1. L12
General Equilibrium

2. Review Model of choice of individual We know preferences and
we find demands
With many such agents:
Q1: How prices are formed?
Q2: Are markets efficient?

3. “Economy” with apples and oranges
Two consumers, A and B.
Total resources available
Feasible allocation
and

4. Geometric representation
Four numbers and geometric representation
Insane?
No: Edgeworth box
Collection of all feasible allocations

5. Edgeworth Box OB OA

6. Desirable Allocation: Pareto Efficient
When allocation is “socially” efficient?
- Maximizing sum of utilities? NO!
- Weaker notion: Pareto efficiency!
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

7. Pareto Efficiency OB OA

8. Pareto Efficiency=TangenencyOB OA

9. Contract Curve
The contract curve is the set of all Pareto-optimal allocations. OB OA

10. Cobb-Douglass example

11. Contract Curve
The contract curve is the set of all Pareto-optimal allocations. OB OA

12. How do Markets Work? How do markets work?
Individuals respond optimally to prices
Prices are such that markets clear
We call a competitive equilibrium

13. Excess supply, Demand OB OA

14. Excess Demand, Supply, EquilibriumOB OA

15. Excess Demand, Supply, EquilibriumOB OA

16. Cobb-Douglass example

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