委托代理模型与供给诱导需求.docx
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委托代理模型与供给诱导需求.docx
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委托代理模型与供给诱导需求
Principal-AgentModelandSupplierInducedDemand
Introduction
Lasttopicshowedimportanceofinformation–incaseofhealthinformationisnotalwaysperfectorelseitmaybeasymmetric.Owingtolackofinformationagencyproblemsarisewherebybuyers/sellersrelyonotherpartiestomakedecisionsontheirbehalf.
Wehavealreadyencounteredasymmetricinformationincaseofinsurancemarketwhereitledtoproblemofadverseselection–insurancecompaniesdidnotknowwhetherpatientswerehighriskorlowrisk–incertaincasescanleadtomarketfailure.
Hereweconcentrateonagencyissuesandparticularcaseofsupplierinduceddemand.
Firstwebrieflyaskquestion:
whatistheextentofinformationproblemsinhealthsector?
Asymmetryofinformationmayexistbetweenpatientanddoctorandalsobetweeninsurancecompanyandspecialist.
Butmanyitemsofhealthcareexpendituresarecharacterisedbyareasonabledegreeofinformatione.g.regularmedicalcheck-upsorpurchaseofstandardmedications-alsomanymarketsarecharacterisedbylackofperfectinformatione.g.marketsforinsurance,cars,hi-fiequipmentetc.
Alsoifasufficientnumberofwell-informedconsumersexisttheymaybesufficientinnumbertoimposemarketdisciplinee.g.inmarketforpersonalcomputers.
Therearealsomechanismstodealwiththeseproblemstosomedegreee.g.licensure,certification,threatoflegalactionetc.Butalsonotethatinsomecasesthesemayjustbewaysofperpetuatingrestrictivepractices!
Butmaybeproblemwithhealthisthatifmistakesaremadetheymaybeverydifficulttoreverseunlikemistakesmadeinpurchaseofothergoods.
TheAgencyRelationship
Agencyrelationshipisformedwhenaprincipal(e.g.apatient)delegatesdecision-makingauthoritytoanotherpartytheagent(e.g.adoctor).Canalsohave,say,DepartmentofHealthdelegatingdecisionstoindividualGPs.
Motivebehindsuchdelegationisthatprincipalsrecognizetheyarerelativelyuninformedaboutmostappropriatedecisionstobemade–thisissolvedbyuseofaninformedagent.Thusasymmetryofinformationiscentraltoagencyissues.
Otherexamplewouldbeshareholderswhodelegatedecisionsretheircompanytoamanagingdirector.
Welookattwoexamplesofproblemsinagency
(1)problemofahealthauthorityorhealthdepartmentintermsofdecisionsmadebyGPs
(2)problemsindividualpatientshavewithdoctors.
Supposehealthauthoritywishestomaximisenethealthbenefitsofitspopulation–bynetbenefitswemeanvalueofgrosshealthbenefitslesssalariespaidtoGPs.Healthauthoritycanonlyobservegrosshealthbenefitsbutcannotobserveunderlyingcauses.
Weassumethatmonetaryvaluescanbeputonhealthoutcomes(wediscussthislater).
By“stateoftheworld”wemeanrandomfactorswhichwillaffecthealthoutcomesbutwhichareoutofcontrolofGPe.g.geneticcharacteristicsofpatients,weather,otheraspectsofpatientbehaviourwhichGPcannotcontrol.
Weassumethisvariablecantakeoneofthreevalues,low,mediumorhigh(wherehighrepresentscasewherethesefactorsleadtogoodhealthoutcomes).
AlsoassumethatGPcanchoosebetweentwolevelsofeffort,high
(1)orlow(0).Tablebelowshowscombinationsofgrosshealthoutcomes,effortandtheprobabilityofvariousstatesofworld.
StateofWorld
Low
Medium
High
Probability
0.25
0.5
0.25
Effort=0
100
100
400
Effort=1
100
400
400
HealthoutcomesdependuponeffortsofGPandstateofworld,soifoutcomeof100isobservedhealthboarddonotknowifthisisduetobadstateofworldandhigheffortormediumstateofworldandloweffort.
SupposethatGPsutilityisgivenby
whereyisincomeandeiseffort.AlsoassumethatthebesttheGPcandooutsideofmedicineisutilityof10.Thusexpectedutilitymustlieabove10ifGPistostayinmedicine(knownasparticipationconstraint).
Notethatfunctionalformofutilityfunctionimpliesdecliningmarginalutilityofincomei.e.
i.e.MUfallsasyrises–thisimpliesthatGPisriskaverse.
IfGPispaidflatsalary,unrelatedtohealthoutcomes,thennoincentivetoputinanyeffortotherthan0.Thenbestflatsalaryofferedwillbe100,sincethisgivesutilityof10wheneffortis0.
Expectedgrosshealthoutcomesarethen0.25x100+0.5x100+0.25x400=175.Nethealthoutcomesforhealthboardisthen175-100=75.
Healthboardcandobetteriftheyofferbonusforgoodhealthoutcomesi.e.changecontractofGPssoastoimproveperformance.
GPmaybetemptedtoworkharderbuteffortcomesatcostsinceifGPisriskaversehemustbeofferedhigheraveragesalarytocompensateforgreaterrisk.Ifaveragesalarytoohighthenintermsofnethealthoutcomesthisistooexpensive.
