Equilibrium and Optimal Fertility with Increasing Returns to Population and Endogenous Mortality

We present a general equilibrium dynamic model that characterizes the gap between optimal and equilibrium fertility and investment in human capital. In the model, the aggregate production function exhibits increasing returns to population arising from specialization but households face the standard quantity-quality trade-off when deciding how many children they have and how much education these children receive. In the benchmark model, we solve for the equilibrium and optimal levels of fertility and investment per child and show that competitive fertility is too low and investment per child too high. We next introduce mortality of young adults in the model and assume that households have a precautionary demand for children. Human capital investment raises the likelihood that a child survives to the next generation. In this setup, the model endogenously generates a demographic transition but, since households do not internalize the positive effects of a larger population on productivity and the negative effects of human capital on mortality, the demographic transition takes place much later in the equilibrium solution compared with the efficient solution. The efficient solution produces a demographic transition 10000 years earlier than the equilibrium solution. Our model can be interpreted as a bridge between the literature on endogenous demographic transitions and the scarce papers that study welfare issues associated with fertility and human capital decisions. Moreover, our results can be used to shed light on understanding demographic transitions in currently developing countries and to formulate policy recommendations to enhance welfare during these transitions.