General Equilibrium (cont)

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Presentation transcript:

General Equilibrium (cont)

Big ideas: Tuesday: Edgeworth box Pareto efficiency (normative theory) Today: Competitive equilibrium (positive theory) First welfare theorem

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 Pareto efficiency = equality of MRS All Pareto efficient allocations=contract curve

Pareto efficiency OB OA

Competitive (Walrasian) Equilibrium Walras, and then Arrow + Debreu Individuals respond optimally to prices Prices are such that markets clear We call a competitive equilibrium

Competitive (Walrasian) Equilibrium Competitive Equilibrium A positive model of free market economy Walras, then Arrow and Debreu Extensively used by ``practitioners’’

Excess supply, Demand OB OA

Excess Demand, Supply, Equilibrium OB OA

Excess Demand, Supply, Equilibrium OB OA

Cobb-Douglass Calculation Equilibrium = 6 numbers 3 tricks that simplify calculation Market clearing for one market (Walras Law) Use Magic Formulas Solve for relative price (only)

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:

Other Preferences Quasilinear Perfect complements