Beyond Piketty musings

Piketty takes a fairly long view of capitalism, but is it long enough? Here is what I am starting to think about:

During Piketty's roughly two hundred year analysis the world (and capitalists) faced a positive second derivative growth curve. In this environment there should be increasing demand for capital and thus support for r > g. (There are elasticities to consider in all this).

One of my research projects suggests we are now entering a negative second derivative growth period for the first time since the Industrial Revolution. We are past the inflection point. If true, surely the demand for capital will slow, and I wonder if the support for r > g will not also fade.

Eventually, later this century if my model holds at all, growth will go negative first derivative. Then demand for capital will surely shrink. And what will happen to capitalists then is unclear to me.

I guess it is time for some maths; I do not have time right now, but wanted to see if anyone else has thought through these scenarios.