Quoting here in full the only full paragraph on page 439 of Thomas Piketty’s Capital in the Twenty-First Century  (emphasis added); this paragraph is in a chapter titled “Global Inequality of Wealth in the Twenty-First Century”:
For example, if the top thousandth enjoy a 6 percent rate of return on their wealth, while global wealth grows only at 2 percent a year, then after thirty years the top thousandth’s share of global capital will have more than tripled. The top thousandth would then own 60 percent of global wealth, which is hard to imagine in the framework of existing political institutions unless there is a particularly effective system of repression or an extremely powerful apparatus of persuasion, or perhaps both. Even if the top thousandth’s capital returned only 4 percent a year, their share would still practically double in thirty years to nearly 40 percent. Once again, the force for divergence at the top of the wealth hierarchy would win out over the global forces of catch-up and convergence, so that the shares of the top decile and centile would increase significantly, with a large upward redistribution from the middle and upper-middle classes to the very rich. Such an impoverishment of the middle class would very likely trigger a violent political reaction. It is of course impossible at this stage to be certain that such a scenario is about to unfold. But it is important to realize that the inequality r > g, amplified by inequality in the return on capital as a function of initial portfolio size, can potentially give rise to a global dynamic of accumulation and distribution of wealth characterized by explosive trajectories and uncontrolled inegalitarian spirals. As we will see, only a progressive tax on capital can effectively impede such a dynamic.
(r is the return to capital; g is economic growth)
I’m nearly finished reading Piketty’s tome. I share the above paragraph with you because it condenses and conveys well in less than a single page much of Piketty’s world view. The following list is not meant to be an exhaustive enumeration of all relevant angles of Piketty’s world view (as I understand that view from having now read his monster book). Only some of the most important aspects of that view are indeed here.
(1) Total wealth is not strictly fixed in amount, but its growth is largely independent of human agency. Gigantic convulsions, such as war and Soviet-style communism, can destroy much of it. But in the absence of gargantuan destructive events, wealth reproduces itself, not just from the perspective of the individual but from that of society as a whole.
(2) The return to capital mysteriously grows faster, over long periods of time, than does the economy. How does such differential growth happen? What is it about capital that allows its fortunate owners not only to ‘claim’ all the additional wealth generated by economic growth, but to ‘claim,’ under some circumstances, even more than that every year – to take from non-capitalists (or non-‘rentiers‘) – so that the absolute amount of wealth ‘claimed’ over time by the non-rich shrinks absolutely? While Piketty acknowledges elsewhere in the book that r need not, as a matter of logic, grow faster than g, he’s quite sure that something in the nature of capitalism practically assures that r will almost always grow faster than g.
Yet capitalism has been around for more than 200 years and the living standards of the masses have skyrocketed – arguably by more than have the living standards of the rich. Salvation from starvation and moving into dwellings with hard floors and solid roofs (rather than sleeping on straw and dirt beneath rodent-infested and highly flammable thatched roofs) is a far greater improvement in absolute living standards than is traveling in a first-class seat on a 747 rather than in a first-class cabin on a sailing ship. So why is capitalism waiting to start its practically inevitable impoverishment of the masses? What’s with the delay? Why do even the poorest people in capitalist society continue to grow absolutely wealthier (measured as it counts: in their ability to consume real goods and services)? Is it because we’ve had the good fortune to be blessed since capitalism’s dawn by wealth-destroying calamities such as world wars?
(3) While Piketty’s figures of a 2 percent rate of economic growth combined with a 6 percent rate of return on the wealth of the rich would indeed, over 30 years, mean a reduction in the absolute amount of wealth enjoyed by the bottom 999th (out of 1,000) portion of the global population, his alternative rate of return on capital of 4 percent would still allow the bottom 999th portion of the global population to enjoy an increasing absolute amount of wealth as time passes. The share of wealth of the 999th portion of the people would fall relative to the share of the top one-thousandth portion of the people – but not the absolute amount. Yet Piketty writes as though a 6 percent rate of return on capital and (alternatively) a 4 percent rate of return on capital both bring about a large upward redistribution of wealth from the middle and upper-middle classes to the very rich. Indeed, even the 4-percent figure causes “impoverishment” even of the middle-class. That is, in Piketty’s telling, capitalism can cause people to simultaneously grow absolutely richer and to suffer impoverishment.
(4) Piketty has a peculiarly strange “then a miracle occurs ” step in his analysis. He argues that one justification for powerful efforts to redistribute incomes and wealth more equally is that the rich are disproportionately likely to abuse power for their own greedy and socially destructive ends. So what to do? Answer: increase government’s power! Qu’est-ce que c’est?! (Piketty is like too many economists: ignorant of public-choice.)
(5) Piketty – both in his calling for a progressive tax on capital and in his reliance on the r > g formula – largely ignores any disincentives that such taxes inject into the market processes that generate economic growth.