General Equilibrium (Social Efficiency)

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?

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

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

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 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

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

Pareto Efficiency Assume Cobb Douglass preferences Necessity of tangency OB OA

Pareto Efficiency Sufficiency of tangency OB OA

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

Example: OB OA

Quiz Let Is allocation Pareto efficient Yes No Depends

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

Cobb-Douglass example

Contract Curve Cobb Douglass OB OA

Contract Curve Perfect substitutes OB OA

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