Do Cigarette Excise Tax Rates Maximize Revenue?
Merriman, David, Economic Inquiry
Cigarettes are a heavily taxed commodity. In 1989 for example, federal excise taxes were sixteen cents per pack and state taxes averaged an additional twenty-two cents. Cigarette excise taxes accounted for approximately 26 percent of the retail price. These taxes may be justified by a number of arguments--on one hand, cigarette taxes may discourage use of a product that is physically addictive, medically harmful to the user and which possibly imposes significant external diseconomies on nonusers. On the other hand, cigarette taxes provide significant revenues to state and local governments (about 5.1 billion dollars in 1989). Since cigarettes are an addictive product for which the price elasticity of demand--at least in the short-run--is quite low, cigarette taxes may impose a smaller excess burden than taxes on other commodities. Ramsey's rule, which states that relative tax rates should be inversely proportional to demand elasticities, may therefore justify relatively high cigarette taxes.
Given politicians' desire to raise revenue together with their desire to please both smoking and non-smoking constituents, how do they choose the level of cigarette taxes? In particular, is it possible that rational elected officials choose cigarette tax rates so high that a cut in tax rates would cause revenues to increase? Buchanan and Lee  have argued that rational but short-sighted elected officials may choose tax rates beyond the point of long-run diminishing returns even for nonaddictive, nonharmful goods.
Figures l(a) and l(b) replicate the analysis of Buchanan and Lee . Figure l(a) shows the relationship between cigarette sales and the tax rate. The curve drawn in bold ([D.sub.L]) reveals the quantity of cigarettes demanded at any tax rate after that tax rate has been in effect "a period sufficiently long to allow for full behavioral adjustment". At a permanent tax rate of T* a quantity of Q* is sold. Because consumers adjust to price changes gradually, unanticipated increases (decreases) in the tax rate cause the quantity demanded to exceed (fall below) its long-run level, as shown by the "short-run" (period 0) demand curve [Mathematical Expression Omitted]. Over time the short-run demand curve will gradually move from [Mathematical Expression Omitted] to [Mathematical Expression Omitted] to [D.sub.L] as shown.
Each demand curve has a rate-revenue curve associated with it as shown in Figure l(b). Curve LRRR is the long-run rate-revenue curve associated with the long-run demand curve [D.sub.L]. Along this curve zero tax rates yield no revenue but, as tax rates increase, revenues rise gradually and then fall. [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are the short-run curves associated with the two short-run demand curves shown in Figure 1(a).
Elected officials are assumed to have utility functions with tax revenues (a good) and tax rates (a bad) as arguments. These officials seek points of tangency between their indifference curves (shown as I1, I2, and I3 in Figure 1(b)) and the rate-revenue curve. However, because officials have limited time horizons (perhaps due to voters' limited time horizons) they seek a tangency with a short-run rate-revenue curve. Long-run stability of the equilibrium requires that this tangency must also be on the long-run curve LRRR. Since an increase in the tax rate causes revenue to increase more in the short run than in the long run, Buchanan and Lee's theory guarantees that in equilibrium "the tax rate will be above that which would be chosen by a government whose time horizon is as long as the period required for taxpayers to make full adjustments to rate changes" [1982, 350].
Buchanan and Lee hypothesized that rational elected officials might choose equilibrium positions along the downward sloping portion of the rate-revenue curve.(1) This is illustrated in Figure 1(b). The optimal rate-revenue combination (from the elected officials' viewpoint) is the point of tangency between I1 and [Mathematical Expression Omitted] on the downward sloping portion of the long-run rate-revenue curve. …