Piketty's main theoretical prediction is that a small elite will own all wealth if capitalism is left to its own devices.
We formulate and calibrate a Post-Keynesian model with an endogenous distribution of wealth between workers and capitalists.
The model permits Piketty's corner solution of all wealth held by capitalists; however, it also shows that interior solutions
with a stable, non-zero wealth share of workers, a stable wealth-to-income ratio, and a stable and positive gap between the
profit and the growth rate are determined by the Cambridge equation. Furthermore, simulations show that the model conforms
to Piketty's empirical findings in a transitional phase, in which the wealth share of capitalists rises to over 60 percent,
the wealth-to-income ratio increases, and income inequality rises. Finally, we show that the introduction of a wealth tax
as suggested by Piketty could neutralise the rise in wealth concentration.