Any tax system imposing selective commodity taxation must have procedures for assigning diﬀerent goods to tax rate categories. Real-world tax legislation does this on the basis of observable characteristics, allowing the tax system to handle a constantly evolving set of available goods. We recast the theory of optimal taxation in the language of characteristics using the Gorman-Lancaster model of consumer behavior, and present a theory of tax-driven product innovation and optimal line drawing. The paper consists of two parts. The ﬁrst part presents optimal tax rules showing that characteristics can be used to gauge optimal tax rates in an intuitive way: the closer two goods are in characteristics space, the greater their substitutability and the smaller the optimal tax rate diﬀerential. The second part starts from the observation that, whenever the number of tax instruments is ﬁnite, tax systems have to draw lines that deﬁne tax-rate regions in characteristics space. Such lines are associated with notches in tax liability as a function of characteristics, creating incentives to introduce new goods (i.e., new characteristics combinations) in order to reduce tax liability. New goods introduced this way are socially inferior to existing goods. Second-best optimal tax systems draw lines so as to avoid such tax-driven product innovations; only goods on the characteristics possibility frontier are allowed in the market. Hence, although the tax system is second-best, the set of goods produced is ﬁrst-best given the demand for characteristic
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