Optimal tax policy and expected longevity: a mean and variance approach

This paper studies the normative problem of redistribution between agents who can influence their survival probability through private health spending, but who differ in their attitude towards the risks involved in the lotteries of life to be chosen. For that purpose, we develop a two-period model where agents's preferences on lotteries of life can be represented by a mean and variance utility function allowing, unlike the expected utility form, some – agent-specific – sensitivity to what Allais (1953) calls the 'dispersion of psychological values'. It is shown that if agents ignore the impact of their health expenditures on the return of their savings, the decentralization of the first-best optimum requires not only intergroup lump-sum transfers, but, also, group-specific taxes on health spending. Under asymmetric information, we find that a subsidy on savings is optimal, whereas group-specific taxes on health spending are of ambiguous signs.