On Existence, Efficiency and Bubbles of Ramsey Equilibrium with Borrowing Constraints
Robert A. Becker
Indiana University Bloomington - Department of Economics
Cuong Le Van
Université Paris I Panthéon-Sorbonne
Aix-Marseille University - Aix-Marseille School of Economics
NOVEMBER 11, 2012
We address the fundamental issues of existence and efficiency of an equilibrium in a Ramsey model with many agents, where agents have heterogeneous discounting, elastic labor supply and face borrowing constraints.
The existence of rational bubbles is also tackled. In the first part, we prove the equilibrium existence in a truncated bounded economy through a fixed-point argument by Gale and Mas-Colell (1975). This equilibrium is also an equilibrium of any unbounded economy with the same fundamentals. The proof of existence is eventually given for an infinite horizon economy as a limit of a sequence of truncated economies. Our general approach is suitable for applications to other models with different market imperfections. In the second part, we show the impossibility of bubbles in a productive economy and we give sufficient conditions for equilibrium efficiency.
Number of Pages in PDF File: 44
Keywords: Ramsey equilibrium, existence, efficiency, bubbles, heterogeneous agents, endogenous labor supply, borrowing constraint
JEL Classification: C62, D31, D91, G10
Date posted: February 13, 2012 ; Last revised: December 1, 2012