Population Change with Endogenous Birth and Mortality Rates, Wealth Accumulation, and Renewable Resource Change

This paper is concerned with dynamic interactions between population change, wealth accumulation, and resource dynamics. Our model synthesizes economic mechanisms of some well-known models within a compact framework. Wealth accumulation is built on the Solow growth model. Dynamics of birth and mortality rates are influenced by the Haavelmo population model and the Barro-Becker fertility choice model. Resource change is modelled on the basis of some growth models with renewable resources. The available time is distributed between work time, leisure time and time of children fostering. We synthesize these dynamic forces in a compact framework by applying an alternative utility function proposed by Zhang. The two-sector model describes a dynamic interdependence between population change, wealth accumulation, and resource dynamics with endogenous time distribution in a perfectly competitive market. We simulate the model to demonstrate existence of equilibrium points and motion of the dynamic system. We also examine effects of changes on the motion of the economic system in the propensity to have children, the propensity to consume goods, the propensity to consume resources, the resource capacity, human capital, and time required for children fostering.