ASYMMETRICINFORMATION
(Varian,Chapter37)
ASYMMETRICINFORMATION
• InpurelycompeBBvemarketsallagentsarefullyinformedabouttradedcommodiBesandotheraspectsofthemarket.
• Whataboutmarketsformedicalservices,orinsurance,orusedcars?– Adoctorknowsmoreaboutmedicalservicesthandoesthebuyer.– Aninsurancebuyerknowsmoreabouthisriskinessthandoestheseller.– Ausedcar’sownerknowsmoreaboutitthandoesapotenBalbuyer.
ASYMMETRICINFORMATION
• Marketswithonesideortheotherimperfectlyinformedaremarketswithimperfectinforma-on.• ImperfectlyinformedmarketswithonesidebeOerinformedthantheotheraremarketswithasymmetricinforma-on.
ASYMMETRICINFORMATION
Applica-onsconsidered:• Adverseselec-onreferstosituaBonswhereonesideofthemarketcan’tobservethetypeorqualityofthegoodsonothersideofthemarket(someBmescalledhiddeninforma-onproblem).
• Signalingconsistsonagentsof“goodquality”takingacBonstosignaltheirtypeanddifferenBatethemselvesfromthe“lowqualityagents”.
ASYMMETRICINFORMATIONApplica-onsconsidered:• MoralhazardreferstosituaBonswhereonesideofthemarketcan’tobservetheacBonsoftheother(hiddenacBonproblem).
• Incen-vecontrac-ngconsistsondesigningincenBvesystemssothattheagentdoesnottakeundesiredacBonsaTercontracBngtakesplace.
SituaBonswithasymmetricinformaBontypicallyresultintoofewtransacBonsbeingmade,sotheequilibriumoutcomeswillalwaysbeinefficientrelaBvetotheequilibriumwithfullinformaBon.
AdverseselecBon• Considerausedcarmarketwithtwotypesofcars,“lemons”and“peaches”:– Lemonsellerswouldaccept$1000,andbuyerswouldpayatmost$1200.
– Peachsellerswouldaccept$2000,andbuyerswouldpayatmost$2400.
• Gains-to-tradearegeneratedwhenbuyersarewellinformed:ifeverybuyercantellapeachfromalemon,thenlemonssellforbetween$1000and$1200,andpeachessellforbetween$2000and$2400.
AdverseselecBon
• Supposenobuyercantellapeachfromalemonbeforebuying;whatisthemostabuyerwillpayforanycar?– LetqbethefracBonofpeachesand1−qthefracBonoflemons.
– Hence,theexpectedvaluetoabuyerofanycarisEV=1200(1−q)+2400q
Lemonmarketexample
• SupposeqissuchthatEV<2000– ApeachsellercannotnegoBateapriceabove$2000andwillexitthemarket.
– Soallbuyersknowthatremainingsellersownlemons.– Buyerspayatmost$1200andonlylemonsaresold.
• Hence“toomany”lemons“crowdout”thepeachesfromthemarketandgains-to-tradearereduced.
• Thepresenceofthelemonsinflictsanexternalcostonbuyersandpeachowners.
Lemonmarketexample
• Howmanylemonscanbeinthemarketwithoutcrowdingoutthepeaches?– Buyerswillpay$2000foracaronlyifqissuchthatEV=1200(1−q)+2400q≥2000
– Soifq<2/3,thenonlylemonsaretraded.
Lemonmarketexample
• Amarketequilibriuminwhichonlyoneofthetwotypesofcarsistraded,orbotharetradedbutcanbedisBnguishedbythebuyers,isasepara-ngequilibrium.
• AmarketequilibriuminwhichbothtypesofcarsaretradedandcannotbedisBnguishedbythebuyersisapoolingequilibrium.
AdverseselecBonwithmorethantwotypes
• Supposethatcarqualityisuniformlydistributedbetween$1000and$2000,andanycarthatasellervaluesat$xisvaluedbyabuyerat$(x+300).
• Whichcarswillbetraded?– Buyer’sexpectedvalueis$1500+$300=$1800.– Sosellerswithcarsabove$1800exitthemarket.– Theexpectedvalueofanyremainingcartoabuyeris$1400+$300=$1700.
– Sonowsellerswithcarsbetween$1700and$1800exitthemarket.
AdverseselecBonwithmorethantwotypes
• Wheredoesthisunravelingofthemarketend?– LetvHbethehighestsellervalueofanycarremaininginthemarket.
