This paper examines the steady-state welfare and comparative statics implications of fair social security in an overlapping generations model with uncertain lifetime. The model is designed to capture the effects of lifetime uncertainty extending over the individual's entire lifespan, the effects of intentional and unintentional bequests, and the effects of the earning profile. He shows that the welfare effects depend on the size of the benefits and the structure of the social security tax. In particular, even fair social security may have negative welfare implications if the underlying tax structure is ill-designed. Some comparative statics implications are analyzed.