The overlapping generations model pioneered by Paul Samuelson is used to address an issue in Social Security. In the 1983 Social Security reform, Congress chose to build a substantial trust fund, with principal and interest both to be used for later benefits. That is, Congress chose payroll tax rates higher than pay-as-you-go levels while the baby-boomers were in the labor force in order to have payroll tax rates lower than pay-as-you-go while the baby-boomers were retired. The impact on national capital of these higher payroll taxes, with the implied trust fund buildup, has been controversial. The impact depends on the response of the rest of the government budget as well as the responses of individuals to these government actions. It also depends on the effects of future tax changes as well as initial tax changes. This paper explores a simple model distinguishing two types in each cohort - life-cycle savers and nonsavers, and allowing an income tax change to offset a fraction of the additional revenue from any payroll tax change. Analyzing a permanent trust fund increase, even if the unified budget is always balanced, the trust fund buildup increases national capital initially when payroll taxpayers have a lower propensity to save out of payroll taxes than income taxpayers do out of the income tax, as is plausible. The long run impact on capital depends on the fraction of the payroll tax revenue increase that is offset by an income tax decrease. Keywords: Social Security, government budget, national savings. JEL Classifications: H55, H20.