HART EFFECT AND EQUILIBRIUM IN INCOMPLETE MARKETS I

Abstract

In this paper I reconsider the problem of the existence for GEI models. It is well known that existence for this kind of models can fail since there are bad spot prices. Using tools from Algebraic Geometry I show that the set of bad spot prices is tipically empty if the information tree, the number of secruities and the number of tradable goods at each node satisfy a well defined inequality. Even if such inequality is not staisfied I show that the set of bad spot price can be fully characterized and described using an algorithm and I give an universal bound for the cardinality of this set. Moreover, using these results, I prove that the equilibrium always exists for all endowment profiles.