# Population Economics Fall 2005 by yurtgc548

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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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