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