Endogenous Education Duration, Fertility Choice, and Mortality: A Framework for Optimal Population Policy

This paper characterizes optimal education and population policies within a continuous-time overlapping generations (OLG) framework where fertility, schooling duration, and health expenditures are endogenous. In this model, mortality risk is driven by a negative congestion effect from population growth and a positive spillover effect from education duration. We demonstrate that when labor productivity is tied to schooling length, traditional fiscal instruments – such as taxes on newborns – are insufficient to achieve social efficiency. Instead, we propose a multi-faceted policy framework integrating public health provision, education grants, and a corrective poll tax, supported by government-backed student loans to mitigate liquidity constraints. Our analysis yields three optimality conditions. First, public health care must be expanded until its marginal product equals that of private health care. Second, the student grant must be proportional to the marginal rate of substitution between education and health care, but inversely proportional to the interest rate and cohort size. Third, the poll tax must cover public health costs while reflecting the marginal rate of transformation between congestion and private health care. These findings advocate for a strategic policy pivot: shifting from the Pigouvian management of population quantity toward fostering the quality and longevity of human capital.