Quantity-quality trade-off of children and school finance

To understand income inequality and intergenerational mobility of income, it is essential to account for the fertility differential between the poor and the rich because it affects the human capital investment through the quantity-quality trade-off of children. We develop a dynamic general equilibrium in which parents choose the quantity of children, transfer a preschool ability to their children, determine the quality of children by choosing private expenditures on basic education (in addition to public expenditures), and leave a bequest that could be used to finance college education. We find that incorporating fertility behavior, especially differential fertility is crucial to capture human capital formation in the U.S. economy. We also analyze the impact of basic education subsidies and college subsidies on welfare, inequality, and intergenerational mobility.