This paper aims at investigating whether or not a utilitarian social planner should subsidize longevity-enhancing expenditures in an economy with a pay-as-you-go pension system. For that purpose, a two-period overlapping-generations model is developed, in which the probability of survival to the second period can be raised by private health spending. Focusing on the steady state, it is shown that the sign of the optimal subsidy on health expenditures tends to be negative when the replacement ratio is sufficiently large. Moreover, the optimal health subsidy is also shown to depend significantly on individual preferences and on the longevity production process.