Human capital and pensions with endogenous fertility and retirement

We study an OLG model with child policies and a PAYG pension with endogenous retirement and fertil- ity. The result of the planned economy is compared to the decentralized competitive equilibrium deriving optimal policies. We show that in the presence of a PAYG pension system, the optimal policy mix includes an education subsidy and a subsidy for the supply of labor in old age. Fertility should be taxed or incen- tivized depending on whether there is full or partial retirement, and on the parameters. We focus on the parameter reflecting the deterioration of human capital and show that a child tax may be required.