Varying Life Expectancy and Social Security

Life expectancy di¤ers across socio economic groups and according to indi-vidual health endowments. In this paper, we shall argue that the scarcity of studies on the design of PAYG system with heterogenous life expectancy is due to simplifying assumptions. As a matter of fact, most applied papers addressing normative questions make a double assumption of additivity (ad-ditively separable individuals utility functions across time and a utilitarian social welfare function). In this case, the allocation within a given period of time is independent of the allocation in other periods of life. In this paper, the cardinal individual utility function is given by a (non linear) transfor-mation of an additive utility function. The social optimum is obtained when individuals living longer retire later and consume less than short lived indi-viduals. In a second best framework, we \u85nd that the \u85rst best optimum cannot be implemented. Every agents bene\u85ciate from a lower consumption when retired. Agents with higher life expectancy are left with higher level of instantaneous post-retirement consumption. Still pre-retirement consump-tion is decreasing with life expectancy. Finally, in order to implement this second best optimum, the Social Security design introduces a positive tax on continued activity but only after individualsoptimal retirement age.