Optimal population and education

If raising and educating children is a private cost to households, while the availability of skilled labor supply resulting from the households' fertility and education choices is a public good, then competitive equilibria typically deliver a suboptimal mix of size and skills of the population. In particular, households would underinvest in their children education compared to the optimal level. This is the case even if households are aware of the increase in savings returns implied by a higher supply of skilled labor and manage to coordinate to try to exploit this effect. In a setup devoid of altruistic motives, this paper shows that a tax-financed compulsory education is unlikely to implement the optimal steady state, even if the mandatory level of education is the optimal one (the system of equations is overdetermined). Nevertheless, a pensions scheme that makes payments contingent to the household fertility and investment in its children's education can implement the first-best steady state. The pension scheme is balanced period by period by financing pensions through a payroll tax on the increase in children's labor income resulting from their parents' human capital investment.