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Microeconomic Theory - Brousseau

Microeconomic Theory AndreuMas-Colell MichaelD. Whinston and Jeny R. Green N e wY o rk Oxfor d OXFORD UNIVERSITY PRESS r995. C H A P T E R. AdverseSelection, Signaling, T3. and Screening Introduction One of the impiicit assumptionsol the fundamentaiwelfaretheoremsis that the characteristics of all commodities areobservable to all marketparticipants. Without thiscondition,distinctmarketscannotexist for goodshavingdiffering characteristics, and so the completemarketsassumption reality,however,this kind of informationis often asymmetricallyheld by market foliowingthreeexamples: (i) When a firm hiresa worker,the firm may know lessthan the worker does about the worker'sinnateabilitv. (ii) Whenan individuai, theindividual mayknow morethanthecompanyaboutherinherentdrivin gskill and hence about her probabilityof havingan accident. (iii) In the used-car market,theseilerof a car may havemuchbetterinformation abouther car'squalitythan a prospective buyerdoes.

Microeconomic Theory Andreu Mas-Colell Michael D. Whinston and Jeny R. Green New York Oxford OXFORD UNIVERSITY PRESS r995

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Transcription of Microeconomic Theory - Brousseau

1 Microeconomic Theory AndreuMas-Colell MichaelD. Whinston and Jeny R. Green N e wY o rk Oxfor d OXFORD UNIVERSITY PRESS r995. C H A P T E R. AdverseSelection, Signaling, T3. and Screening Introduction One of the impiicit assumptionsol the fundamentaiwelfaretheoremsis that the characteristics of all commodities areobservable to all marketparticipants. Without thiscondition,distinctmarketscannotexist for goodshavingdiffering characteristics, and so the completemarketsassumption reality,however,this kind of informationis often asymmetricallyheld by market foliowingthreeexamples: (i) When a firm hiresa worker,the firm may know lessthan the worker does about the worker'sinnateabilitv. (ii) Whenan individuai, theindividual mayknow morethanthecompanyaboutherinherentdrivin gskill and hence about her probabilityof havingan accident. (iii) In the used-car market,theseilerof a car may havemuchbetterinformation abouther car'squalitythan a prospective buyerdoes.

2 A number of questionsimmediatelyarise about thesesettings of asynme ic information: How do we characterize , equilibriain thepresence of asymmetric information?What are the propertiesof theseequilibria?Are therepossibilities .?{F. for welfare-improvingmarket intervention? In this chapter,we study thesequestions, whichhavebeenamongthe most activeareasof research in Microeconomic Theory duringthe last twentyyears. We begin,in ,by introducingasymmetric informationinro a simple seethat in the presence of asymmetricinformation, marketequilibriaoften fail to be tendency for inefficiencyin thesesettingscan be strikinglyexacerbated by the phenomenon known as 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 adverseselectionis present,uninformedtraderswill be wary of any informedtrader who wishesto tradewith them,and their willingness to pay for the productoffered 436.}

3 A r t v A 9 v c h 5 t s L E C T T O N. 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 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 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 Pareto-improving marketinterventioncan be achievedby suchan authorityonly whenthe equilibriumallocationfails to be a constrained general,the centralauthority'sinabilityto observe individuals'privatelyheld informationleadsto a more stringenttest for pareto- improvingmarketintervention.

4 #+ "'-In Sections' ' ; we studyhow mark'eibehaviormay ad pi in response to theseinformationalasymmetries. In ,we considerthe possibilitythat informedindividualsmay find waysto signalinfot'mationabouttheir unobservable knowledge throughobservable 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 ,we considerthe possibilitythat uninformed partiesmay developmechanisms to distinguish, or screen, informedindividualswho have 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 both sections, weconsiderthewelfarecharacter- isticsof theresultingmarketequilibriaand thepotentialfor Pareto-improving market intervention.

5 For expositional purposes, we presentall theanalysisthat followsin termsof the labormarketexample(i)' we shouldnevertheless emphasize thewiderangeof settings and fieldswithin economics in which theseexamples are developed in the exercisesat the end of the chaoter. 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 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.

6 " For this reason,this type oi model is sometimesreferredto as a Iemonsmodel. 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 ,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 that we can always write f (n, yle) : fr(nle)fr(yln, e). rl fz}lz,e) doesnot dependon e, then the f2(.) termsin condition( ) againcancel out and theoptimalcompensation package doesnot dependon y. Thisconditionoi is equivalentto the statisticalconceptthat z is a suficient 1r y1n,e7. 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.

7 SeeHoimstrom(1979)for furtherdetails. A numberof extensions of this basicanalysishavebeenstudiedin the 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.)

8 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 regardless of how earlyprofit reaiizations turn out.

9 Their analysisillustratesa more generalidea, namely,that complicatingthe nature of the incentiveproblem can actuallylead to simplerformsfor illustrations of this point, seeExercises The exercises at the end of the chapterexploresomeof theseextensions. HiddenInformation(andMonopolisticScreeni ng). 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 not observable afterthecontractis signedis therandomrealizationoi the manager's disutilityfrom example, the managermaycometo find himselfwellsuited low disutility to thetasksrequiredat thefrrm,in whichcasehighefforthasa relatively associated with it, or the oppositemay be ,only the managercomes to Beforeproceeding, we note that the techniques we develophere can also be screeningwhere,in a settingcharacterized by appliedto modelsof monopolistic p'rrrortrnrtualinformational asymmetries, a singleuninformedindividual offers a of contractsin order to distinguish,or screen,informedagentswho have differinginformationat the time ol contracting( an analysisof :1'::j ;H*,#i il 1, ili#,i?)

10 , ,ru'.,*: ::,'n:"':1'-':l::,i'.1:il!,',:,:.'.:". model,we supposethat To formulateour hidden informationprincipal-agent effort can be measuredby a one-dimensional variablee e [0, .o). Gross profits (excluding any wagepaymentsto the manager)are a simpledeterministic function 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 the contractis signedand that only the managerobserves. We assumethat 0 e R, 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 functiong(e,g) measures the disutilityof effortin assume g that g(0,0) : 0 for all and,lettingsubscripts that denotepartialderivatives, g " ( ' , { ' ?ff oo rr ee >: 00. L : U. 9""(e,0) > 0 for all e ge@,0) < 0 for all e , ^ . f. 0 fore>0. o"ele,a)\:g fore:0.]}


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