PAYG pensions and fertility drop: some (pleasant) arithmetic

This paper explores whether the common belief that the currently observed fertility drop is a threat (or, conversely, the invoked fertility recovery is beneficial) for PAYG pensions is really always validated by the basic accounting of the PAYG pension budget. It is shown, through a simple arithmetic, that, rather surprisingly, in the long run a fertility drop may be beneficial, while, conversely, a fertility recovery may be harmful for pensions, under rather realistic conditions as regards both fertility changes and time costs of childrearing. Furthermore, this result also holds a fortiori in the short run.