The literature can justify increasing and decreasing marginal taxes (IMT & DMT) on top income under different social objectives and income distributions. Even if DMT are optimal, they are often politically infeasible. Then a flat tax seems to be a constrained optimal solution. We show however that, if we want to maximize the utility of a poor majority any flat tax can be inferior to some IMT. We provide a sufficient condition for (two-band) IMT to dominate any flat tax and further generalize this result to allow different welfare weights, declining elasticity of labor supply and more tax bands.

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