The dynamics of capital accumulation in the US: simulations after piketty

We develop a dynamic model where a competitive firm uses labor and capital, with market clearing rates of return. Individuals are heterogeneous in skills, with an endowment in capital/wealth increasing in skill. Individuals aspire to a socially determined consumption level, with a constant marginal propensity to consume out of income above this level. We also study three variants of the model: one with a higher rate of return for large capitals than for smaller ones, one with a capital levy financing a lump sum transfer, and one with social mobility. We calibrate the model to the US economy and obtain that a steady state exists in all variants, and we obtain convergence to the steady state from the 2012 US wealth distribution. The reduction in the level of the aspirational consumption level is the only way to create wealth for the bottom half of the distribution.