PAYG pensions, tax-cum-subsidy and A-Pareto efficiency

An overlapping generation’s small open economy with endogenous fertility and time cost of children is analysed to show that the command optimum can be decentralised in a market setting using a PAYG transfer from the young to the old and a tax-cum-subsidy policy (i.e., a linear wage tax on labour income collected and rebated in a lump-sum way within the younger working-age generation). Indeed, the latter instrument stimulates fertility and then reduces the opportunity cost of children. Moreover, by applying the generalised notion of Pareto efficiency introduced by Golosov et al. (2007) in a context of endogenous population, some normative conclusions can be drawn: since only the utilities of those who are actually born are evaluated, we apply the concept of A-efficiency and conclude that when PAYG pensions are in existence, the tax-cum-subsidy policy can effectively be used as an alternative to the child allowance to internalise the externality of children, while also representing an A-Pareto improvement.