Title: The discrete-time Ramsey model with a decreasing population growth rate: stability and speed of convergence

Authors: Juan Gabriel Brida; Gastón Cayssials; Juan Sebastián Pereyra

Addresses: Departamento de Métodos Cuantitativos, Universidad de la República, Uruguay ' Departamento de Métodos Cuantitativos, Universidad de la República, Uruguay ' ECARES - Solvay Brussels School of Economics and Management, Universite Libre de Bruxelles, Belgium

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 characterised by the Euler equation. It is shown that there is a unique non-trivial equilibrium, which is a saddle point. In addition, the speed of convergence to the steady state is characterised.

Keywords: decreasing population; population growth rate; discrete time models; Ramsey growth model; economic growth; stability; convergence speed; modelling; optimal capital accumulation; 3D dynamical systems; Euler equations; saddle point.

DOI: 10.1504/IJDSDE.2016.079027

International Journal of Dynamical Systems and Differential Equations, 2016 Vol.6 No.3, pp.219 - 233

Received: 30 Oct 2015
Accepted: 11 Jan 2016
Published online: 09 Sep 2016 *

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