This paper examines the second-best tax policy to minimize envy in the sense of Chaudhuri (1986) and Diamantaras and Thomson (1990). An allocation is $\lambda$-equitable if no agent prefers a proportion $\lambda$ of any other agent's bundle. We study the allocations that maximize $\lambda$ among the second-best Pareto efficient allocations. In the standard two-class economy with identical preferences, the Chaudhuri-Diamantaras-Thomson allocation coincides with the leximin allocation. In many-agent economies, it is possible to order the class of second-best Pareto efficient allocations graded by progressivity in the sense of Hemming and Keen (1983), with respect to the intensity of envy. Envy is then minimized in the most progressive tax system.
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