Commodity Taxes under Partial Separability Cannot Be Undistorted

The nature of optimal commodity taxes and tax reform are not well understood in the literature under the separability of subset of consumption goods. We show in this paper that, contrary to the claims of previous researches, under the combination of non-linear income tax and linear commodity taxes, a tax reform towards uniform taxes of the subset of commodities may not be welfare-improving. Furthermore, a distortion of production that alters the relative wages has additional benefit through mimickers’ consumption choices. We also newly characterize the optimal commodity taxes in this setting to show that, to quench possible heterogeneous impacts to the cross-substitution effects on the other commodities, optimally uniform tax towards the separated goods requires uniform income effects across income classes, so that the constraint on the Engel curves in the corresponding optimally linear income and commodity taxes cannot be fully omitted.