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General Equilibrium (cont)

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Presentation on theme: "General Equilibrium (cont)"— Presentation transcript:

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
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 Geometry OB OA

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

15 Perfect substitutes: Efficiency
OB OA

16 Perfect substitutes: Equilibrium
Competitive equilibrium:

17 Other Preferences Quasilinear Perfect complements

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