1. Population Economics Fall 2012 Productivity Growth Can Trump Aging in a Pure Pay-As-You-Go System

2. How a Pure Pay-As-You-Go System Works Every Year Tax Collections = Benefits Paid Taxes =Total Wages (W) * tax rate (t) Benefits = Average Benefit (b)* Retirees (R) W*t = b*R

3. Assuming (b) is Fixed, How High Must the Tax Rate (t) be? W*t = b*R Therefore: t = (b*R)/Wages The tax rate must be equal to the ratio of Benefits to Total Wages

4. Total Wages Equals the Average Wage times the Number of Workers W = w * N Thus we can calculate the needed tax rate as: t = (b*R) / (w *N)

5. Now Rearrange Terms t = (b*R) / (w*N) becomes t = (b/w) * (R/N) Where b/w is the Replacement Rate And R/N is the Dependency Rate

6. The Needed Tax Rate is the Replacement Rate * the Dependency Rate t = RR * DR RR is Determined by Economics DR is Determined by Demography

7. Convert to Growth Rates The needed growth in the tax rate is (g t ) g t = g RR + g DR

8. If the Repacement Rate is Fixed the Needed Tax Rate Will Grow with the Dependency Rate G RR = 0 means that G t = G DR

9. But RR is Not Fixed RR is equal to b/w therefore gRR = g b – g w g w depends on the rate of growth of labor productivity If g w is greater than g b, RR will fall

10. The needed tax rate depends of the growth rate of wages (productivity) g t = g RR + g DR g t = (g b – g w ) + g DR g t = (g b +g DR ) - g w

11. The tax rate need not grow if: g w = (g b +g DR ) Or productivity growth equals the growth in the average benefit plus the growth in the Dependency Ratio

12. The End