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Part I General Equilibrium - Harvard University

HartNotesMatthewBasilicoApril,2013 PartIGeneralEquilibriumChapter15- General EquilibriumTheory:Examples PureexchangeeconomywithEdgeworthBox Pro ductionwithOne-Firm,One-Consumer [SmallOp enEconomy] :TheEdgeworthBoxDe nitionsandSetUpPureExchangeEconomy Aneconomyinwhichtherearenopro ductionopp ossessendowments,eco-nomicactivityconsis tsoftradingandconsumptionEdgeworthBoxEco nomy Preliminaries Assumeconsumersactaspricetakers Twoconsumersi= 1,2;Twocommo ditiesl= 1,2 ConsumptionandEndowment Consumeri sconsumptionvectorisxi= (x1i,x2i) Consumeri sconsumptionsetisR2+ Consumerihaspreferencerelation%iovercons umptionvectorsinthisset Consumeri sendowmentvectoris i= ( 1i, 2i) Totalendowmentofgo o dlis l= l1+ l2 Allo cation1 Anal locationx R4+isanassignmentofanonnegativeconsumpti onvectortoeachcon-sumer x= (x1,x2) = ((x11,x21),(x12,x22)) A

Any Walrasian equilibirum allocation x necessarily belongs to the Pareto Set 2nd Welfare Theorem erbally:V Under convexity assumptions (not required for 1st WT), a planner can achieve any desired Pareto optimal allocation by appropriately redistributing wealth in a lump-sum fashion and then letting the market work

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