Endogenous differential mortality, non monitored effort and optimal non linear taxation

This paper studies the normative problem of redistribution among individuals who can influence their longevity through a non-monetary effort but have different taste for effort. As benchmarks, we first present the laissez-faire and the first best. In the first best, the level of effort is always lower than in the laissez-faire as the social planner takes into account the consequences of higher survival on the budget constraint. However, since we suppose that effort is private and non-monetary (like exercising), it is reasonable to think that the social planner has no control over it. Thus, we modify our framework and assume for the rest of the paper that effort is determined by the individual while the social planner only allocates consumptions. Under full information with non monitored effort, early consumption is preferred to future consumption and the high-survival individual obtains higher future consumption. Under asymmetric information, the distortion is identical for the low-survival individual while the direction of the distortion for the high-survival individual is ambiguous. We finally show how to decentralize these allocations through a perfect annuity market and (positive or negative) taxes on annuities.