This column by J. Bradford Delong is meant to criticize Thomas Picketty, but in the process he has a good summary of Picketty’s work:

Our reversion to the economic and political patterns of the Gilded Age is to be expected as the economies of North America and Europe return to what is normal for a capitalist society.

In a capitalist economy, Piketty argues, it is normal for a large proportion of the wealth to be inherited. It is normal for its distribution to be highly unequal. It is normal for a plutocratic elite, once it has formed, to use its political power to shape the economy in a way that enables its members to capture a large chunk of a society’s income. And it is normal for economic growth to be slow; rapid growth, after all, requires creative destruction; and, because what would be destroyed would be the plutocrats’ wealth, they are unlikely to encourage it.

Later Delong talks about how Keynes might rebut this argument:

Unequal wealth distribution, in this view, produces what Keynes called “the euthanasia of the rentier, and, consequently, the euthanasia of the cumulative oppressive power of the capitalist to exploit the scarcity-value of capital.” The result is an economy with relatively equal income distribution and a polity in which the wealthy have a relatively small voice.

So as the rich corral more and more of the wealth, they become more and more of a minority. Initially the 1% preys on the 99%, then the 0.1% on the 99.9%, and so on. At some point, there is not enough wealth or economic energy remaining for everyone else that the 0.001% need in order to keep accumulating wealth. At that point, they can try to employ some combination of propaganda and force to stay in power. When that breaks down, the balance of the force is restored (sorry, I just saw Star Wars today.) But what happens when the means of production and economic activity is almost entirely automated, and lies in the hands of a tiny minority? What if there is no limit to the force they are able to employ?