Piketty is concerned that the return on capital is greater than the rate of economic growth, concludes that this will necessarily involve an increasing concentration of economic power among a select few, and recommends that the coercive power of the state to tax wealth (not income but wealth, i.e. an expropriation) is the solution. The first argument that r>g is debatable but with good evidence on both sides. The second argument is also debatable but for different reasons (all systems tend to concentrate power but whether there is a particular risk arising from r>g is unclear). The third argument, the recommendation for wealth taxes is widely discredited on an empirical basis even though it is a policy fondly sought in some ideological corners.
Alex Tabarrok brings an insightful alternative to the table in Two Surefire Solutions to Inequality by Alex Tabarrok. He starts from the premise that Piketty's argument is well founded. If you accept that inequality is an evil that needs to be eradicated and that it needs to be eradicated via government policy, he points out that there are alternative policies to that of simply taxing away the wealth.
The War on Poverty has proceeded for fifty years, touching at least three generations. It remains unclear to what extent that war has been successful.
Taxing wealth has very real and well documented risks. How long would it take for such a tax to reduce income inequality? No one is saying, but likely on the same order of time as the War on Poverty, particularly given the concerns about the negative consequences of wealth taxes. In the same time frame, with much greater certainty of results and much less risk, there is an alternative policy.
Here is a surefire solution to inequality–Increase fertility among the rich. If the rich had more children, capital would grow more slowly across the generations and perhaps not at all. If r=4 and g=2 then capital doubles as a share of the economy in 35 years (using the rule of 70). That figure is actually too low as it assumes that the wealthy save all of their capital income but let’s stick with 35 years and call that a generation. Wealth per rich person, however, only doubles if every wealthy family has just 2 children. If every wealthy family has 4 children, wealth per person doesn’t increase and so inequality does not increase even when r>g. If the wealthy consume about 20% of their capital income (still a very high savings rate) and have just 3 children then again we have approximate balance and no increase in inequality over the generations. With a more reasonable figure on r-g or with more children, wealth per person actually declines.This is a policy grounded on simple maths. There is a second policy, which is likely just as beneficial (and which Tabarrok does not mention) - cut the fertility rate among the poorest.
Now anything that smacks of demographic management has the whiff of eugenics and is anathema to anyone with an ounce of fondness for life and liberty. But Tabarrok's recommendation has a lot to support it. It is necessarily true. It averts the negative consequences of expropriation. It sustains economic growth. It improves life quality for everyone. Why wouldn't you do this (other than the philosophical objection to intrusive government, a concern little apparent among Piketty supporters)?
Obviously, this is not about outcomes. An alternative policy that is more likely to work beneficially for everyone is not the objective. The objective appears to be to punish those that the supportive clerisy envy and to increase the scope of centralized power with which they might be involved. That's a harsh reading, but I am afraid not far from the likely truth. Tabarrok's alternative recommendation, which I assume is offered in jest, highlights the logical paradox of the Piketty supporters and helps shed light on real objectives versus the feel good bromides that have been advanced.