Positivity and bubbles in overlapping generations models

Bubbles, such as money, cannot be valued in efficient equilibria in overlapping generations models (a borderline case aside). Analysts frequently attribute this result to the fact that if bubbles were valued, the bubble must eventually exceed the endowment of the young. This implies negative consumption by the young, invalidating the equilibrium path. This argument is misleading because it depends on the assumption that negative consumption is infeasible. But negative consumption is admissible under some utility functions, raising questions about the generality of the argument. To investigate this, we characterize equilibrium in an overlapping generations model with negative exponential utility, which allows negative consumption. We show that if the endowment allocation is Pareto optimal, equilibrium paths incorporating valued money at some date eventually reach a point at which the equilibrium path has no continuation.