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The Solow-Swan model with endogenous population growth

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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  • 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.

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

    Citation:

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

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

    Figure 3.  Speed of convergence

    Figure 4.  Even amount of equilibrias

    Figure 5.  Possible dynamic solution

    Figure 6.  Multiplex equilibria

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