Pt
(fr,, êr) and an isoprofitcurvelor the owner.This tangencyoccursat point (frs, eT,)
involveseffort levelef becauseall points of tangency
in the figure,and necessarily
betweenthe manager'sstateg, indifferencecurvesand the owner'sisoprofit curves
by condition(14'C'7)for j: H]'
occur at effort level ef [they are characterized
Note that this point of tangencyoccursstrictly to the right of effort ievelé" because
êr<eT<efr..
A secondarypoint emergingfrom the proof of Lemma 14'C.3is that only the
truth-tellingconstraintfor stateg" is bindingin the optimalcontract.This property
in the literature.l6
is commonto many of the other applications
In any optimal contract,eL<eti that is, the effort level in state
Lemma 14.C.42
g. is necessarilystrictlybelow the level that would arise in state 01 if 0 were
observable.
Proof: Again,this point can be seengraphically.Supposewe start with (w7,et):
thestateott outcome,
thisdetermines
By Lemma14.C.3,
(r'T.,ef),asin Figure 14.C.7.
denotedby (vi", ef) in the figure.Note that by thedefinitiono[(wf, ef), the isoprofit
curve.
state0" indifference
curvethroughthis point is tangentto the manager's
Recallthat the absolutedistancebetweenthe origin and the point whereeach
the profit the ownerearnsin
state'sisoprofitcurvehits the verticalaxis represents
that state.The owner'soverallexpectedprofit with this contractoffer is therefore
the incentive
16. In modelswith more than two types,this proPertytakesthe form that only
(See
Exercise
l4'C'l')
direction'
one
in
so
only
do
they
and
bind,
constraintsbetweenadjacenttypes
498
cHAprER
T H E
P R I N C I P A L . A G E N TP R O B L E M
u(w-g(e,?nD=un>u
Isoprofit
Curves
u(w-g(e,0))=u
B'
}J
1 w ie. i )
State
0,,
indiffercnce
u ( w - g ( e , 0 r ) ) = r i Curves
(rl, ei)
@i,ê')
(fruê)
$,n, eï)
(wa,etr)
(il,",ef )
u -' ( t )
ProfitLoss
in State0r{-
u-'(t)
êL ei
êL ei
(b)
Figure14.c.8 (a) The changein profits in state 0, from lowering e, siightly below ef . (b) The changein profitsin llllt
from lowering e, slightly below ef and optimally adjusting w".
equal to the averageof thesetwo profit levels(with weightsequai to the relative
probabilitiesof the two states).
We now arguethat a changein the state0, outcomethat lowersthis state'seffort
levelto one slightlybeiow ef necessarily
raisesthe owner'sexpectedprofit. To see
this,startby movingthe state0, outcometo a slightlylowerpoint,(frt,êr), on the
manager's
state9r indifference
curve.Thischangeis illustratedin Figure14.C.8,
along
with the owner'sisoprofit curve through this new point. As is evidentin Figure
14.C.8(a),
this changelowersthe profit that the ownerearnsin state0r. However,it
also relaxesthe incentiveconstrainton the stategn outcomeand, by doing so, it
allowsthe ownerto offera lowerwagein that state.Figure14.C.8(b)
showsthe new
state0r, outcome,say (rô", efi), and the new (higher-proût)isoprofit curve through
this point.
Overall,this changeresuitsin a lowerprofit for the ownerin stateAranda higher
profit for the owner in state0". Note, however,that because
we startedat a point
of tangencyat (wf, ef), the profit lossin state0. is smallrelativeto the gain in state
0". Indeed,if we wereto look at the derivativeof the owner'sprofit in state0r with
respectto an infnitesimalchangein that state'soutcome,we would find that it is
zero.In contrast,the derivativeof profit in state0, with respectto this infinitesimal
changewould be strictly positive.The zero derivativein state 9, is an envelope
theoremresult:becausewe startedout at the first-bestlevelof effort in state0., a
smallchangein (wr, e") that keepsthemanager's
state0r utility at ù hasno first-order
effecton the owner'sprofit in that state;but because
it relaxesthe state0" incentive
constraint,for a small-enough
changethe owner'sexpected
profit is increased.r
How far shouldthe ownergo in loweringe'!In answering
thisquestion,the owner
must weighthe marginallossin profit in state0, againstthe marginalgain in state
0r [note that oncewe moveawayfrom (*T'et), the enveloperesultno longerholds
and the marginalreductionin stategr's profit is strictlypositive].It shouldnot be
surprisingthat the extentto which the ownerwantsto make this trade-offdepends
on the relativeprobabilitiesoi the two states.In particular,the greaterthelikelihood
of state0", the more the owneris willing to distortthe state0, outcometo increase
profit in stategH.In the extremecasein which the probabilityof state0, getsclose
tozero,the ownermay setêr:0 and hire themanagerto work only in state0o.r7
The analysisin Appendix B confirmsthis intuition.There we show that the
the followingfirst-ordercondition:
optimallevelof e. satisfies
1
l n ' ( e ) - Q " ( e t , 0 " ) f+
*lg"(er,0*)
- Q " ( e t , g r ) l: 0 .
