人大中级微观经济学讲义 Exchange

ChapterThirtyExchange交换Exchange•Twoconsumers,AandB.•Theirendowmentsofgoods1and2are•E.g.•ThetotalquantitiesavailableAAA(,)12BBB(,).12andA(,)64B(,).22and11628AB22426ABunitsofgood1unitsofgood2.andareExchange•EdgeworthandBowleydevisedadiagram,calledanEdgeworthbox,toshowallpossibleallocationsoftheavailablequantitiesofgoods1and2betweenthetwoconsumers.1845-1926StartinganEdgeworthBoxWidth=11628ABHeight=22426ABThedimensionsoftheboxarethequantitiesavailableofthegoods.FeasibleAllocations•Whatallocationsofthe8unitsofgood1andthe6unitsofgood2arefeasible?•HowcanallofthefeasibleallocationsbedepictedbytheEdgeworthboxdiagram?•Onefeasibleallocationisthebefore-tradeallocation;i.e.theendowmentallocation.Width=11628ABHeight=22426ABTheendowmentallocationisA(,)64B(,).22andTheEndowmentAllocationB(,)22OAOB684622TheEndowmentAllocationA(,)64B(,)22OAOB684622TheendowmentallocationTheEndowmentAllocationOtherFeasibleAllocations•denotesanallocationtoconsumerA.•denotesanallocationtoconsumerB.•Anallocationisfeasibleifandonlyif(,)xxAA12(,)xxBB12xxABAB1111xxABAB2222.andFeasibleReallocationsOAOB11ABxA222ABxA1xB1xB2FeasibleReallocationsOAOB11ABxA222ABxA1xB1xB2FeasibleReallocations•Allpointsinthebox,includingtheboundary,representfeasibleallocationsofthecombinedendowments.•Whichallocationswillbeblockedbyoneorbothconsumers?•Whichallocationsmakebothconsumersbetteroff?AddingPreferencestotheBox2A1AxA2xA1OAForconsumerA.AddingPreferencestotheBox2A1AxA2xA1ForconsumerA.OAAddingPreferencestotheBox2B1BxB2xB1ForconsumerB.OBAddingPreferencestotheBoxxB2xB1ForconsumerB.OB2B1BAddingPreferencestotheBox2B1BxB1xB2ForconsumerB.OBAddingPreferencestotheBox2A1AxA2xA1OAForconsumerA.Edgeworth’sBox2A1AxA2xA1OA2B1BxB1xB2OBPareto-Improvement•AnallocationoftheendowmentthatimprovesthewelfareofaconsumerwithoutreducingthewelfareofanotherisaPareto-improvingallocation.•WherearethePareto-improvingallocations?Edgeworth’sBox2A1AxA2xA1OA2B1BxB1xB2OBPareto-Improvements2A1AxA2xA1OA2B1BxB1xB2OBThesetofPareto-improvingallocationsPareto-Improvements•Sinceeachconsumercanrefusetotrade,theonlypossibleoutcomesfromexchangearePareto-improvingallocations.•ButwhichparticularPareto-improvingallocationwillbetheoutcomeoftrade?Pareto-Improvements2A1AxA2xA1OA2B1BxB1xB2OBThesetofPareto-improvingreallocationsPareto-ImprovementsTradeimprovesbothA’sandB’swelfares.ThisisaPareto-improvementovertheendowmentallocation.Pareto-ImprovementsNewmutualgains-to-traderegionisthesetofallfurtherPareto-improvingreallocations.TradeimprovesbothA’sandB’swelfares.ThisisaPareto-improvement(帕累托改进)overtheendowmentallocation.Pareto-ImprovementsFurthertradecannotimprovebothAandB’swelfares.Pareto-Optimality(帕累托最优)BetterforconsumerBBetterforconsumerAPareto-OptimalityAisstrictlybetteroffbutBisstrictlyworseoffBisstrictlybetteroffbutAisstrictlyworseoffBothAandBareworseoffBothAandBareworseoffPareto-OptimalityTheallocationisPareto-optimalsincetheonlywayoneconsumer’swelfarecanbeincreasedistodecreasethewelfareoftheotherconsumer.Pareto-OptimalityTheallocationisPareto-optimalsincetheonlywayoneconsumer’swelfarecanbeincreasedistodecreasethewelfareoftheotherconsumer.TheMarginalRatesofSubstitutionAreEqual.Pareto-Optimality2A1AxA2xA1OA2B1BxB1xB2OBAlltheallocationsmarkedbyaarePareto-optimal.Pareto-Optimality•Thecontractcurve(契约线)isthesetofallPareto-optimalallocations.Pareto-Optimality2A1AxA2xA1OA2B1BxB1xB2OBAlltheallocationsmarkedbyaarePareto-optimal.ThecontractcurvePareto-Optimality•Buttowhichofthemanyallocationsonthecontractcurvewillconsumerstrade?•Thatdependsuponhowtradeisconducted.•Inperfectlycompetitivemarkets?Byone-on-onebargaining?TheCore(核心)2A1AxA2xA1OA2B1BxB1xB2OBThesetofPareto-improvingreallocationsTheCore2A1AxA2xA1OA2B1BxB1xB2OBTheCore2A1AxA2xA1OA2B1BxB1xB2OBPareto-optimaltradesblockedbyBPareto-optimaltradesblockedbyATheCore2A1AxA2xA1OA2B1BxB1xB2OBPareto-optimaltradesnotblockedbyAorBarethecore.TheCore•ThecoreisthesetofallPareto-optimalallocationsthatarewelfare-improvingforbothconsumersrelativetotheirownendowments.•Rationaltradeshouldachieveacoreallocation.TheCore•Butwhichcoreallocation?•Again,thatdependsuponthemannerinwhichtradeisconducted.TradeinCompetitiveMarkets•Considertradeinperfectlycompetitivemarkets.•Eachconsumerisaprice-takertryingtomaximizeherownutilitygivenp1,p2andherownendowment.Thatis,...TradeinCompetitiveMarkets2A1AxA2xA1OAForconsumerA.pxpxppAAAA11221122xA2*xA1*TradeinCompetitiveMarkets•Sogivenp1andp2,consumerA’snetdemandsforcommodities1and2arexAA11*xAA22*.andTradeinCompetitiveMarkets•And,similarly,forconsumerB…TradeinCompetitiveMarkets2B1BxB2xB1ForconsumerB.OBxB1*xB2*pxpxppBBBB11221122TradeinCompetitiveMarkets•Sogivenp1andp2,consumerB’snetdemandsforcommodities1and2arexBB11*xBB22*.andTradeinCompetitiveMarkets•Ageneralequilibriumoccurswhenpricesp1andp2causeboththemarketsforcommodities1and2toclear;i.e.xxABAB1111**xxABAB2222**.andTradeinCompetitiveMarkets2A1AxA