COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 764

"Existence, Regularity, and Constrained Suboptimality of Competitive Allocations
When the Asset Market is Incomplete"

John Geanakoplos and Heracles M. Polemarchakis

August 1985

Let assets be denominated in an a priori specified numeraire.

Whether or not the asset is complete, a competitive equilibrium exists as long as arbitrage is possible when assets are free. Generically, the set of competitive equilibria is finite, and the equilibrium prices and allocations in the commodity spot markets are uniquely determined by the asset allocation in a neighborhood of a competitive equilibrium.

If the asset market is incomplete, a competitive equilibrium allocation is generically constrained suboptimal: there exists an arbitrarily small reallocation of the existing assets, which leads to a Pareto improvement in welfare when prices and allocations in the commodity spot market adjust to maintain equilibrium.

JEL Classification: 313

Keywords: Asset markets, Competitive equilibria, Incomplete asset markets