On existence and bubbles of Ramsey equilibrium with borrowing constraints

Abstract

We study the existence of equilibrium and rational bubbles in a Ramsey model with heterogeneous agents, borrowing constraints and endogenous labor. Applying Kakutani’s fixed-point theorem, we prove the existence of equilibrium in a time-truncated bounded economy. A common argument shows this solution to be an equilibrium for any unbounded economy with the same fundamentals. Taking the limit of a sequence of truncated economies, we eventually obtain the existence of equilibrium in the Ramsey model. In the second part of the paper, we address the issue of rational bubbles and we prove that they never occur in a productive economy à la Ramsey.