With an overlapping generations model, Williamson and Jones [1983] demonstrated that the long-run savings ratio in the U.S. was not affected by the introduction and the reform of the unfunded social security system. This paper extends their model by including a production sector, endogenous labor supply and a wage profile. Simulations show that incorporating general equilibrium and (exogenous) leisure is sufficient to generate a declining savings ratio in the steady state. Reforms of the social security system are evaluated in welfare terms. The new features of the model may significantly change the sign and the magnitude of the welfare gains for steady state generations.