AssumebasicsalaryisSandletbonusbeB.Bonusispaidifoutcomeis400ratherthan100.
Ifmanageristoputinhigheffort,thenwemusthave
.Thisisparticipationconstraint.
ContractmustalsobedesignedsothathealthboardgetslevelofeffortitwantsfromGPi.e.itmustbeintheinterestofGPtochoosee=1,comparedtoe=0.Thuswemusthave
i.e.
.
Thisistheincentivecompatibilityconstraint.
BysettingtheseinequalitiesasequalitiessincehealthboardwillwanttokeepSandBaslowaspossibleconsistentwithachievingdesiredoutcomewefindS=64andB=192,givingexpectednethealthoutcomesof117,whichishigherthanthatachievablebyflatsalary.
ThusingeneralitpaystoofferGPsabonussystembasedonoutcome(oranytypeorworkerwherethisagencyrelationshipapplies).
However,applicationofthistypeofarrangementmaybeverydifficultinhealthcare.
Partsofservicemaynotbemeasurable–bytyingrewardstoobservablevariablesthenotherdistortionsmaycomein.
SupposeGPisrewardedonnumberofpatientshe/sheseesi.e.feeperservicetypearrangement.
Problemswiththisare:
GPisbeingrewardedonquantityofmedicalcarebeingprovided(i.e.theinput)ratherthanwhathealthboardisreallyinterestedin:
thehealthofthepopulation(theoutput).
Thisarrangementmayalsogiveincentivesforqualitytobesacrificedforquantityi.e.GPseesmanypatientsbutqualityofcare(unobservabletohealthboard)isreduced.
Finally,suchanarrangementmayalsogiveincentiveforGPtoinducedemandfromhispatientsabovetheamounttheyreallyneed.SincethereisanasymmetryofinformationbetweenGPandpatienttheywillaccepthisadviceanddemandmorecarethantheyneed,thusboostinghissalary.Thisissupplier-induced-demandorSID.
Supplier-Induced-Demand
Thisisthephenomenonwheredoctorsusetheirsuperiorinformationtoinfluencedemandforhealthcareintheirownself-interest.ConditionsforSIDmadepossiblebydoctor’sdualroleasadvisortopatientandproviderofservices.
Inidealworld,doctorsandpatientswouldbeequallywellinformedordoctorswouldalwaysactinthebestinterestsoftheirpatients.
D2*
D2
S2
S1
D1
P2*
P1
P2
P3
O
Q1Q3Q2Q2*
HereS1andD1representinitialsupplyanddemandfordoctorserviceswithequilibriumatP1andQ1.NowsupposesupplyofdoctorsincreasestoS2.IfdemandcurveisunchangedthenweseehigherQandlowerPatQ3,P3.
Totalspendingupondoctorsserviceswillriseorfalldependinguponelasticityofdemand.Ifweassumethatdoctorsservicesareinelasticthentotalspendingfallsandsincemoredoctorsaredividingupasmalleramountofrevenueearningsofeachdoctorwillfall.
IfthephenomenonofSIDholdshowever,riseinSwillbeaccompaniedbyriseinD.Doctorsusetheirinfluencetogenerateanincreaseindemandtooffsettheeffectoftheincreasedsupplyontheirearnings.
IfdemandshiftstoD2,thefurtherincreaseinQandpriceonlyfallstoP2.IfincreaseindemandissufficientlylargethenitcouldgotoD2*withpriceP2*andquantityQ2*.
Thusnewequilibriumfeemaybehigherorlower.Incountrieswherefee-per-serviceisfixed,incentiveforSIDisevenhigher.
Incaseswherefee-per-serviceisnotfixed,thenariseinPisclearevidenceofSID.
However,manystudieswhichclaimtofindSIDinterpretapositivecorrelationbetweendoctoravailabilityandutilisationratesasevidence–butsuchanoutcomeisalsoconsistentwithamodelwherethereisnoSID
ThuscasewheresupplyshiftedtoS2andtherewasnochangeindemandstillledtohigherequilibriumquantity.Thusdistinctionmustbemadebetweenshiftindemandcurve(SID)andmovementsalongademandcurve(notSID).
NotealsothatitispossibletohavesmallshiftinDcurvewithoutSID–ifopportunitycostofpatienttraveltimeissignificantcomponentoftotalcostthenhighernumberofdoctorswillreducethesecostsandmayshiftdemandcurve.
WenowexaminesomepotentialexplanationsforSID.
PriceRigiditiesandSID
Onepossibleexplanationliesinpricerigidities(appliesparticularlyincaseoffixedfee-per-service)–PdoesnotreactquicklytochangesinDandS.SupposefollowingincreaseinSPdoesnotfalltoP3butstaysatP1.AtP1thereisnowanexcesssupplyofdoctors.
Thustoeliminatetheexcesssupplydoctorsinducehigherdemandfrompatients.
Notetheremayalsobecoststoinducement–costsintermsoftime,orpatientswhofeelthatdoctorisnotactinginbestinterestofpatientswhichinturnleadstolossofreputation.
DifficulttoknowexactlyhowfarDcurvecanbeinducedtoshift–dependsuponrelationshipbetweencostsofinducementandincrementalearningsofdoctor.
TargetIncomeModel
Ifdoctorshavea“targetincome”thenanyreductioninpricecausedbyhighersupplyofdoctorswillbeoffsetbyinducingextrademand.
Problemwiththisexplanationisthatitdoes
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