On optimal redistributive capital taxation

This paper addresses conflicting results regarding the optimal taxation of capital income. Judd proves that in a steady state, there should be no taxation of capital income. Lansing studies a logarithmic example of one of Judd's models and finds that the optimal steady‐state tax on capital income is not always zero—it is positive in some specifications and negative in some others. There appears to be a contradiction. However, I show that Lansing derives his result by relaxing the convergence hypotheses of Judd's theorem. With less restrictive hypotheses, a wider range of primitives (parameter values, initial condition, etc.) satisfy the hypotheses and because each specification of primitives generates its own optimal time path(s) for the model's variables, it follows that a wider range of time paths with a wider range of steady‐state properties is possible. This raises a question. What happens if the convergence hypotheses are weakened further so that they are satisfied by a wider yet range of primitives? I find that at any interior steady state for the model's optimal tax equilibrium, either the capital tax is zero or else the elasticity of marginal utility is unitary which is satisfied identically in Lansing's log example. In effect, Lansing's example illustrates the only way in which an interior steady state can violate the zero tax result.