The Solow Model in Discrete Time and Decreasing Population Growth Rate

Abstract

This paper reformulates the neoclassical Solow model of economic growth in discrete time by introducing a generic population growth law that verifies the following properties: 1) population is strictly increasing and bounded; 2) the rate of growth of population is decreasing to zero as time tends to infinity. We show that in the long run the capital per worker of the model converges to the non-trivial steady state of the Solow-Swan model with zero labor growth rate. In addition we prove that the solutions of the model are asymptotically stable.

Keywords: Solow model, discrete time, population model

JEL Classification: C62, O41