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We examine the impact of a stylized pay-as-you-go (PAYGO) Social Security program in an economy of overlapping generations with equilibrium growth. We adopt realistic mortality and other demographic assumptions and allow for the presence or absence of life annuities. In all cases steady-state economies with PAYGO Social Security programs grow more slowly than those without. Also, we find that lifetime expected utilities are lower for existing and future households in steady-state economies with Social Security. We also report the effect of Social Security on the age profile of consumption and explore the effects of longer life expectancy, compensating Social Security program changes, and capital subsidies.