Pre-print, Working paper: This paper studies the optimal linear tax-transfer policy in an economy where agents differ in productivity and in genetic background, and where longevity depends on health spending and genes. It is shown that, if agents internalize imperfectly the impact of genes and health spending on longevity, the utilitarian social optimum can be decentralized with type-specific redistributive lump sum transfers and Pigouvian taxes correcting for agents' myopia (leading to undersaving and underinvestment in health), and for their incapacity to perceive the effect of health spending on the resource constraint of the economy (causing overinvestment in health). The second-best problem is also examined under linear taxation instruments. Our main result is that it may be optimal to tax health spending, in particular under a complementarity of genes and health spending in the production of longevity.