(14.c.9)
is zerodt er: ef andis strictlypositiveat e"< ef;
The first term of this expression
the secondterm is alwaysstrictly negative.Thus,we must haveer<eT. to satisfy
Differentiatinsthisexpression
thiscondition,confirmingour frndingin Lemma14.C.4.
âr'idnt'às'
Ïiir :îj'tilbiir'f 1'r \ n":'
fréîr"rr trràiitreciptimàirÈvèi'àr
Thesefindingsare summarizedin Proposition 14.C.3,
p r o p o s i t i o1n4 . C . 3 I: n t h e h i d d e ni n f o r m a t i opnr i n c i p a l - a g em
n to d e lw i t h a n i n f i n i t e l y
managerthe optimalcontractsetsthe levelof effortin stategs at its
risk-averse
first-best(full observability)level e[. The effort level in state 01 is distorted
d o w n w a r df r o m i t s f i r s t - b e s lte v e l e f . I n a d d i t i o nt,h e m a n a g e ri s i n e f f i c i e n t l y
insured,receivinga utilitygreaterthan 17in state?raand a utilityequalto u in
state0.. The owner'sexpectedpayoffis strictlylower than the expectedpayoff
h e r e c e i v e sw h e n I i s o b s e r v a b l ew
manager's
, h i l e t h e i n f i n i t e l yr i s k - a v e r s e
expected
u t i l i t yi s t h e s a m ea s w h e n0 i s o b s e r v a b l (ei t e q u a l sù ) . t 8 ' t e
point that emerges
A basic,and verygeneral,
from this analysisis that theoptimal
contractfor the ownerin this settingof hiddeninformationnecessarily
distorrsthe
effort choice of the managerin order to amelioratethe costs of asymmetric
information,which heretakethe form of the higherexpectedwagepaymentthat the
ownermakesbecausethe managerhasa utility in state0" in excess
of u.
Note that nothingwould changeif the profit levelz werenot publiclyobservable
(andso could not be contractedon), sinceour analysisreliedonly on the fact that
the effort levele was observable.
Moreover,in the casein which n is not publicly
observable,
we can extendthe model to allow the relationshipbetweenprofitsand
effortto dependon the state;that is, the owner'sprofitsin states0rand 0u given
effort level e might be given by the functionsn"(e) and nr(e).to As long as
17. In fact,this can happenonly if 9"(0,0r) > 0.
18. Recall that an infinitely risk-aversemanager'sexpectedutility is equal to his lowest utility
level acrossthe two states.
19. Note, however,that while the outcomehere is Pareto inefficient,it is a constrainedPareto
optimum in the senseintroducedin Section13.8; the reasonsparallel those given in footnote
9 oiSection14.Bfor the hiddenactionmodel(althoughhereit is 0 that the authoritycannotobserve
rather than e).
20. The nonobservability of profits is important for this extension becauseif z could be
contractedupon,the managercould be punishedfor misrepresenting
the stateby simplycomparing
the realizedprofit level with the profit level that should have beenrealizedin the announcedstate
ior the specifiedlevel of effort.
C H A P T E R 1 4 :
T H E
P R t N C t P A L - A G E N TP R O B L E M
n'n(e)> n'r(e)> 0 for all e ) 0, the analysisof this modelfollowsexactlyalongthe
linesof the analysiswe havejust conducted(seeExercise14.C.5).
As in the caseof hiddenaction models,a number of extensionsof this basic
hiddeninformationmodei have beenexpioredin the literature.Someof the most
generaltreatmentsappearin the context of the "mechanismdesign" literature
associated
with socialchoicetheory.A discussion
of thesemodelscan be found in
Chapter23.
The Monopolistic ScreeningModel
In Section13.D,we studieda modelof competitiue
in which firms try to designtheir
screening
employmentcontractsin a manner that distinguishes
among workers who, at the time of
contracting,havedifferentunobservable
productivitylevels(i.e.,thereis precontractualasymmetricinformation).The techniques
that we havedeveloped
in our studyof the principal-agent
model with hidden informationenableus to formuiateand solve a model of monopolistic
sueeningin which, in contrastwith the anaiysisin Section13.D, only a singlefirm offers
employmentcontracts(actually,this might more properlybe calleda monopsonisric
screening
model becausethe singiefrrm is on the demandsideof the market).
To seethis,supposethat,as in the modelin Section13.D,thereare two possibletypesof
- SQ,0)
workerswho differin theirproductivity.A workerof type0 hasutility u(w,tl0):,
when he receivesa wage of w and lacestask levei r. His reservationutility level is u. The
productivities
of the two typesof workersare 0, and 0r, with 0" > 0L> 0. The fractionof
workersof type 0, is Àe(0,1).We assumethat the firm's profits,which are not publicly
observable,
are given by the function nr(t) îor a type 0, worker and by zr(r) for a type 0,
worker,and that n'n(t)> nL\)> 0 for all r > 0 [e.g.,as in Exercise13.D.1,we could have
n,(t) : 0,(l - pt) for p > 0f."
