L 12 General Equilibrium Social Efficiency Review Model

L 12 General Equilibrium (Social Efficiency)

Review • • Model of choice of individual We know preferences and we find demands • With many such agents: Q 1: How prices are formed? Q 2: Are markets efficient?

Big ideas: Today: • Edgeworth box • Pareto efficiency Next lecture • Competitive equilibrium • First welfare theorem

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

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

Edgeworth Box OB OA

Socially Desirable Allocation Pareto Efficiency u When allocation is “socially” efficient? - Maximizing sum of utilities? NO! - Weaker notion: Pareto efficiency! u 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

Quiz u Consider a two agent economy with Q: Is allocation A) Yes B) No C) Depends Pareto efficient

Pareto Efficiency u Assume Cobb Douglass preferences u Necessity of tangency OB OA

Pareto Efficiency u Sufficiency of tangency OB OA

Equivalent Characterization u Assume Interior Allocations u Allocation is Pareto efficient if and only if indifference curves are tangent (equal MRS) u Are initial endowments efficient?

Example: OB OA

Quiz u Let u Is allocation A) Yes B) No C) Depends Pareto efficient

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

Cobb-Douglass example

Contract Curve u Cobb Douglass OB OA

Contract Curve u Perfect substitutes OB OA

Contract Curve u Other preferences A) General Perfect substitutes B) Perfect Complements C) Quasilinear