“Optimal Population and Education” by Julio Davila
If raising and educating children is a private cost to households, while the availability of skilled labor supply resulting from the fertility and educations choices made by households is a public good, then at competitive equilibria typically deliver a suboptimal mix of size and skills of the population. In particular, under such conditions households would underinvest in their children education compared to the optimal level. This is shown to be the case even if the agents are aware of the increase in savings returns implied by the resulting future increase in skilled labor and manage to coordinate to try to exploit this effect. In a setup devoided of altruistic motives, it is shown in this paper that imposing a tax-financed compulsory education is unlikely to implement the optimal steady state, even if the mandatory level of education is the optimal one. Nevertheless, a social security scheme that makes pension payments to a household contingent to its fertility and investment in its children's education allows to implement the first-best steady state. The social security budget is balanced period by period financing pensions through a payroll tax on the increase in children's labor income that is due to the human capital investment effort of their parents.