# American Institute of Mathematical Sciences

July  2020, 7(3): 197-208. doi: 10.3934/jdg.2020014

## The Solow-Swan model with endogenous population growth

 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

Fund Project: 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)

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.

Citation: Gaston Cayssials, Santiago Picasso. The Solow-Swan model with endogenous population growth. Journal of Dynamics & Games, 2020, 7 (3) : 197-208. doi: 10.3934/jdg.2020014
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##### References:
Evolution of the world population. Period 1750-2100

Source: Max Roser and Esteban Ortiz-Ospina (2019) – "Future population growth". Published online at OurWorldInData.org. Retrieved from: https://ourworldindata.org/world-population-growth [Online Resource].

World population growth rate. Period 1950-2100

Source: United State Census Bureau (September 2018) and United Nations (2019).

Speed of convergence
Even amount of equilibrias
Possible dynamic solution
Multiplex equilibria
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