1. General Equilibrium (Social Efficiency)

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. Big ideas: Today: Edgeworth box Pareto efficiency Next lecture
Competitive equilibrium
First welfare theorem (Adam Smith)

4. “Economy” with apples and oranges
Two consumers, A and B.
Aggregate endowment (total resources)
Feasible allocation
and

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

6. Edgeworth Box OB OA

7. Socially Desirable Allocation Pareto Efficiency
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

8. Quiz Consider a two agent economy with
Q: Is allocation Pareto efficient
Yes No
Depends

9. Remarks Pareto efficiency is a weak notion Not necessarily fair
Implies lack of gains to trade

10. Simple characterization
Assume Cobb Douglass preferences
Necessity of tangency OB OA

11. Pareto Efficiency Assume Cobb Douglass preferences
Necessity of tangency OB OA

12. Pareto Efficiency
Sufficiency of tangency OB OA

13. Equivalent Characterization
Assume Interior Allocations
Allocation is Pareto efficient
if and only if indifference curves are tangent (equal MRS)
Is allocation efficient?

14. Example: OB OA

15. Quiz
Let
Is allocation Pareto efficient
Yes No
Depends

16. Contract Curve
Contract curve is the set of all Pareto-optimal allocations. OB OA

17. Cobb-Douglass example

18. Contract Curve
Identical Cobb Douglass OB OA

19. Contract Curve
Different Cobb Douglass OB OA

20. Contract Curve
Identical Perfect substitutes OB OA

21. Contract Curve Contract curve for preferences A) Cobb-Douglas
B) Perfect substitutes
B) Perfect Complements
C) Quasilinear
Identical and heterogeneous preferences