In this paper we develop a quantitative theory of earnings and wealth inequality that accounts for the U.S. earnings and wealth distributions almost exactly, and we use this theory to measure the steady-state trade-offs that arise when switching from the current progressive income tax system, to a tax system in which income is proportionally taxed. Our theory is based on households that face an uninsurable idiosyncratic process on wages, that go through the life cycle stages of retirement and death, and that have altruistic feelings towards their progenie. Moreover, unlike some of the recent research on wealth inequality, the households in our model economies are equally patient. The main steady-state trade-offs implied by our policy experiment are the following: on the one hand we find that output, wealth and, to a very small extent, the labor input are higher in the model economy with proportional income taxes (4.4, 11.4 and 0.9% higher, respectively). On the other hand we find that in this model economy the distributions of wealth and consumption are significantly more unequal (their Gini indices increase by 10.4 and 13.0%, respectively). Finally, we find that the inequality of earnings and the earnings and wealth mobility of households remain almost unchanged.