– TheexpectedsellervalueofacarisEV=1000+(vH−1000)/2=(1000)/2+(vH/2)
– Soabuyerwillpayatmost(1000/2)+(vH/2)+300– Thismustbethepricewhichthesellerofthehighestvaluecarremaininginthemarketwilljustaccept.
– Hence,(1000/2)+(vH/2)+300=vH⇒vH=1600.– Hence,adverseselecBondrivesoutallcarsvaluedbysellersatmorethan$1600.
AdverseselecBonwithqualitychoice
• Noweachsellercanchoosethequality,orvalue,ofherproduct.
• Example:twoumbrellas,high-qualityandlow-quality(notdisBnguishable).Whichwillbemanufacturedandsold?– Buyersvalueahigh-qualityumbrellaat$14andalow-qualityumbrellaat$8.
– ThemarginalproducBoncostofare$11forhigh-qualityumbrellasand$10forlow-qualityumbrellas.
AdverseselecBonwithqualitychoice
• Supposeeverysellermakesonlyhigh-qualityumbrellas.– Then,everybuyerpays$14andsellers’profitperumbrellais$14-$11=$3.
– Butthenasellercanmakelow-qualityumbrellasforwhichbuyerssBllpay$14,soincreasingprofitto$4.
– Hence,thereisnomarketequilibriuminwhichonlyhigh-qualityumbrellasaretraded.
• Isthereamarketequilibriuminwhichonlylow-qualityumbrellasaretraded?– Ifallsellersmakeonlylow-qualityumbrellas,buyerspayatmost$8foranumbrella,whilemarginalproducBoncostis$10.
– Hence,thereisnomarketequilibriuminwhichonlylow-qualityumbrellasaretraded.
AdverseselecBonwithqualitychoice
• Isthereanequilibriuminwhichbothtypesofumbrellaaremanufactured?– SupposeafracBonqofsellersmakehigh-qualityumbrellas,where0<q<1.
– Buyers’expectedvalueofanumbrellaisthenEV=14q+8(1−q)=8+6q.
– High-qualitymanufacturersmustrecoverthemanufacturingcost,EV=8+6q>11⇒q>1/2.
– Soatleasthalfofthesellersmustmakehigh-qualityumbrellasfortheretobeapoolingmarketequilibrium.
AdverseselecBonwithqualitychoice
– Butthenahigh-qualitysellercanswitchtomakinglow-qualityandincreaseprofitby$1.
– Sinceallsellersreasonthisway,qwillshrinktowardszeroandthenbuyerswillpayonly$8.
– Hence,thereisnoequilibriuminwhichbothumbrellatypesaretraded.
• Themarkethasnoequilibriumwithbothumbrellatypestraded,sothemarkethasnoequilibriumatall.
• Adverseselec-onhasdestroyedtheen-remarket!
Signaling• AdverseselecBonisduetoaninformaBonaldeficiency.• WhatifinformaBoncanbeimprovedbyhigh-qualitysellerssignalingcrediblythattheyarehigh-quality?– Examples:warranBes,professionalcredenBals,referencesfrompreviousclients.
• Example:alabormarketwithtwotypesofworkers,high-abilityandlow-ability.– Ahigh-abilityworker’smarginalproductisaH,andalow-abilityworker’smarginalproductisaL,whereaL<aH.
– AfracBonhofallworkersarehigh-ability,andafracBon1−harelow-abilityworkers.
– Eachworkerispaidhisexpectedmarginalproduct.
Signaling
• Iffirmskneweachworker’stypetheywouldpayeachworkerhermarginalproduct:wH=aH,wL=aL.
• Iffirmscannottellworkers’typestheneveryworkerispaidtheexpectedmarginalproduct:wP=(1−h)aL+haH.
• SincewP=(1−h)aL+haH<aH• High-abilityworkershaveanincenBvetofindacrediblesignal.
EducaBonasacrediblesignal• WorkerscanacquireeducaBon:– SupposeeducaBoncostsahigh-abilityworkercHperunitandcLalow-abilityworker,wherecL>cH.
– SupposealsothateducaBonhasnoeffectonworkers’producBviBes.
• High-abilityworkerswillacquireeHeducaBonunitsif– acquiringeHunitsofeducaBonbenefitshigh-abilityworkers:wH−wL=aH−aL>cHeH,
– andacquiringeHeducaBonunitshurtslow-abilityworkers:wH−wL=aH−aL<cLeH.
EducaBonasacrediblesignal
• Low-abilityworkersdonotacquireanyeducaBon,sincetheywillbepaidwL=aLsolongastheydonothaveeHunitsofeducaBon.
• AcquiringsuchaneducaBonlevelcrediblysignalshigh-ability,allowinghigh-abilityworkerstoseparatethemselvesfromlow-abilityworkers.
