Equilibrium with exponential utility and non-negative consumption

Abstract

We study a multi-period Arrow-Debreu equilibrium in a heterogeneous economy populated by agents trading in a complete market. Each agent is represented by an exponential utility function, where additionally no negative level of consumption is permitted. We derive an explicit formula for the optimal consumption policies involving a put option depending on the state price density. We exploit this formula to prove the existence of an equilibrium and then provide a characterization of all possible equilibria, under the assumption of positive endowments. Via particular examples, we demonstrate that uniqueness is not always guaranteed. Finally, we discover the presence of infinitely many equilibria when endowments are vanishing.