L14

1
L14

• General Equilibrium (cont)

2
Big ideas

• Tuesday
• Edgeworth box
• Pareto efficiency (normative theory)
• Today
• Competitive equilibrium (positive theory)
• First welfare theorem

3
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 allocationscontract curve

5
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
OA
9
Excess Demand, Supply, Equilibrium
OA
10
Excess Demand, Supply, Equilibrium
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
OA
14
Invisible Hand (Adam Smith)

• Are markets (Pareto) efficient?
• First Welfare Theorem allocation in Competitive
  equilibrium is Pareto optimal
• Proof

OA
15
Perfect substitutes Efficiency
OA
16
Perfect substitutes Equilibrium

• Competitive equilibrium

17
Other Preferences

• Quasilinear
• Perfect complements