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General Equilibrium (cont)
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Big ideas: Tuesday: Edgeworth box Pareto efficiency (normative theory)
Today: Competitive equilibrium (positive theory) First welfare theorem
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Edgeworth Box OB OA
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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
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Pareto efficiency OB OA
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Competitive (Walrasian) Equilibrium
Competitive Equilibrium A positive model of free market economy Walras, then Arrow and Debreu Extensively used by ``practitioners’’
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Competitive (Walrasian) Equilibrium
Consider Individuals respond optimally to prices Prices are such that markets clear We call a competitive equilibrium
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Excess supply, Demand OB OA
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Excess Demand, Supply, Equilibrium
OB OA
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Excess Demand, Supply, Equilibrium
OB OA
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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)
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Cobb-Douglass general
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Example
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Geometry OB OA
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Invisible Hand (Adam Smith)
Are markets (Pareto) efficient? First Welfare Theorem: allocation in Competitive equilibrium is Pareto optimal Proof OB OA
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