Title

Edgeworth Equilibria

Document Type

Discussion Paper

Publication Date

6-1-1985

CFDP Number

756R

CFDP Revision Date

1987-09-01

CFDP Pages

39

Abstract

The paper studies pure exchange economies with infinite dimensional commodity spaces in the setting of Riesz dual systems. Several new concepts of equilibrium are introduced. An allocation ( x 1 , …, x m ) is said to be a) an Edgeworth equilibrium whenever it belongs to the core of every n -fold replication of the economy; and b) an ε- Walrasian equilibrium whenever for each ε > 0 there exists some price p not equal to 0 with p ∙ω = 1 (where ω = Σω i is the total endowment) and with x ≥ i x i implying p times x ≥ p ∙ω i – ε. The major results of the paper are the following: Theorem I: Edgeworth equilibria exist. Theorem II: An allocation is an Edgeworth equilibrium if and only if it is an ε-Walrasian equilibrium. Theorem III: If preferences are proper, then every Edgeworth equilibrium is a quasi-equilibrium.

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