  We offer mathematical tractability and new insights for a framework of
exponential utility with non-negative consumption, a constraint often omitted
in the literature giving rise to economically unviable solutions. Specifically,
using the Kuhn-Tucker theorem and the notion of aggregate state price density
(Malamud and Trubowitz (2007)), we provide a solution to this problem in the
setting of both complete and incomplete markets (with random endowments). Then,
we exploit this result to provide an explicit characterization of complete
market heterogeneous equilibria. Furthermore, we construct concrete examples of
models admitting multiple (including infinitely many) equilibria. By using
Cramer's large deviation theorem, we study the asymptotics of equilibrium zero
coupon bonds. Lastly, we conduct a study of the precautionary savings motive in
incomplete markets.

Portfolio Management;Optimization and Control