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.