The Chronicle has a lot to say about Thomas Piketty and modern economics. Piketty has done a great job assembling new data sources to document long run trends in inequality. As I understand it, his explanation hinges on how the returns to capital and the rate of economic growth evolve over time. If the return to capital is greater than the rate of economic growth then economic inequality increases as the "rentier" capitalists become relatively richer.
At the University of Chicago, we were taught that human capital is the ultimate capital stock. How does human capital fit into the Piketty framework? When you die, your brain can't be handed to your children. You build up your brain during the investment period and then you earn a flow of income during your productive years. Human capital investment offers both a high return and is risky. If you get hit by tree branch, you lose your productive capacity.
Imagine an economy in which the market risk free interest rate is 3% and the economy is growing by 2%. Piketty would say that because r > g that inequality will rise.
If owners of physical capital invest in other people's human capital, then this would tend to flip the inequality (I believe that increases in the stock of human capital would feed through a Lucas or Romer growth model into a higher rate of g). Why would owners of physical capital invest in people? They would do so depending on the risk/return frontier for the set of all assets they are considering investing in. Imagine if a mutual fund that consists of a 10% stake in 1000 people's future earnings. Some of these people will succeed while others will fail but this portfolio would give the capitalist an incentive to "buy in".
My point is that Piketty's argument hinges on market structure for investing in human capital and the general equilibrium incidence of such investment. The rich can be a catalyst to a rising "g" if there are complete markets for investing in human capital of young people. Jim Heckman should discuss how the Heckman Equation links to Piketty's argument.