General Equilibrium (cont)

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Presentation transcript:

General Equilibrium (cont)

Edgeworth Box OB OA

Desirable Allocation: Pareto Efficient Allocation x Pareto efficient, if there does not exist allocation y that is A) at least as good as x for all B) is strictly better for at least one All Pareto efficient allocations=contract curve

Pareto efficiency OB OA

Competitive equilibrium Definition: Competitive equilibrium optimal given such that markets clear Two tricks Only relative price determined Walras Law: second market will clear auctomatically

Cobb-Douglass example

Geometry OB OA

Invisible Hand (Adam Smith) Are markets (Pareto) efficient? First Welfare Theorem: allocation in Competitive equilibrium is Pareto optimal Proof OB OA

Perfect substitutes: Efficiency OB OA

Perfect substitutes: Equilibrium Competitive equilibrium:

Perfect substitutes: Equilibrium OB OA

Other Preferences Quasilinear Perfect complements

Application: Irving Fisher r Determination of competitive interest rate

Application: Irving Fisher r Competitive equilibrium

Geometry OB OA

Application: Uncertainty Arrow Securities: No idiosyncratic risk in equilibrium

Geometry OB OA