Deinonychus antirrhopus

You basically have it. Each benefit factor will assymptote to zero. However, the limit will NOT be for Social Security to go to zero. For illustrative simplicity, let's ignore the bend points, AIME[j] is the AIME in year j, PIA[j] is the Primary insurance amount in year j, rw is the real wage, i is the inflation rate, and let's let P be the bend factor.

Right now, basically, PIA[j]=P*AIME[j]=P*AIME[j-1]*(1+rw)*(1+i), since AIME[j]=AIME[j-1]*(1+rw)*(1+i)

In words, the PIA increases by inflation and because of a real wage change. if rw=0, then the PIA increases by P*(1+i) in any given year.

The President's commission would create a series I'll call P[j] which is the bend factor in year j. P[j]=P[j-1]/(1+rw) by definition.

The "President's" plan is as follows: (substituting in the recursive P[j] and AIME[j] formulas)

PIA[j]=P[j]*AIME[j]=P[j-1]*AIME[j-1]*(1+i)

Now, notice that PIA[j-1]=P[j-1]*AIME[j-1]

Substitution shows that PIA[j]=PIA[j-1]*(1+i), what I'll call the PIA recursion formula.

Or, in words, benefits are constant in real terms. I'm pretty sure it works, although I did compose this entire argument in this tiny text box.

Separately, you can show that keeping the bend points increasing with the wage index is exactly the way to do it to have the overall benefits increase with the CPI, so the progressivity of the PIA formula is not a problem.

Notice that even though P[j] goes to zero as j goes to infinity, PIA[j] increases without bound. That's because AIME increases without bound, and rw > i. In words, the benefit as a fraction of income goes to zero, incomes go to infinity, the benefit as an absolute is kept in place at the real benefit level in place when the system began.

Kind of a cool way to do it, actually, which is perhaps why I totally missed it at first. You have to dig into the benefit scheme to really see how it all fits together to make the end result come out right.

And, of course, none of this negates your previous posts noting that the CPI likely overstates cost-of-living increases, so when we say the "real benefit level is constant" here, that's a bit of a misnomer.

Hope that helps. I do feel very guilty for screwing the pooch on this one initially. The Lowest Deep and some others are in there with me, however, and I haven't seen very many commentators be error free on these details.

Thanks Victor, good work. This part was what triggered the "Ah-ha!" moment,

AIME[j]=AIME[j-1]*(1+rw)*(1+i)

As soon as I saw that it all fell into place. By dividing through by (1+rw) all that is left is the real growth rate.

I wish I had time to look at it more closely, but something more important came up...the kids Birthday....well that and I never pass up a chance to go to Pink's Hot Dogs. The Pastrami Burrito Dog (two hot dogs in a flour tortilla with pastrami, chili, swiss cheese and onions is to die for...literally if you eat them too often.

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