Endogenous population with human and physical capital accumulation

This paper proposes an economic growth model with population growth and physical and human capital accumulation. The physical capital accumulation is built on the Solow growth model (Solow in Q J Econ 70:65–94, 1956). The education and human capital accumulation is influenced by the Uzawa–Lucas model (Uzawa in Int Econ Rev 6:18–31, 1965; Lucas in J Monet Econ 22:3–42, 1988). The population dynamics are influenced by the Haavelmo population model (Haavelmo in a study in the theory of economic evolution. Haavelmo, Amsterdam, 1954) and the Barro–Becker fertility choice model (Barro and Becker in Econometrica 57:481–501, 1989). We synthesize these dynamic forces in a compact framework, applying an alternative utility function proposed by Zhang (Econ Lett 42:105–110, 1993). The model describes a dynamic interdependence between population change, wealth accumulation, human capital accumulation, and division of labor. We simulate the model to demonstrate the existence of equilibrium points and to plot the motion of the dynamic system. We also examine the effects of changes in the propensity to have children, the mortality rate parameter, the propensity to receive education, the human capital utilization efficiency, and the mortality rate elasticity of human capital upon dynamic paths of the system.