Issues surrounding the social security system in the U.S. have generated a large volume of academic research as well as wide public discussion. When the system was first started, the main public policy objective was to provide funds for consumption during old age. Since then, economists and policy makers have raised concerns over the adverse effect of social security on private saving, its negative impact on the labor supply, the incentive it creates for early retirement, and the overall impact on the lifetime welfare of individuals. The purpose of this research is to develop and calibrate a dynamic, stochastic general equilibrium model to address issues like these concerning the social security system. The focus will be to estimate the quantitative impact of the social security system on lifetime welfare and on the capital stock under lifetime uncertainty, liquidity constraints, and individual income risk. Numerical methods will be used to solve a finite horizon, dynamic programming problem and to computed competitive equilibria of the model. This research will result in useful new insights about designing an optimal social security system.