PAYG pensions, tax-cum-subsidy and optimality

Using a simple OLG small open economy with endogenous fertility we show that the command optimum can be decentralised in a market setting using both a PAYG transfer from the young (old) to the old (young) and a tax-cum-subsidy (subsidy-cum-tax) policy, to redistribute within the working age generation. The latter instrument, in fact, reduces (increases) the opportunity cost of bearing children and, hence, stimulates (depresses) fertility. The policy implications are straightforward: when PAYG transfers exist and child rearing is time consuming, a tax-cum-subsidy (subsidy-cum-tax) policy can be used to internalise the externality of children, while also representing a Pareto improvement.