Endogenous Population Dynamics and Economic Growth with Free Trade between Countries

This paper builds a model to deal with dynamic interdependence between different countries' birth rates, mortality rates, populations, wealth accumulation, and time distributions between working, leisure and children caring. The model shows the role of human capital, technological and preference changes on national differences in birth rates, mortality rates, time distributions, population change, and wealth accumulation. The economic mechanisms of wealth accumulation, production and trade are based the Solow growth model and the Oniki-Uzawa trade model. We use the utility function proposed by Zhang to describe the behavior of households. We model national and gender differences in human capital, propensity to have children, propensity to use leisure time, and children caring efficiency. We describe the dynamics of global economic growth, trade patterns, national differences in wealth, income, birth rates, mortality rates, and populations with differential equations. We simulate the model to show the motion of the system and identify the existence of equilibrium point. We also examine the effects of changes in the propensity to have children, the propensity to save, woman's propensity to use leisure, woman's human capital, and woman's emotional involvement in children caring on the dynamics of the global and national economies.