Social Security and uncertain lifetime

In this paper, we study the optimal pension design when individuals are di¤ering in their length of life. Life duration takes the form of a survival probability (in this sense life expectancy is uncertain) and individuals may have a higher / lower survival probability depending on some random characteristic (health, gender, socio-professional category). The individuals utility function is of multiplicative form with per period consumption and age of retirement as function arguments. The multiplicative form accounts for the possible risk aversion toward length of life of this individual. We \u85rst transform the individuals lifetime utility into an expected utility function and we then derive the problem of a utilitarian social planner who would like to compensate individuals for di¤erent life expectancies. In a \u85rst best setting where the social planner is able to observe perfectly survival probabilities, the high type individual will consume less at each period and retire later than the low-survival probability individual. In a second best framework, we \u85nd the usual result of no distortion at the top for the high survival probability individual while there exists a tax on consumption in earlier periods of life for the low type individual; still there is no tax on work for this individual. JEL classi\u85cation