On existence and bubbles of Ramsey equilibrium with borrowing constraints

We address the issues of existence of Ramsey equilibrium under bor- rowing constraints and occurrence of rational bubbles. First, we consider a time-truncated economy. Since the feasible allo- cations sets of our economy are uniformly bounded, we prove that there exists an equilibrium in a time-truncated bounded economy by Gale and Mas-Colell's (1975) theorem. Actually, this equilibrium turns out to be an equilibrium for the time-truncated economy as the uniform bounds are relaxed, as is commonly shown in general equilibrium proofs of existence for ffnite-dimensional commodity spaces. Second, we take the limit of a sequence of truncated, unbounded economies, and prove the existence of an intertemporal equilibrium in the limit economy. Third, rational bubbles never occur in our productive economy.