This paper provides a counterexample to the simplest version of the redistribution models considered by Judd (1985) in which the government chooses an optimal distortionary tax on capitalists to finance a lump-sum payment to workers. I show that the steady-state optimal tax on capital income is generally non-zero when the capitalists' utility is logarithmic and the government faces a balanced-budget constraint. With log utility, agents' optimal decisions depend solely on the current rate of return, not any future rates of return or tax rates. This feature of the economy effectively deprives the government of a useful policy instrument because promises about future tax rates can no longer influence current allocations. When combined with a lack of other suitable policy instruments (such as government bonds), the result is an inability to decentralize the allocations that are consistent with a zero limiting capital tax. I show that the standard approach to solving the dynamic optimal tax problem yields the wrong answer in this (knife-edge) case because it fails to properly enforce the constraints associated with the competitive equilibrium. Specifically, the standard approach lets in an additional policy instrument through the back door.