Optimal Commodity Taxation for Reduction of Envy

This paper derives optimal commodity taxes in a two-class economy, based on Chaudhuri (1986) and Diamantaras and Thomson's (1990) λ-equitability. An allocation is λ-equitable if no agent envies a proportion λ of the bundle of any other agent. We examine the properties of Pareto undominated allocations for various λ-equitability requirements. In contrast with the classic Ramsey rule and its extension, ceteris paribus, the goods preferred by the low skilled agent and/or of high Hicksian elasticities are taxed more heavily. As to the total tax burden, the envying agent may bear a higher tax burden, since the good which he likes should be taxed more heavily to reduce envy. Also, due to the conflict between welfare of the envying agent and his envy, there exists an economy in which the Diamantaras-Thomson allocation -- an allocation which maximizes λ in the range of Pareto efficient allocations -- is the Pareto efficient allocation which minimizes the welfare of the envying agent.