The Ramsey Model in Discrete Time and Decreasing Population Growth Rate

20 Pages Posted: 28 Mar 2014

See all articles by Juan Gabriel Brida

Juan Gabriel Brida

Universidad de la República

Gastón Cayssials

Universidad de la Republica

Juan Sebastián Pereyra

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

Date Written: January 8, 2014

Abstract

This paper extends the Ramsey-Cass-Koopmans growth model of optimal capital accumulation in discrete time by introducing a generic population growth law that satisfies the following properties: population is strictly increasing and bounded, and the population growth rate is decreasing to zero as time tends to infinity. We show that the optimization problem admits a unique solution that can be characterized by the Euler equation. A closed-form solution of the model is presented for the case of a Cobb-Douglas production function and a logarithmic utility function. In contrast to the original model, the solution is not always monotone.

Keywords: Ramsey economic growth model, discrete time, decreasing population growth rate, closed-form solution

JEL Classification: C62, O41

Suggested Citation

Brida, Juan Gabriel and Cayssials, Gastón and Pereyra, Juan Sebastián, The Ramsey Model in Discrete Time and Decreasing Population Growth Rate (January 8, 2014). Available at SSRN: https://ssrn.com/abstract=2417005 or http://dx.doi.org/10.2139/ssrn.2417005

Juan Gabriel Brida

Universidad de la República ( email )

Av. 18 de Julio
Montevideo, 1968
Uruguay

Gastón Cayssials

Universidad de la Republica ( email )

Gonzalo Ramirez 1926
Montevideo, 11200
Uruguay

Juan Sebastián Pereyra (Contact Author)

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

Register to save articles to
your library

Register

Paper statistics

Downloads
244
Abstract Views
1,115
rank
123,560
PlumX Metrics