The debt burden calculated over the complete sequence

The burden of a debt on a generation in any sensible social welfare function is proportional to the proportional reduction in that generation's consumption needed to finance the debt, and all generations are on an equal footing. When r < g, you can boost the relative well-being of a current generation at a very low cost in terms of the reduced well-being of a far-future generation. So even though debt is not a free lunch when r < g, it is a very, very cheap lunch indeed.

Brad, you social welfare function is estimated over the complete generation cycle. So your solution, r < g, is the solution over the entire generational cycle. If not you are using the expectation function with a spectrally incomplete sample and you cannot equate short and long term.

Instead, look at the stable rate of real interest rate, interest charges divided by debt You will see that Congress pays 2.5%, more or less, even though the ten year is only 1.75% or so. Real growth, after all the revisions, is now slightly under 2% so g< r.

You social welfare function is easy to predict.  Boomers had an overlap meeting with the WW2 generation, and will soon have now overlap meeting with millennials, some 30 years later. That is the spectral limit on your welfare function, you need the complete generation series to estimate it.  We finally calculate the boomer welfare function in a few years, after our MMT moment. Unitl then, your best bet is to get spectral completeness, get the MMT done wisely soon, for example.

The better Hilbert model is one where guests are moving in and guests are moving out. You are logistically limited to one move in one day, maximum.  As one queue backs up, or seems to, they will band together and send one representative to handle multiple transaction. Both sides do it, entries and exists. So we still get the recursive encapsulation of potential unlimited countables. What we change is items per basket, and what we ask is if the basket size is bound.  Or, can entries/exits come to a value that maximizes its own round off error, it is least likely to be semi repeatable and rarely needs requantization of basket sizes.  Least likely to be semi repeatable is maximum entropy.

Or something like that. When we estimate the entry and exit generators we have a finite Hilbert system, it selects the closest fractional approximation to the ratio of entry to exit, which should lead to maximum liquidity.  Sandbox theory, filling in the horizontal lines on Hayek's triangle.

But the main point is we have spectral bound, we need to change basket sizes between generations, usually twice per generation.  And the samples are symmetric and balanced only after two tries.  The boomers will likely cheat a bit, and the millennials do same on their second go around. But we have to compute the basket size millennials need to get a life cycle, so they can unfold their finite set of recursively finite baskets.  The goal is to do this twice as often, cut the volatility in half, do better basket planning.