The main point is that: Wealth to income ratio & rate of return on capital to GDP growth ratio are increasing = Top very few already wealthy are getting wealthier and wealthier = Widening inequality.
 The ratio of wealth to income is rising in all developed countries. Absent extraordinary interventions, we should expect that trend to continue. If it continues, the future will look like the 19th century, where economic elites have predominantly inherited their wealth rather than working for it. The best solution would be a globally coordinated effort to tax wealth.
Highly concentrated income was in the hands not just of the top 10 or 20 percent of households but the top 1, 0.1, or even 0.01 percent. [...]The dynamic towards wealth inequality is built into capitalism rather than any one country's economic policies. [...]In the long run the economic inequality that matters won't be the gap between people who earn high salaries and those who earn low ones, it will be the gap between people who inherit large sums of money and those who don't. [...]Piketty says we are headed for a world of patrimonial capitalism where the Forbes 400 list will be dominated not by the founders of new companies but by the grandchildren of today's super-elite.
Basically, inherited wealth + higher retention of income from the use of factors of production make wealthy folks even wealthier. Looks like an accumulative process that kick-starts entrepreneurship up to a certain threshold but then widens income inequality after that threshold is breached. Finding a fine balance/non-static equilibrium may be the trick now (= at least some form of progressive redistribution without stymieing entrepreneurship). Piketty advocates a global wealth tax.