This paper computes the optimal progressivity of the income tax code in a dynamic general equilibrium model with household heterogeneity in which uninsurable labor pro- ductivity risk gives rise to a nontrivial income and wealth distribution. A progressive tax system serves as a partial substitute for missing insurance markets and enhances an equal distribution of economic welfare. These bene…cial eects of a progressive tax system have to be traded oagainst the e¢ciency loss arising from distorting endoge- nous labor supply and capital accumulation decisions. A determination of the optimal progressivity of the income tax code therefore calls for a quantitative exploration. Using a utilitarian steady state social welfare criterion we …nd that the optimal US income tax is well approximated by a‡ at tax rate of19:5% and a …xed deduction of about $3;700: The steady state welfare gains from a fundamental tax reform towards this tax system are equivalent to 0:4% higher consumption in each state of the world. An explicit computation of the transition path induced by a reform of the current towards the optimal tax system indicates, however, that a majority of the population currently alive would suer welfare losses, calling into question the political feasibility of such