Existence, uniqueness, and stability of equilibrium in an overlapping-generations model with productive capital

Abstract

This paper analyzes the existence, uniqueness, and stability of a steady-state equilibrium in an overlapping-generations model with productive capital. It is shown that for any feasible set of well-behaved preferences there exists a production function that satisfies the Inada conditions under which the economy experiences global contraction and the steady-state equilibrium is characterized by the absence of production and consumption. The study establishes a strengthened Inada condition which is necessary to preclude global contraction. and sufficient conditions for the existence of a unique and globally stable non-trivial steady-state equilibrium.