Dynamic Aggregation and Computation of Equilibria in Finite-Dimensional Economies with Incomplete Financial Markets *

Abstract

This paper constructs a representative agent supporting the equilibrium allocation in ¡°event-tree¡± economies with time-additive preferences and possibly incomplete securities markets. If the equilibrium allocation is Pareto optimal, this construction gives the usual linear welfare function. Otherwise, the representative agent¡¯s utility function is state-dependent, even when individual agents have state-independent utilities and homogeneous beliefs. The existence of a representative agent allows us to provide a characterization of equilibria which does not rely on the derivation of the agents¡¯ intertemporal demand functions for consumption and investment and transforms the dynamic general equilibrium problem into a static one. This characterization is therefore especially well suited for numerical computation of equilibria in economies with incomplete financial markets.

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