The Discrete-Time Ramsey Model with a Decreasing Population Growth Rate: Stability and Speed of Convergence

Abstract

This paper studies an extension of the Ramsey growth model of optimal capital accumulation in discrete time by departing from the standard assumption of constant population growth rate. More concretely, this rate is assumed to be decreasing over time and a general population growth law with this characteristic is introduced. In this setup, the model can be represented by a three dimensional dynamical system which admits a unique solution characterized by the Euler equation. It is shown that there is a unique nontrivial equilibrium which is a saddle point. In addition, the speed of convergence to the steady state is characterized.