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.
Geanakoplos, John and Polemarchakis, Heracles M., "Existence, Regularity, and Constrained Suboptimality of Competitive Allocations When the Asset Market Is Incomplete" (1985). Cowles Foundation Discussion Papers. 1005.