This paper examines the implications of adverse selection in the private annuity market for the pricing of private annuities and the consequest effects on consumption and bequest behavior. With privately known heterogeneous mortality probabilities, adverse selection causes the rate of return on private annuities to be less than the actuarially fair rate based on population average mortality. However, a fully funded social security system with compulsory participation can offer an implied rate of return equal to the actuarially fair rate based on population average mortality. Thus, since social security offers a higher rate of return than private annuities, consumers cannot completely offset the effects of social security by transacting in the private annuity market. Using an overlapping generations model with uncertain lifetimes, we demonstrate that the introduction of actuarially fair social security reduces the steady state rate of return on annuities. In addition, it raises the steady state levels of average bequests and average consumption of the young, if factor prices are fixed exogenously. The steady state national capital stock rises or falls according to the strength of the bequest motive.