We investigate the welfare implications of changing the mix between capital and labor taxes for a model economy in which heterogeneous households face uninsurable labor income risk. The stochastic process for labor earnings we construct is consistent with empirical estimates of earnings risk, and also implies a distribution of asset holdings across households closely resembling that in the United States. We find that a vast majority of households prefers the status quo to eliminating capital taxes. This finding is interesting in light of the fact that this reform would be optimal if we abstracted from heterogeneity and assumed a representative agent. A second finding is that a utilitarian government prefers the current calibrated U.S. capital income tax rate (39.7 percent) to any increase or decrease in the capital tax rate.