L12Review“Economy” with apples and orangesGeometric representationEdgeworth BoxDesirable Allocation: Pareto EfficientPareto EfficiencyPareto Efficiency=TangenencyContract CurveCobb-Douglass exampleSlide 11How do Markets Work?Slide 13Slide 14Slide 15Slide 16Slide 17L12General EquilibriumModel of choice of individualWe know preferences and we find demandsWith many such agents:Q1: How prices are formed? Q2: Are markets efficient?Review1 2 1 2, , ,p p w w*2*1, xx21xxU 1 2,p p“Economy” with apples and orangesTwo consumers, A and B.Total resources availableFeasible allocationand)4,6(A).2,4(BBA1112 2 2A Bw w w= + =1 2( , )A Ax x1 2( , )B Bx x1 1 1A Bx x w+ =2 2 2A Bx x w+ =Geometric representationFour numbers and geometric representationInsane?No: Edgeworth boxCollection of all feasible allocationsEdgeworth BoxOA)1,6(A(4, 4) (10,5)Bw w= � =AwwOBDesirable Allocation: Pareto EfficientWhen allocation is “socially” efficient?- Maximizing sum of utilities? NO!- Weaker notion: Pareto efficiency!Allocation x Pareto efficient, if there does not exist allocation y that is A) at least as good as x for allB) is strictly better for at least oneOBPareto EfficiencyOAxOBPareto Efficiency=TangenencyOAxxContract CurveOAOBThe contract curve is the set of all Pareto-optimal allocations.Cobb-Douglass example)5,10(1 2 1 1( , ) ln lniU x x a x b x= +,i A B=Contract CurveOAOBThe contract curve is the set of all Pareto-optimal allocations.How do Markets Work?How do markets work?Individuals respond optimally to prices Prices are such that markets clearWe call a competitive equilibriumBAxx**,*p1*1*1BAxx* *2 2 2A Bx x w+ =* * *, ,A Bx x pOBOAAw1 210, 1p p= =Excess supply, DemandOBOAAw1 21, 10p p= =Excess Demand, Supply, EquilibriumOBOAAw1 25, 5p p= =Excess Demand, Supply, Equilibrium1 220, 20?p p= =Cobb-Douglass example(6,1), (4, 4)A Bw w= =1 2 1 1( , ) ln lniU x x x x= +,i A B=OBOAAwInvisible HandAre markets (Pareto) efficient?First Welfare Theorem: allocation in Competitive equilibrium is Pareto
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