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

16 Pages Posted: 22 Oct 2015

See all articles by Juan Gabriel Brida

Juan Gabriel Brida

Universidad de la República

Gaston Cayssials

Universidad de la Republica - Facultad de Ciencias Económicas y de Administración

Juan Sebastián Pereyra

Universidad de la República - Facultad de Ciencias Económicas; El Colegio de México

Date Written: October 22, 2015

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.

Keywords: Ramsey economic growth model, discrete time, decreasing population growth rate

JEL Classification: C62, O41

Suggested Citation

Brida, Juan Gabriel and Cayssials, Gaston and Pereyra, Juan Sebastián, The Discrete-Time Ramsey Model with a Decreasing Population Growth Rate: Stability and Speed of Convergence (October 22, 2015). Available at SSRN: https://ssrn.com/abstract=2677716 or http://dx.doi.org/10.2139/ssrn.2677716

Juan Gabriel Brida

Universidad de la República ( email )

Av. 18 de Julio
Montevideo, 1968
Uruguay

Gaston Cayssials (Contact Author)

Universidad de la Republica - Facultad de Ciencias Económicas y de Administración ( email )

Gonzalo Ramirez 1926
Montevideo, 11200
Uruguay

Juan Sebastián Pereyra

Universidad de la República - Facultad de Ciencias Económicas ( email )

Gonzalo Ramírez 1926
CP 11200 Montevideo
Uruguay

El Colegio de México ( email )

Gonzalo Ramírez 1926
CP 11200 Montevideo
Uruguay

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