Limited Arbitrage is Necessary and Sufficient for the Existence of a Competitive Equilibrium With or Without Short Sales
30 Pages Posted: 9 Apr 2009
Date Written: January 1, 1995
Abstract
A condition of limited arbitrage is defined on the endowments and the preferences of the traders in an Arrow-Debreu economy. Theorem 1 establishes that limited arbitrage is necessary and sufficient for the existence of the competitive equilibrium in markets with or without short sales. Limited arbitrage bounds utility arbitrages. the diversity of the traders in the economy, and the gains from trade which they can afford from initial endowments (Proposition 2); it is related to but nonetheless different from the no-arbitrage condition used in finance. Theorem 2 establishes that an Arrow-Debreu economy has a competitive equilibrium if and only if every one of its subeconomies with N I traders does, where N is the number of commodities. Limited arbitrage has been shown elsewhere to be equivalent to the existence of the core [16], to the contractibility of spaces of preferences and to the existence of continuous anonymous social choice rules which respect unanimity.
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Limited Arbitrage is Necessary and Sufficient for the Existence of a Competitive Equilibrium
-
Limited Arbitrage is Necessary and Sufficient for the Existence of an Equilibrium
-
Competitive Equilibrium in Sobolev Spaces Without Bounds on Short Sales
-
Social Diversity, Arbitage, and Gains from Trade: A Unified Perspective on Resource Allocation
-
Intersecting Families on Sets and the Topology of Cones in Economics
-
Limited Arbitrage is Necessary and Sufficient for the Non-Emptiness of the Core