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L13

L13. General Equilibrium (cont). O B. Edgeworth Box. O A. 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

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L13

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  1. L13 General Equilibrium (cont)

  2. OB Edgeworth Box OA

  3. 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

  4. OB Pareto efficiency OA

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

  6. Cobb-Douglass example

  7. OB Geometry OA

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

  9. OB Perfect substitutes: Efficiency OA

  10. Perfect substitutes: Equilibrium • Competitive equilibrium:

  11. OB Perfect substitutes: Equilibrium OA

  12. Other Preferences • Quasilinear • Perfect complements

  13. Application: Irving Fisher r • Determination of competitive interest rate

  14. Application: Irving Fisher r • Competitive equilibrium

  15. OB Geometry OA

  16. Application: Uncertainty Arrow Securities: No idiosyncratic risk in equilibrium

  17. OB Geometry OA

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