GeneralEquilibriumpricetaking1(伦敦经济学院高级.pptx

GeneralEquilibriumpricetaking1(伦敦经济学院高级.pptx

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Microeconomics,GeneralEquilibrium:

pricetaking,ExcessDemand,Decentralis-ationandTrade,Amany-personeconomy,RobinsonCrusoesProblem,ExcessDemand,Decentralis-ationandTrade,RobinsonCrusoesProblem,GeneralEquilibrium,Whyprice-taking?

Amany-personeconomy,Overview.,Sofarwevefocusedoncompetitiveequilibriumanalysis.Butwhy?

Whyconcentrateonequilibrium?

Whyassumecompetitivebehaviour?

Letsstartbyhavinganotherlookattheexchangeeconomy.WellredrawtheEdgeworthbox,Somepuzzlesincompetitiveequilibriumanalysis,Generalequilibrium,RobinsonCrusoesproblem,Decentrali-sationandTrade,Amany-personEconomy,Whyprice-taking?

Excessdemand,Thesolutionconcept,PricesandtheCore,Thesolutionconcept,Anexchangeeconomy,PricesandtheCore,Whyprice-taking?

WhatwouldIdooutofequilibrium?

Andwhatwouldhedo?

Letslookattheinnerworkings.,BuildinganEdgeworthbox,x1a,R1a,R2a,x2a,Oa,ThesituationfromAlfspointofview,HowAlfrespondsasp1/p2changes.,x1a,R1a,R2a,x2a,Oa,Alfsoffercurve,WhataboutBill?

x1b,R1b,R2b,x2b,Ob,Thesituationfromhispointofview,.asanAustralian,x1b,R1b,R2b,x2b,Ob,HowBillrespondsasp1/p2changes.,x1b,R1b,R2b,x2b,Ob,Billsoffercurve,Thetwooffercurves,1,x2b,Ob,x1a,x2a,Oa,x1b,R1b,R1a,R2a,R2b,Offersareonlyconsistentwherecurvesintersect,But,byconstruction.,Thisisthecompetitiveequilibrium,Satisfiesmaterialsbalance,E,D,equilibriumhere,endowmenthere,Price-takingutility-maximisingBill,endowmenthere,equilibriumhere,Price-takingutility-maximisingAlf,Butwhycompetitivebehaviour?

WhyshouldAlfandBillbehavethatway?

Wheredothepricescomefrom?

Givencompetitivebehaviour,theCEistheonlyconsistentallocation,subjectto,hh,SpixiM,i=1,U（x）,max,nhh,SpixiM,Sowheredothepricescomefrom?

WeneedamoregeneralsolutionconceptThenexaminehowprice-takingequilibriumrelatestothis.Letsdeveloptheapproachfortheexchangeeconomy,thoughitcouldapplytomoreinterestingeconomies.,Afreshapproach,Generalequilibrium,RobinsonCrusoesproblem,Decentrali-sationandTrade,Amany-personEconomy,Whyprice-taking?

Excessdemand,Thesolutionconcept,PricesandtheCore,Anexchangeeconomy,PricesandtheCore,Anexchangeeconomy,Whyprice-taking?

Viewthepopulation.,.asnseparateindividuals,Acoalition.,Thecoalitionconceptgivesusanimportantclue.,.isformedbyanysubgroup,wevegotourendowmentswithus,Onedayyoutakeyourbundlealongtotheswapshop.andsomebossypersonistherewhoproposes（insistson?

