The Solow-Swan model with endogenous population growth

Gaston Cayssials; Santiago Picasso

doi:10.3934/jdg.2020014

Article Contents

2020, Volume 7, Issue 3: 197-208. Doi: 10.3934/jdg.2020014

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The Solow-Swan model with endogenous population growth

Gaston Cayssials^1, and
Santiago Picasso^2,

1.
Departamento de Métodos Cuantitativos - Facultad de Ciencias Económicas y de Administración, Universidad de la República (Uruguay), Eduardo Acevedo 1139, Montevideo, CP 11200, Uruguay
2.
Instituto de Economía - Facultad de Ciencias Económicas y de Administración, Universidad de la República (Uruguay), Lauro Müller 1921, Montevideo, CP 11200, Uruguay

Received: February 2020

Revised: April 2020

Published: July 2020

Our research was supported by CSIC-UDELAR (project "Grupo de investigación en Dinámica Económica"; ID 881928, Initiation to Research Program - 2017 "Crecimiento económico y dinámica de la población: teoría y análisis empírico"; ID 406)

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Abstract

This paper presents a reformulation of the classical Solow-Swan growth model where a dynamic of the endogenous population is incorporated. In our model, the population growth rate continually depends on per capita consumption. We find that – as in the classic Solow-Swan model – there is a steady state for the capital-labour ratio, which is always lower than that deduced from the original model with zero population growth rate, but it is not necessarily unique. Under certain conditions, there is an odd amount, and only the smallest and the largest are locally stable. Finally, a study of comparative static of stationary states is performed by varying the total factor productivity, and the results are compared with those of the original model. It is found that the effects of exogenous variables on endogenous variables differ from the original model.

Keywords:

Mathematics Subject Classification: Primary: 91B62, 91B55; Secondary: 91B52.

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Figure 1. Evolution of the world population. Period 1750-2100

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Figure 2. World population growth rate. Period 1950-2100

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Figure 3. Speed of convergence

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Figure 4. Even amount of equilibrias

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Figure 5. Possible dynamic solution

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Figure 6. Multiplex equilibria

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