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