One of the more common complaints about Piketty’s model of capital inequality in Capital in the 21st Century is that it does not properly account for diminishing returns to the accumulation of capital. Consider Larry Summers’s concern:

[Piketty’s narrative] presumes, first, that the return to capital diminishes slowly, if at all, as wealth is accumulated and, second, that the returns to wealth are all reinvested. Whatever may have been the case historically, neither of these premises is likely correct as a guide to thinking about the American economy today.

If the returns to capital diminish to any significant degree, there may be a manageable limit to how much capital the rich care to accumulate vis-a-vis the poor, and that would complicate the story of ever increasing inequality. By downplaying the DMU of capital, Piketty can claim that the return to capital has been around 4%, on average, for decades.

But doesn’t this claim undermine the strongest progressive objection to privatizing social security? Progressives say that the stock market is an unreliable wealth generator, even in the long-run, for the lower economic classes. But if Piketty is right, this story is likely incorrect. The poor and middle-class could invest and get about a sizeable yearly return, on average, over several decades. As more and more people invest, the returns to capital shouldn’t diminish all that much. Perhaps as millions of people invested, DMU would kick in pretty hard. However, Piketty doesn’t think DMU kicks in when the superrich invest large amounts, so why would it kick in if lots of people invested small amounts?

I’m not an economist, so I need help seeing what’s wrong with the argument. Perhaps the level of risk on Piketty’s view is still high enough to justify the progressive conclusion about privatized pensions. Or perhaps the average rate of return conceals enormous volatility among returns to capital, such that only the rich can ride them out. But surely there’s a tension between Piketty’s model and progressive complaints, right?