Why is the Long-Run Tax on Capital Income Zero? Explaining the Chamley-Judd Result

Why is it optimal not to tax capital income in the long-run in Chamley (1986) and Judd (1985)? This paper demonstrates that the answer follows standard intuitions from the commodity tax literature. In the steady state, Engel curves for consumption are linear in labour earnings, irrespective of the utility function adopted. Thus, in the steady state, consumption demands in each period become equally complementary to leisure over time. This renders taxes on capital income redundant, since they cannot alleviate distortions from taxing labour income. The argument that taxes on capital income should be zero because distortions explode in finite time is relevant only if restrictions are imposed on the utility function. We show how these restrictions imply that consumption demands in each period are equally complementary to leisure over time. We also demonstrate that the optimal tax on capital income is zero irrespective of whether the gross interest rate is endogenous. This contradicts arguments that the entire burden of capital income taxes is shifted to labour through general equilibrium effects on the interest rate.