Market Substitution and the Pareto Dominance of Ad Valorem Taxation

1. IntroductionExcise taxes take two basic forms: unit taxes based on quantity sold and ad valorem taxes based on sales value. While these two versions of excise taxes are equivalent in perfectly competitive markets,1 in noncompetitive markets ad valorem taxation has been shown to welfare dominate unit taxation.2Ad valorem taxation also Pareto dominates unit taxation in monopoly and, in some cases, oligopoly markets, in the sense that, under an isorevenue constraint, replacing unit taxation with ad valorem taxation increases both consumer welfare and producer profits (Skeath and Trandel 1994).3In this paper, we depart from the homogeneous product oligopoly markets assumed in previous literature by adopting a model of heterogeneous products developed by Dixit and Stiglitz (1977). First, we study the Pareto dominance of ad valorem taxation in short-run equilibrium, where a fixed number of firms produce imperfectly substitutable goods and engage in Bertrand competition. We define market demand as a weighted sum of firm quantities demanded and market price as a similarly weighted average of firm prices. By assuming that market demand is isoelastic with respect to market price, our framework allows the elasticity of substitution among the goods in the taxed market and the price elasticity of market demand to bear on the comparison of the two forms of excise taxes.We find that, in the short run, ad valorem taxation always dominates unit taxation both in terms of consumer welfare and overall welfare (the precise meaning of overall welfare is made clear later). However, Pareto dominance of ad valorem taxation never exists if market demand is inelastic because, in this case, firms always earn lower profits under ad valorem taxation. Restricting our analysis to the case where market demand is elastic, we find that ad valorem taxation Pareto dominance is more likely the smaller the within-market elasticity of substitution or the larger the market demand elasticity. We also generalize a prior result for homogenous products: Increasing the number of firms in a market decreases the likelihood of ad valorem taxation Pareto dominance. Finally, we find that for a sufficiently large within-market elasticity of substitution, ad valorem taxation Pareto dominance is more likely the smaller the tax level, contrary to an existing result for the homogenous product case.Given the results of previous literature that unit taxation tends to be welfare dominated by equal-revenue ad valorem taxation in noncompetitive environments, the existence of both types of taxes must be explained by nonoptimal behavior on the part of government.4 One possible explanation for the coexistence of unit and ad valorem taxes, despite the welfare dominance of ad valorem taxation, is that a government only cares about the amount of revenue collected from each market, and the choice between these two taxes in a specific market is dictated by producers' interests, which are more concentrated than consumers' interests in general. Given this hypothesis concerning the political economy of choice between the two major forms of excise taxes, the results of this paper make testable predictions with respect to how the relative desirability of ad valorem taxation (from the perspective of producers) changes with several important characteristics of a market: the elasticity of substitution among goods in the market, the market demand elasticity, the number of firms in the market, and the level of taxation in the market.Extending our analysis to long-run equilibrium, where entry and exit provides an additional market equilibrating mechanism and where firms always earn zero profits, we show that an equal-revenue switch from unit to ad valorem taxation has welfare effects on consumers through two channels. …