Commodity taxation in a differentiated oligopoly

We introduce commodity taxation into a duopoly model of vertical product differentiation. Our setting differs from the existing Iiterature in two respects. First, we consider price competition and, second, we allow for endogenous product selection. As usual, firms choose the quality of their products prior to making their pricing decisions. We first show that a uniform ad valorem tax, where the same rate applies to all variants of the product, lowers both equilibrium qualities and distorts the allocation of consumers between firms. More interestingly, we then establish that a number of familiar properties are no longer valid in our setting. In particular, it appears that the tax lowers the consumer prices of both variants and that the decrease in consumer prices is larger than the decrease in production costs brought about by the reduction in qualities. Even more surprisingly, it turns out that a small uniform ad valorem tax whose proceed are redistributed in a lump-sum way is always welfare-improving over the no-tax equilibrium. Finally, we allow for the possibility of a non-uniform tax with different rates applying to different variants of the commodity. It turns out that depending on the parameter values such a differentiation of tax rates mayor may not be desirable on welfare grounds. If a welfare improvement is possible through a non-uniform tax, it is always the high-quality variant which must be taxed at a higher rate.