A Characterization of Equilibrium in Incomplete Markets with Real Assets

A closed-form solution of equilibrium outcomes is generally un-available in a general equilibrium model with incomplete markets (GEI model). Competitive equilibrium may not be directly computable from the aggregate ex-cess demand functions because they need not be continuous in GEI economies. This paper provides a new characterization of competitive equilibrium in the GEI model by putting into a new perspective the sudden shrinkage of risk-sharing op-portunities at a spot price that makes some of the assets redundant and thus, may cause the discontinuity of demand functions. The new characterization is based on the notions of 'pre-GEI equilibrium' and 'test equilibrium'. Pre-GEI equi-librium outcomes yield a computational equivalent of competitive equilibrium while test equilibrium outcomes may provide existential information on equilib-rium. Competitive equilibrium for the GEI model is generically computable as an outcome of pre-GEI equilibrium without resort to any element of the Grass-mann manifold.