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L14

L14. General Equilibrium (cont). Big ideas:. Tuesday: Edgeworth box Pareto efficiency (normative theory) Today: Competitive equilibrium ( positive theory) First welfare theorem. O B. Edgeworth Box. O A. Desirable Allocation: Pareto Efficient.

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L14

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  1. L14 General Equilibrium (cont)

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

  3. OB Edgeworth Box OA

  4. 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

  5. OB Pareto efficiency OA

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

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

  8. Excess supply, Demand OB OA

  9. Excess Demand, Supply, Equilibrium OB OA

  10. Excess Demand, Supply, Equilibrium OB OA

  11. 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)

  12. Cobb-Douglass example

  13. OB Geometry OA

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

  15. OB Perfect substitutes: Efficiency OA

  16. Perfect substitutes: Equilibrium • Competitive equilibrium:

  17. Other Preferences • Quasilinear • Perfect complements

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