北大微观经济学英文版-文档资料

ChapterTwenty-NineExchangeExchangeTwoconsumers,AandB.Theirendowmentsofgoods1and2areE.g.Thetotalquantitiesavailableandandunitsofgood1unitsofgood2.andareExchangeEdgeworthandBowleydevisedadiagram,calledanEdgeworthbox,toshowallpossibleallocationsoftheavailablequantitiesofgoods1and2betweenthetwoconsumers.StartinganEdgeworthBoxStartinganEdgeworthBoxWidth=StartinganEdgeworthBoxWidth=Height=StartinganEdgeworthBoxWidth=Height=Thedimensionsoftheboxarethequantitiesavailableofthegoods.FeasibleAllocationsWhatallocationsofthe8unitsofgood1andthe6unitsofgood2arefeasible?HowcanallofthefeasibleallocationsbedepictedbytheEdgeworthboxdiagram?FeasibleAllocationsWhatallocationsofthe8unitsofgood1andthe6unitsofgood2arefeasible?HowcanallofthefeasibleallocationsbedepictedbytheEdgeworthboxdiagram?Onefeasibleallocationisthebefore-tradeallocation;i.e.theendowmentallocation.Width=Height=TheendowmentallocationisandTheEndowmentAllocationWidth=Height=TheEndowmentAllocationOAOB68TheEndowmentAllocationOAOB6846TheEndowmentAllocationOAOB684622TheEndowmentAllocationOAOB684622TheendowmentallocationTheEndowmentAllocationMoregenerally,…TheEndowmentAllocationTheEndowmentAllocationOAOBTheendowmentallocationOtherFeasibleAllocationsdenotesanallocationtoconsumerA.denotesanallocationtoconsumerB.AnallocationisfeasibleifandonlyifandFeasibleReallocationsOAOBFeasibleReallocationsOAOBFeasibleReallocationsAllpointsinthebox,includingtheboundary,representfeasibleallocationsofthecombinedendowments.FeasibleReallocationsAllpointsinthebox,includingtheboundary,representfeasibleallocationsofthecombinedendowments.Whichallocationswillbeblockedbyoneorbothconsumers?Whichallocationsmakebothconsumersbetteroff?AddingPreferencestotheBoxOAForconsumerA.AddingPreferencestotheBoxMorepreferredForconsumerA.OAAddingPreferencestotheBoxForconsumerB.OBAddingPreferencestotheBoxMorepreferredForconsumerB.OBAddingPreferencestotheBoxMorepreferredForconsumerB.OBAddingPreferencestotheBoxOAForconsumerA.AddingPreferencestotheBoxOAOBEdgeworth’sBoxOAOBPareto-ImprovementAnallocationoftheendowmentthatimprovesthewelfareofaconsumerwithoutreducingthewelfareofanotherisaPareto-improvingallocation.WherearethePareto-improvingallocations?Edgeworth’sBoxOAOBPareto-ImprovementsOAOBThesetofPareto-improvingallocationsPareto-ImprovementsSinceeachconsumercanrefusetotrade,theonlypossibleoutcomesfromexchangearePareto-improvingallocations.ButwhichparticularPareto-improvingallocationwillbetheoutcomeoftrade?Pareto-ImprovementsOAOBThesetofPareto-improvingreallocationsPareto-ImprovementsPareto-ImprovementsPareto-ImprovementsTradeimprovesbothA’sandB’swelfares.ThisisaPareto-improvementovertheendowmentallocation.Pareto-ImprovementsNewmutualgains-to-traderegionisthesetofallfurtherPareto-improvingreallocations.TradeimprovesbothA’sandB’swelfares.ThisisaPareto-improvementovertheendowmentallocation.Pareto-ImprovementsFurthertradecannotimprovebothAandB’swelfares.Pareto-OptimalityBetterforconsumerBBetterforconsumerAPareto-OptimalityAisstrictlybetteroffbutBisstrictlyworseoffPareto-OptimalityAisstrictlybetteroffbutBisstrictlyworseoffBisstrictlybetteroffbutAisstrictlyworseoffPareto-OptimalityAisstrictlybetteroffbutBisstrictlyworseoffBisstrictlybetteroffbutAisstrictlyworseoffBothAandBareworseoffPareto-OptimalityAisstrictlybetteroffbutBisstrictlyworseoffBisstrictlybetteroffbutAisstrictlyworseoffBothAandBareworseoffBothAandBareworseoffPareto-OptimalityTheallocationisPareto-optimalsincetheonlywayoneconsumer’swelfarecanbeincreasedistodecreasethewelfareoftheotherconsumer.Pareto-OptimalityTheallocationisPareto-optimalsincetheonlywayoneconsumer’swelfarecanbeincreasedistodecreasethewelfareoftheotherconsumer.Anallocationwhereconvexindifferencecurvesare“onlyjustback-to-back”isPareto-optimal.Pareto-OptimalityWhereareallofthePareto-optimalallocationsoftheendowment?Pareto-OptimalityOAOBPareto-OptimalityOAOBAlltheallocationsmarkedbyaarePareto-optimal.Pareto-OptimalityThecontractcurveisthesetofallPareto-optimalallocations.Pareto-OptimalityOAOBAlltheallocationsmarkedbyaarePareto-optimal.ThecontractcurvePareto-OptimalityButtowhichofthemanyallocationsonthecontractcurvewillconsumerstrade?Thatdependsuponhowtradeisconducted.Inperfectlycompetitivemarkets?Byone-on-onebargaining?TheCoreOAOBThesetofPareto-improvingreallocationsTheCoreOAOBTheCoreOAOBPareto-optimaltradesblockedbyBPareto-optimaltradesblockedbyATheCoreOAOBPareto-optimaltradesnotblockedbyAorBTheCoreOAOBPareto-optimaltradesnotblockedbyAorBarethecore.TheCoreThecoreisthesetofallPareto-optimalallocationsthatarewelfare-improvingforbothconsumersrelativetotheirownendowments.Rationaltradeshouldachieveacoreallocation.TheCoreButwhichcoreallocation?Again,thatdependsuponthemannerinwhichtradeisconducted.TradeinCompetitiveMarketsConsidertradeinperfectlycompetitivemarkets.Eachconsumerisaprice-takertryingtomaximizeherownutilitygivenp1,p2andherownendowment.Thatis,...TradeinCompetitiveMarketsOAForconsumerA.TradeinCompetitiveMarketsSogivenp1andp2,consumerA’snetdemandsforcommodities1and2areandTradeinCompetitiveMarketsAnd,similarly,forconsumerB…TradeinCompetitiveMarketsForconsumerB.OBTradeinCompetitiveMarketsSogivenp1andp2,consumerB’snetdemandsforcommodities1and2areandTradeinCompetitiveMarketsAgeneralequilibriumoccurswhenpricesp1andp2causeboththemarketsforcommodities1and2toclear;i.e.andTradeinCompetitiveMarketsOAOBTradeinCompetitiveMarketsOAOBCanthisPOallocationbeachieved?TradeinCompetitiveMarketsOAOBBudgetconstraintforconsumerATradeinCompetitiveMarketsOAOBBudgetconstraintforconsumerATradeinCompetitiveMarketsOAOBBudgetconstraintforconsumerBTradeinCompetitiveMarketsOAOBBudgetconstraintforconsumerBTradeinCompetitiveMarketsOAOBButTradeinCompetitiveMarketsOAOBandTradeinCompetitiveMarketsSoatthegivenpricesp1andp2thereisanexcesssupplyofcommodity1excessdemandforcommodity2.Neithermarketclearssothepricesp1andp2donotcauseageneralequilibrium.TradeinCompetitiveMarketsOAOBSothisPOallocationcannotbeachievedbycompetitivetrading.TradeinCompetitiveMarketsOAOBWhichPOallocationscanbeachievedbycompetitivetrading?TradeinCompetitiveMarketsSincethereisanexcessdemandforcommodity2,p2willrise.Sincethereisanexcesssupplyofcommodity1,p1willfall.Theslopeofthebudgetconstraintsis-p1/p2sothebudgetconstraintswillpivotabouttheendowmentpointandbecomelesssteep.TradeinCompetitiveMarketsOAOBWhichPOallocationscanbeachievedbycompetitivetrading?TradeinCompetitiveMarketsOAOBWhichPOallocationscanbeachievedbycompetitivetrading?TradeinCompetitiveMarketsOAOBWhichPOallocationscanbeachievedbycompetitivetrading?TradeinCompetitiveMarketsOAOBBudgetconstraintforconsumerATradeinCompetitiveMarketsOAOBBudgetconstraintforconsumerATradeinCompetitiveMarketsOAOBBudgetconstraintforconsumerBTradeinCompetitiveMarketsOAOBBudgetconstraintforconsumerBTradeinCompetitiveMarketsOAOBSoTradeinCompetitiveMarketsOAOBandTradeinCompetitiveMarketsAtthenewpricesp1andp2bothmarketsclear;thereisageneralequilibrium.TradingincompetitivemarketsachievesaparticularPareto-optimalallocationoftheendowments.ThisisanexampleoftheFirstFundamentalTheoremofWelfareEconomics.FirstFundamentalTheoremofWelfareEconomicsGiventhatconsumers’preferencesarewell-behaved,tradinginperfectlycompetitivemarketsimplementsaPareto-optimalallocationoftheeconomy’sendowment.SecondFundamentalTheoremofWelfareEconomicsTheFirstTheoremisfollowedbyasecondthatstatesthatanyPareto-optimalallocation(i.e.anypointonthecontractcurve)canbeachievedbytradingincompetitivemarketsprovidedthatendowmentsarefirstappropriatelyrearrangedamongsttheconsumers.Giventhatconsumers’preferencesarewell-behaved,foranyPareto-optimalallocationtherearepricesandanallocationofthetotalendowmentthatmakesthePareto-optimalallocationimplementablebytradingincompetitivemarkets.SecondFundamentalTheoremofWelfareEconomicsSecondFundamentalTheoremOAOBThecontractcurveSecondFundamentalTheoremOAOBSecondFundamentalTheoremOAOBImplementedbycompetitivetradingfromtheendowmentw.SecondFundamentalTheoremOAOBCanthisallocationbeimplementedbycompetitivetradingfromw?SecondFundamentalTheoremOAOBCanthisallocationbeimplementedbycompetitivetradingfromw?No.SecondFundamentalTheoremOAOBButthisallocationisimplementedbycompetitivetradingfromq.Walras’LawWalras’Lawisanidentity;i.e.astatementthatistrueforanypositiveprices(p1,p2),whethertheseareequilibriumpricesornot.Walras’LawEveryconsumer’spreferencesarewell-behavedso,foranypositiveprices(p1,p2),eachconsumerspendsallofhisbudget.ForconsumerA:ForconsumerB:Walras’LawSumminggivesWalras’LawRearranged,Thatis,...Walras’LawThissaysthatthesummedmarketvalueofexcessdemandsiszeroforanypositivepricesp1andp2--thisisWalras’Law.ImplicationsofWalras’LawSupposethemarketforcommodityAisinequilibrium;thatis,ThenimpliesImplicationsofWalras’LawSooneimplicationofWalras’Lawforatwo-commodityexchangeeconomyisthatifonemarketisinequilibriumthentheothermarketmustalsobeinequilibrium.ImplicationsofWalras’LawWhatif,forsomepositivepricesp1andp2,thereisanexcessquantitysuppliedofcommodity1?Thatis,ThenimpliesImplicationsofWalras’LawSoasecondimplicationofWalras’Lawforatwo-commodityexchangeeconomyisthatanexcesssupplyinonemarketimpliesanexcessdemandintheothermarket.