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

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, both the industrial revolution and the demographic transition take place much later than it would have been optimal. Our model can be interpreted as a bridge between the literature on endogenous demographic transitions and papers that study welfare issues associated with fertility and human capital decisions.