Increasing Federal Cigarette Taxes Will Hurt State Cigarette Tax Revenues: The Case of a Double Mark-Up

August 7, 2007

As the federal government discusses raising its cigarette tax rate, one aspect that most policymakers are overlooking is the effect a higher federal rate would have on state cigarette tax revenue: most states would face a decrease in revenue. In industrial organization economics, this is called a case of “double marginalization,” whereby two monopoly layers of production—one upstream firm and one downstream firm—compete to capture the monopoly rents. In the end, a prisoner’s dilemma evolves whereby each firm, acting in its own self-interest, charges too high a price relative to what one vertically integrated firm would charge.

The same type of phenomenon could also occur when multiple levels of government, each trying to increase its own revenue, tax a single commodity like cigarettes or gasoline (especially cigarettes, given their political unpopularity). The federal government and state government combined could overtax a commodity from the perspective of overall revenue maximization, yet each would still be increasing or maximizing its own revenue. In other words, on whole, we could be on the right side of the Laffer Curve, but from the perspective of each layer of government, each could be on the left side and/or at a revenue maximization point.

For those familiar with basic microeconomics, here is a brief illustration:

Double Mark-Up Problem with Federal and State Taxation

Suppose we have a monopoly market for taxable cigarettes with a demand function as follows: P + t = 100 – Q. (t is the per unit tax levied on cigarettes.) For simplicity, suppose the firm has no costs and thereby maximizes revenue, which is P*Q. The optimal quantity for the firm to produce is a function of the tax rate as follows: Q* = 50 – .5t. As we can see, the higher the tax rate, the less the firm produces.

Now from a government’s perspective, t is the combined tax rate at the state and federal level. We will look at two scenarios: (1) a unitary government that sets the tax rate and (2) two layers of government where each layer sets its own rate and whereby t = a + b where a and b are the respective tax rates set by each layer of government.

Under a system of one unitary government, the tax revenue would be t*Q. The optimal tax from a government revenue maximization perspective is t = 50—that is, the tax rate that maximizes government revenue would be a per unit tax rate of 50. At that rate, the government revenue will be 1,250.

Now suppose there are two layers of government, each concerned with maximizing its own revenue. The tax revenue for government A would be equal to its tax rate, a, multiplied by the total quantity sold, Q. However, the total quantity sold is not just a function of its rate. It also depends on the tax rate of the other layer of government. The total tax per pack would be t = a + b. Working out the calculus shows the optimal tax rate of a for this government to be 33.3, based on the fact that the other layer of government, government B, also maximizes revenue, which also turns out to be at a rate of 33.3 per unit. Overall, the combined tax rate turns out to be 66.6 and total tax revenue is $1,111, or $555 for each government.

If the governments could collude, they would set the total tax rate at 50 to maximize revenue. Each party would set a tax rate of 25. However, at the rate of 25, each government would still have an incentive to cheat on that agreement. For example, government A could raise its rate from 25 to 30 and gain tax revenue. Government B would do the same, and eventually they would work their way back to the Nash Equilibrium of each setting a tax rate of 33.33.

This is very similar to the tragedy of the commons whereby each party’s acting in its own self-interest leads to an inferior outcome from a social perspective and every party is made worse off. This can be applied to other taxes that are levied at both levels of government. However, the prisoner’s dilemma can also work in the other direction when it comes to multiple governmental units at each layer competing amongst one another, such as states competing against one another to attract business, by lowering certain tax rates below the socially optimal level in terms of the foregone government services or raising taxes on others.

Cigarettes should not be subjected to this type of revenue maximization by public officials. Rather the tax rate should be based solely on cigarettes’ negative externality. However, given that politicians at both levels of government are now relying (or hope to be relying) on cigarette taxes as a general revenue source and appear bound and determined to get the most out of smokers as they can, they need to understand this double mark-up issue.


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