COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 756R

"Edgeworth Equilibria"

Charalambos D. Aliprantis, Donald J. Brown and Owen Burkinshaw

Revised September 1985

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,…,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 epsilon > 0 there exists some price p not equal to 0 with p times omega =1 (where omega = Sigma omega₁ is the total endowment) and with x >_i x_i implying p times x > p times omega_i - epsilon. 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 epsilon-Walrasian equilibrium.

Theorem III: If preferences are proper, then every Edgeworth equilibrium is a quasi-equilibrium.