Abstract We derive the Pareto-efficient mix of non-linear taxes on labour income and capital income if people differ in their rates of return on capital. We allow for two reasons why rates of return differ: because individuals with higher ability are better able to invest their capital or because wealthier individuals enjoy scale effects in wealth accumulation. In both cases, a strictly positive tax on capital income is part of any Pareto-efficient tax system. We derive a condition for the Pareto-efficient tax mix that relies solely on empirical sufficient statistics—not on social welfare weights—and find that Pareto-efficient taxes on capital income increase with the degree of return heterogeneity. Numerical simulations for empirically plausible return heterogeneity suggest that Pareto-efficient marginal tax rates on capital income are positive and substantial.