We investigate the welfare implications of changing a proportional capital income tax for a model economy in which heterogeneous households face labor income risk and trade only one asset. Labor taxes are adjusted at the time of the reform to maintain long run budget balance. Our stochastic process for labor earnings 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. <p> 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 in the incomplete markets economy, a utilitarian government prefers the current calibrated U.S. capital income tax rate (39.7 percent) to any change in the capital tax rate. If markets were complete, on the other hand, average welfare would be maximized by reducing the capital tax rate to around 30 percent.