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Population Economics Fall 2005

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					Population Economics
      Fall 2007
Productivity Growth Can Trump
       Aging in a Pure
   Pay-As-You-Go System
     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
 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
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)
       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
The Needed Tax Rate is the Replacement
     Rate * the Dependency Rate



       t = RR * DR

  RR is Determined by Economics
 DR is Determined by Demography
     Convert to Growth Rates
• The needed growth in the tax rate is (gt)


• gt = gRR + gDR
If the Repacement Rate is Fixed
• the Needed Tax Rate Will Grow with the
  Dependency Rate


• GRR = 0 means that

• Gt = GDR
         But RR is Not Fixed
• RR is equal to b/w therefore

• gRR = gb – gw

• gw depends on the rate of growth of labor
  productivity

• If gw is greater than gb, RR will fall
 The needed tax rate depends of the
 growth rate of wages (productivity)


• gt = gRR + gDR

• gt = (gb – gw) + gDR

• gt = (gb +gDR) - gw
 The tax rate need not grow if:

• gw = (gb +gDR)

• Or productivity growth equals the
  growth in the average benefit plus
  the growth in the Dependency
  Ratio
The End

				
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