Comparing the Welfare Effects of Income and Excise Taxes in the Presence of the Other Taxation Paradox
Morrison, Clarence C., Atlantic Economic Journal
In 1897 Edgeworth produced an example in which an excise tax on one good would lower the price of that good (inclusive of the tax) and other goods as well . This phenomenon, which has come to be known as the Egdeworth taxation paradox, was popularized by Harold Hotelling , with further discussion by Charles Ferguson  and William Vickrey . In 1938 Hotelling argued that, in terms of welfare, personal levies are superior to excise taxes for the purpose of raising government revenue . Although Hotelling sometimes referred to these levies as "personal income taxes," they were what today are called lump-sum taxes. It is well recognized that what economists refer to today as income taxes are distortionary and do not provide the lump-sum redistribution required for a first-best solution relative to a specific welfare function. However, there is still considerable support for the supposition that income taxes are superior to excise taxes in terms of welfare. In this paper, the author will make numerical comparisons of the welfare effects of income and excise taxation in the presence of a different taxation paradox.
This paper features a taxation phenomenon that is frequently treated as an unimportant curiosity, but for which examples are easily produced using common functional forms and for which there may be empirical evidence of actual occurrence. This "paradox" occurs when a specific excise tax increases the after-tax price of a good by more than the amount of the tax. In 1987 Jeffrey Harris examined the 1983 increase in the federal cigarette excise tax and concluded that the $0.08 increase in the tax may have induced a $0.16 jump in the price of a pack of cigarettes. He further surmised that "quite contrary to the conventional view of the incidence of excise taxes, the federal excise tax may actually have had a multiplier effect upon price" [Harris, 1987, p. 87].
The most popular textbook treatment of monopoly and excise taxation is to compare the effects of an excise tax on a constant (average) cost competitive industry and a constant cost monopoly, where both face a linear market demand curve. For the competitive industry, price increases by the full amount of the tax, but for the monopoly, price rises by only half the amount of the tax. Sometimes this is offered as one of those examples (so dear to the hearts of economists) in which careful economic analysis produces a result that is opposite to the intuitive response of the average man on the street. Two notable exceptions are Joseph Stiglitz's public sector text  and Hal Varian's intermediate price theory text . Both texts discuss the obligatory linear demand case But then point out that the price to the consumer will rise by more than the amount of the tax if the monopolist's demand curve is of the constant elasticity form. (Varian calls this case an easy example.)
This paper will discuss the theoretical possibility of an excise tax (levied on the producer-seller) increasing price by more than the tax in a partial equilibrium context. In addition, it will offer several fairly elaborate numerical general equilibrium examples that are in the spirit of both the Stiglitz-Varian easy example and Harris' conclusion about the cigarette excise tax. It turns out that these examples are also consistent with the supposition that income taxes are superior to excise taxes in terms of welfare. In these examples, relative to a specific welfare function, a flat-rate income tax turns out to be superior (for the optimum rate) to excise taxes (at optimum specific rates).
Much of the optimum tax literature considers the problem of the optimum way of raising a given revenue. In this paper, the author will look for optima in terms of both raising and utilizing a variable government revenue in the context of a closed general equilibrium model. The paper will compare levels of the "sum of satisfactions" welfare function(1) in a general equilibrium model with many agents, monopoly firms, and a government-produced public good. …