• SignalingcanimproveinformaBoninthemarketbutitdoesnotachievetotalefficiencybecauseeducaBonwascostly(totaloutputdidnotchange).
Moralhazard• MoralhazardisareacBontoincenBvestoincreasetheriskofalossandisaconsequenceofasymmetricinformaBon.
• Forexample,ifyouhavebicycle-theTinsurance,areyoulesslikelytolockyourbike?– Ifnoinsuranceisavailable,consumershaveanincenBvetotaketakemaximumpossibleamountofcarebecausebearthefullcost.
– Iftheconsumerhasabicycleinsurance,thecostinflictedtotheconsumerifthebicycleisstolenismuchlower,soshehaslessincenBvestotakecare.
Moralhazard
• Notethetradeoffinvolved:tooliOleinsurancemeansthatpeoplebearalotofrisk;toomuchinsurancemeansthatpeoplewilltakeinadequatecare.
• Iftheamountofcarewasobservable,therewouldbenoproblem.
• Examplesofeffortstosignalcareandavoidmoralhazard:– higherlifeandmedicalinsurancepremiumsforsmokersorheavydrinkersofalcohol
– lowercarinsurancepremiumsforcontractswithhigherdeducBblesordriverswithhistoriesofsafedriving.
IncenBvescontracBng
Example:• Aworkerishiredbyaprincipaltodoatask.• Onlytheworkerknowstheeffortsheexerts(asymmetricinformaBon).
• Theeffortexertedaffectstheprincipal’spayoff.
IncenBvescontracBng
• Theprincipal’sproblem:designanincenBvescontractthatinducestheworkertoexerttheamountofeffortthatmaximizestheprincipal’spayoff.– Letebetheagent’seffort.– Lety=f(e)betheprincipal’sreward.– AnincenBvecontractisafuncBons(y)specifyingtheworker’spaymentwhentheprincipal’srewardisy.
– Theprincipal’sprofitisthusπp=y−s(y)=f(e)−s(f(e))
IncenBvescontracBng
• Togettheworker’sparBcipaBon,thecontractmustoffertheworkerauBlityhigherthanherreservaBonuBlity.
• Letubetheworker’sreservaBonuBlityofnotworking.
• Letc(e)betheworker’suBlitycostofaneffortlevele.
Principal’sopBmalcontract
• Therefore,theprincipal'sproblemisMaxπp=f(e)−s(f(e)) s.t.s(f(e))−c(e)=u(parBcipaBonconstraint)
• Andthecontractthatmaximizestheprincipal’sprofitdeterminesaworkereffortlevele∗thatequalizestheworker’smarginaleffortcosttotheprincipal’smarginalpayofffromworkereffort: fʹ(e∗)=cʹ(e∗)
IncenBvescontracBng
• Howcantheprincipalinducetheworkertochoosee=e∗?– e=e∗mustbemostpreferredbytheworker.– Thecontracts(y)mustsaBsfyanincenBve-compaBbilityconstraint:
s(f(e∗))−c(e∗)≥s(f(e))−c(e)foralle≥0
• ThecommonfeatureofallefficientincenBvecontractsisthattheymaketheworkerthefullresidualclaimantonprofits.i.e.thelastpartofprofitearnedmustaccrueenBrelytotheworker.
ExamplesofincenBvecontracts
Rentalcontracts:• Theprincipalkeepsalump-sumRforhimselfandtheworkergetsallprofitaboveR,s(f(e))=f(e)−R
• Theworker’spayoffiss(f(e))−c(e)=f(e)−R−c(e)sotheworkerchoosese∗s.t.fʹ(e∗)=cʹ(e∗).
• R∗issuchthattheprincipalextractsasmuchrentaspossiblewithoutcausingtheworkernottoparBcipate:f(e∗)−R∗−c(e∗)=u
ExamplesofincenBvecontracts
Variablewagecontracts:• Thepaymenttotheworkeriss(e)=we+K(wisthewageperunitofeffortandKthealump-sumpayment).• Therefore,w=fʹ(e∗)andKmakestheworkerjustindifferentbetweenparBcipaBngandnotparBcipaBng.
ExamplesofincenBvecontracts
Take-it-or-leave-itcontract:• Choosee=e∗andbepaidalump-sumL,orchoosee≠e∗andbepaidzero.
• Theworker’suBlityfromchoosinge≠e∗is−c(e),sotheworkerwillchoosee≠e∗.
• LischosentomaketheworkerindifferentbetweenparBcipaBngandnotparBcipaBng.