CFDP 756R

Edgeworth Equilibria

Author(s): 

Publication Date: June 1985

Revision Date: September 1987

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 (x1, …, xm) 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 = Σωi is the total endowment) and with x ≥i xiimplying p times x ≥ p∙ωi – 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.

See CFP: 691