Table 1 Social Security in a Two-Period World Period Number of young workers Earnings per young worker Taxes paid per young worker Total taxes paid Number of old retirees Benefits to old retirees Taxes paid by old retirees Rate of return 1 100 $20,000 --- --- 2 105 $21,000 $2,100 $220,500 100 $2,205 ∞ 3 110 $22,050 $2,205 $242,550 105 $2,310 $2,100 10% 4 115 $23,153 $2,315 $266,225 110 $2,420 $2,205 10% 5 121 $24,310 115 $2,315 - ∞ Individuals live for two periods, and then die. They are young in the first period, and old in the second. When they are young, they work and pay a tax to support Social Security. When they are old, the collect Social Security. The population grows over time, in this case by 5% per period. Real wages are assumed to rise at 5% as well, due to increased productivity. There is no Social Security program in year 1. The young do not have to pay Social Security taxes. Social Security is started as an unfunded program in year 2, with a 10% payroll tax on the current young. The taxes collected are $220,500; $2,100 per person x 105 young people. This is divided among the 100 elderly. Because the elderly did not pay into the system, yet they collect benefits, their rate of return is infinite. The initial generation (elderly who did not pay) is the big winner from the unfunded system. In year 3, the elderly are those who were young and paying taxes in year 2. Recall they paid in $2,100 each. They now receive $2,310 in benefits, 10% more than they paid in. This return comes from higher total tax collections due to wage growth and population growth. If population and wage growth are high, the rate of return to “middle generations” can be large. Now imagine that in year 5, the young workers scrap the system. They pay no taxes. The elderly in year 5 (who were young in year 4) suffer as a consequence. They paid into the system but got nothing out of it.