）aparticularfeasibleallocation.Youandsomeothersdontlikethexbundleyouwouldgetunderthisallocation.andyoufindthatbyusingjusttheresourcesyouallownyoucouldallgetautilitylevelatleastashighasthatofferedtoyouundertheproposedallocation.Youguysthereforerefusetoacceptit.,yourcoalitionhasblockedtheproposedallocation,Theideaofblocking:

alittlestory,Anallocationisblocked.,.whichcandobetterforitself,ifwecanfindacoalition.,Aproposedallocationforthewholeeconomy,.andthatarefeasible,Q1,2,.,nh,hQ,forsomeh,Acoalition,Bundlesthatarepreferredbymembersofthecoalition.,Aformalapproach,TheCore,isthesetofunblocked,feasibleallocations,Usetheideaofblockingtointroduceabasicsolutionconcept,Alf&Bill,Alf,Bill,Ina2-personworldthereareveryfewcoalitionspossible,UsetheEdgeworthbox.,x2b,Ob,x1a,x2a,Oa,x1b,.togetthecontractcurve,Alfblockstheseallocations.,D,Billblockstheseallocations.,Alf,Bill（together）blockthese.,Endowment,No-onecanblockanallocationhere,The2-personcore,Generalequilibrium,RobinsonCrusoesproblem,Decentrali-sationandTrade,Amany-personEconomy,Whyprice-taking?

Excessdemand,Thesolutionconcept,PricesandtheCore,Anexchangeeconomy,Thesolutionconcept,Anexchangeeconomy,Whyprice-taking?

x2b,Ob,x1a,x2a,Oa,x1b,D,E,Thecompetitiveequilibriumagain,x2b,Ob,x1a,x2a,Oa,x1b,D,E,Anycompetitiveequilibriummustlieinthecore,EveryCEallocationmustbelongtothecoreOfcourseitispossiblethatnoCEexists（seenextlecture）ButwhatofothercoreallocationswhicharenotCE?

Letstakeaclose-uplook,Asimpleresult,D,Theextremesofthe2-personcore,Core,CE,IntroducingAlfandBillslong-losttwinbrothers.,Rememberwearedealingwitha2-personmodel,Butwilltherealwaysbenon-CEpointsinthecore?

Abasicrelation.,AlfandhistwinbrotherArthurhavethesamepreferencesandendowmentsLikewisethetwinsBillandBenNowofcoursetherearemorepossibilitiesofformingcoalitions,Soletsclonetheeconomy,Arthur&Ben,Arthur,Ben,Alf&Arthur,etc,etc,Bill&Ben,Alf,Arthur&Bill,.plussomenewones,Alltheoldcoalitionsarepossible.,Willthesestillbecoreallocationsinthe4-personeconomy?

B,A,AlfnArthurBillnBen,AlfnArthurBillnBen,D,Alf,Arthur,Ben,Bill,G,.leavingtheBentwinoutsidethecoalition,Thisallocationisnotasolution.Butitshowsthatthecorehasbecomesmaller,No.Alf-Arthur-BillcanblockA.,Alfxa+Ra（G）Arthurxa+Ra（G）Billxb（A）BenRb（D）,2Ra+Rb,Thecoalition,Feasible,Howtheblockingcoalitionworks,A,B,D,Canthisallocationbeblocked?

AnA-personwouldbebetteroffsomewherehere,Bingo!

Whatiftherewere500ofeachtype.?

IfNisbiggertheremaybemoreblockingcoalitions,A,B,D,E,Theonlyallocationleftinthe2N-personcore（eventually）.,Asyouclonetheeconomythecorebecomessmaller.Inthelimititcontainsonlycompetitiveequilibriumallocations.ButnoticethatthisrequiresbalancedreplicationoftheAlfandBilltribesAnditassumesthatallthesevariouscoalitionsaresomehowrelevant,Apowerfulresult:

theshrinkingcore,EndowmentsPreferencesAllocationsCoalitionsBlocking,Answertoquestion:

whyprice-taking?

Inalargeeconomywithsuitablysmallagents.itstheonlythingtodo.,Afinalreminder:

Basicconceptsofthecore,AggregatingfirmsAggregatingconsumersWARPPropertiesofdemandsystemsTheSeparationTheorem,Firm#4slides18-26Consumer#4slides39-44Consumer#1slides23.24Consumer#3slides5,6GenEqm#2slides14-20,24,25,.,