The firm's problem is to offer a set of contractsthat maximizesits profits given worker
self-selection
among,and behaviorwithin, its offeredcontracts.Once again, the revelation
principlecan be invokedto greatlysimplifythe firm's problem.Here the firm can restrictits
attentionto offeringa menuof wage-taskpairs[(wo, tu),(wu rr)] to solve
),lnr(tr) - wxf + (1 - À)lnr(t") - w")
Max
wr,tt
à 0, wz,tsl
(i4.c.10)
O
s.t. (i) ,, - g(tr,?r) > u
.
( i i ) w n - Q ( t n , 0 u )> ,
( i i i ) w " - g ( ta , 0r ) > * , - g ( tL , 0H )
( i v )w , - g ( t u 0 r ) . 2 w o - g ( t o , 0 " ) .
This problem has exactly the same structure as (14.C.8)but with the principal's (here the
firm's) profit being a function of the state.As noted above,the analysisof this problem follows
exactly the same lines as our analysisof problem (14.C.8).
This class of models has seen wide application in the literature (although often with a
continuum of types assumed).Maskin and Riley (1984b),for example,apply this modelto the
study of monopolistic price discrimination.In their model, a consumer of type 0 has utility
u(x,0) - I when he consumesx units of a monopolist'sgood and makes a total payment of
?"to the monopolist, and cân earn a reservationutility level of u(0,0) : 0 by not purchasing
from the monopolist. The monopolist has a constant unit cost of production equal to c > 0
21. The model studiedin Section13.D with zi(f) = 0, correspondsto the limiting casewhere
r-0.
o n o
H I o D E N I N F o R M A T I o T { :
H Y E R I D MoDELS
S01
and seeksto offera menuoi (x,,
d) pairsto maximizeits profit.The monopolist,s
problem
::i"il;:T::::
'" (r4'c'r0)
where
wetaker,= xi, lvi= -i,' û=0,
s(t,,01)=-.u(xi,0;),
Baronand Myerson's(1982)analysis
of optimalregulation
of a monopolist
with unknown
costsprovidesanotherexample.There,
a regulatedfirm facesmarket demand
functionx(p)
and hasunobservable
unit costsof 0. The regulator,who
seeksto designa regulatory
poricy
that maximizes
consumersurplus,facesthe monopolist
with a ch, .
(p,,T)'where
p,is theanowed
retairpriceand isa transfe,
{
o"rJ:::;ïliJ;:ïff:tï
the firm' The regulatedfirm is able to
shut down if it cannotearnprofits
of at leastzerofrom
any of the regulator'sofferings'The
regulator's
problemth.n .o...spondsto (r4.c.10)
with
ti : Pi, wi = T, û : 0, g(:ti,0,) = -(p,_
0,)r(p,),and r,(r,) = g "1r; ar.r,
l4'c'7 to l4'c'9 ask
fou to'stuay some.-"*piË! "r monoporistic
screening
,noj.lrttttttt
) HiddenActionsand HiddenInformation:
Hybrid Models
Althoughthe hiddenaction-hidden
informationdichotomization
servesas a usefur
startingpoint for understanding
principal-agent
models,-uny real-worldsituations
(and someof the literatureas weil)
invorveerements
of both probiems.
To consideran exampleof such
a moder,supposethat we augmentthe
simple
hidden information model considered
in Section14.c in the followingmanner:
iet the levelof effort e now be unobservable,
and tet profits be a stochastic
function
of effort, describedby conditional
densityfunction f(nle).In essence,
what we
now have is a hidden action model,
but one in which the owner arsodoes
not
know somethingabout the disutility
of the manager(whichis capturedin
the
state
variable0).
Formal anarysisof this moderis
beyondthe scopeof this chaprer,but
the basic
thrust of the reverationprincipre
extendsto the anarysisor ,h.r. types
of hybrid
problems'In particurar:as
Myerson (i9g2) shows,ih. o*rr., can
now restrict
attentionto contractsof the following
form:
(i) After thestateg is reaiized,
themanagerannounces
whichstatehasoccurred.
(ii) The contractspecifies,
for eachpossibreannouncement
d e €l, the effortlever
e(Ô ttrat the managershourdtake
and a compensation
schemew@l$.
(iii) In everystateg, the manager
is willing to be both truthfurin stage(i)
and
obedient
followingstage(ii) [i.e.,he findsit optimal
to chooseeffortievele(g)
i n s t a t e0 1 .
This contractcan be thoughtof
as a revelationgame,but one in which
the outcome
of the manager'sannouncement
about the staù is a hidden action-style
contract,
that is, a compensation
schemeand a "recommended
action."The requirementof
"obedience"
amountsto an incentiveconstraint
that is like that in the hiddenaction
22. The regulator's objective
function can be generarizedto allow
a weighted averageof
ionsumerand producersurplus,
with greaterweighton .onrurn.rr.
In this case,the functionz,(.)
",rilldependon 0,.
tt