1. General Equilibrium (cont)

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

3. Edgeworth Box OB 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. Pareto efficiency OB OA

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

7. Competitive (Walrasian) Equilibrium
Consider
Individuals respond optimally to prices
Prices are such that markets clear
We call a competitive equilibrium

8. Excess supply, Demand OB OA

9. Excess Demand, Supply, EquilibriumOB OA

10. Excess Demand, Supply, EquilibriumOB 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 general

13. Example

14. Geometry OB OA

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

16. Other Preferences
Quasilinear
Perfect complements