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This paper addresses conflicting results regarding the optimal taxation of capital income. Judd (1985) proves that in steady state there should be no taxation of capital income. Lansing (1999) 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, negative in some others. There appears to be a contradiction. However, I show that Lansing derives his result by relaxing the hypotheses of Judd's theorem -- with less restrictive hypotheses, a wider range of outcomes is possible. This raises the question of whether yet more outcomes are possible with yet weaker hypotheses. I find that the answer is no: the only possible interior steady states for the model are essentially Judd's zero capital tax and Lansing's unitary elasticity of marginal utility.
