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No we're getting closer.

I = investors
W = wages
T = tax rate
B = beneficiaries
b = benefit

I * W * T = B * b

Growth rates:
I: Birth rate ~20 years ago + imigration
W: wage growth rate (but limited to growth under the ceiling)
B: growth is the rate of new retirees less the death rate of retirees.
b: rate of inflation and past wage growth

A way to think about this is the difference between location, velocity and accelleration. Each value has a set value (location), a growth rate (velocity), and an accell/decell rate (accelleration).

If nothing is done all variables except taxes are going to grow (there are more workers, more beneficiaries, wages will grow, and benefits will grow), but the rate of change in those growth rates is going in the wrong direction.

The formula above shows how things must change for SS to be solvent.

I * W * T = B * b
is the same as
(I/B) * W * T = b

I/B = ratio of workers to beneficiaries = R

R * W * T = b

Or, the ratio times wages times the tax rate equals the possible per person benefit. So since R is decreasing (and will for the forseable future), W or T needs to make up the difference. If wages were stagnant then T would have to grow at the rate of inflation * 1/(rate of decline in R) - this is clearly unsustainable since VERY high taxes would be reached quickly and the economy would collapse.

But if you use wage growth to compensate then you reach a paradox because b is also impacted by wage growth (although delayed). So if wage growth is required to maintain a benefit wage growth must accellerate to keep ahead of the increasing benefit.
This problem is clearly shown in the long term solvency figures for SS:

http://www.socialsecurity.org/sstw/sstw03-31-00.pdf

You can see that the current economic boom (i.e., high wage growth) has benefited the system in the short term, but in the long term that wage growth means that 'b' will increase faster in the future thus pushing the system further into debt.

This is true even if R were constant, because you would have to rely on wage growth to compensate for inflation, which recreates the paradox.

Conclusion: Ponzi schemes are inherently unstable.

jbw