We show that minimum wage earners should pay a lower tax than high earners. Though intuitive, this idea is not supported by the existing literature. The optimal maximin tax curve and two-band taxes are usually decreasing. Since decreasing marginal taxes would be unpopular, by continuity a flat tax seems to be superior to increasing marginal taxes and should be a second best solution. However, using a simple utility function and a general income distribution, we find that lowering the marginal tax for minimum wage earners not only dominates the optimal flat tax under maximin, but also make everyone better off.

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