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 determined by the Cambridge equation. Furthermore, simulations show that the model confirms to Piketty's empirical findings in a transitional phase, in which the wealth share of capitalists rises to over 60%, the wealth-toincome ratio increases, and income inequality rises. Finally, we show that the introduction of a wealth tax as suggested by Piketty could neutralize the rise in wealth concentration. / Series: INEQ Working Paper Series