高级微观经济学market as a process.ppt

Lecture13 marketasaprocessGeneralEquilibriumtheoryII Content The core UniquenessofequilibriumStabilityofequilibriumWelfare The core Improveuponanallocation agroupofagentsSissaidtoimproveuponagivenallocationx ifthereissomeallocationx suchthat andIfanallocationcanbeimprovedupon thenthereissomegroupofagentscandobetterwithoutmarket The core Coreofaneconomy afeasibleallocationxisinthecoreoftheeconomyifitcannotbeimproveduponbyanycoalition Ifxisinthecore xmustbeParetoefficient Seethefig The core Walrasianequilibriumisincore Proof let x p betheWalrasianequilibriumwithinitialendowmentwi Ifnot thereissomecoalitionSandsomefeasibleallocationx suchthatallagentsiinSstrictlypreferto andButWalrasianequilibriumimplies The core Equaltreatmentinthecore ifxisanallocationinther coreofagiveneconomy thenanytwoagentsofthesametypemustreceivethesamebundle Proof ifnot Let SoThatisEveryagentbelowtheaveragewillcoalizetoimproveupontheallocation The core Shrinkingcore thereisauniquemarketequilibriumx frominitialendowmentw ifyisnottheequilibrium thereissomereplicationr suchthatyisnotinther core Proof sinceyisnottheequilibrium thereisanotherallocationgimproveuponA orB atleast Thatmeansseethefig Let TandVareintegers The core ReplicatedVtimesoftheeconomy wehave SothecoalitionwithVagentsoftypeAand V T oftypeBcanimproveupony The core Convexityandsize Ifagenthasnon convexpreference istherestillaequilibrium Seethefig Replicationtheeconomy Uniquenessofequilibrium Grosssubstitutes twogoodsiandjaregrosssubstitutesatpricep if Proposition Ifallgoodsaregrosssubstitutesatallprice thenifp isanequilibriumprice thenit stheuniqueequilibriumprice Stabilityofequilibrium Priceadjustmentrule Giissomesmoothsign preservingfunction Consideraspecialcase Thenwehave Seethefig Stabilityofequilibrium WARPimpliesstability if andifp isanequilibrium thenallpathofpricefollowingWARPwillconvergetop Proof Liaponovfunction Welfare Paretocriterion ifandonlyifCompensationcriterion Kaldor ifthereissuchthatand Assignment Textbook ex 21 2 Coreofanecono