Elasticities and the Deadweight Loss of a Tax

We know that the deadweight loss from an excise tax arises because it prevents some mutually beneficial transactions from occurring. In particular, the producer and consumer surplus that is forgone because of these missing transactions is equal to the size of the deadweight loss itself. This means that the larger the number of transactions that are prevented by the tax, the larger the deadweight loss.

This fact gives us an important clue in understanding the relationship between elasticity and the size of the deadweight loss from a tax. Recall that when demand or supply is elastic, the quantity demanded or the quantity supplied is relatively responsive to changes in the price. So a tax imposed on a good for which either demand or supply, or both, is elastic will cause a relatively large decrease in the quantity transacted and a relatively large deadweight loss. And when we say that demand or supply is inelastic, we mean that the quantity demanded or the quantity supplied is relatively unresponsive to changes in the price.

As a result, a tax imposed when demand or supply, or both, is inelastic will cause a relatively small decrease in the quantity transacted and a relatively small deadweight loss.

The four panels of Figure 7-10 illustrate the positive relationship between a good’s price elasticity of either demand or supply and the deadweight loss from taxing that good. Each panel represents the same amount of tax imposed but on a different good; the size of the deadweight loss is given by the area of the shaded triangle. In panel (a), the deadweight-loss triangle is large because demand for this good is relatively elastic—a large number of transactions fail to occur because of the tax. In panel (b), the same supply curve is drawn as in panel (a), but demand for this good is relatively inelastic; as a result, the triangle is small because only a small number of transactions are forgone. Likewise, panels (c) and (d) contain the same demand curve but different supply curves. In panel (c), an elastic supply curve gives rise to a large deadweight-loss triangle, but in panel (d) an inelastic supply curve gives rise to a small deadweight-loss triangle.

Deadweight Loss and Elasticities Demand is elastic in panel (a) and inelastic in panel (b), but the supply curves are the same. Supply is elastic in panel (c) and inelastic in panel (d), but the demand curves are the same. The deadweight losses are larger in panels (a) and (c) than in panels (b) and (d) because the greater the price elasticity of demand or supply, the greater the tax-induced fall in the quantity transacted. In contrast, the lower the price elasticity of demand or supply, the smaller the tax-induced fall in the quantity transacted and the smaller the deadweight loss.

The implication of this result is clear: if you want to minimize the efficiency costs of taxation, you should choose to tax only those goods for which demand or supply, or both, is relatively inelastic. For such goods, a tax has little effect on behavior because behavior is relatively unresponsive to changes in the price. In the extreme case in which demand is perfectly inelastic (a vertical demand curve), the quantity demanded is unchanged by the imposition of the tax. As a result, the tax imposes no deadweight loss. Similarly, if supply is perfectly inelastic (a vertical supply curve), the quantity supplied is unchanged by the tax and there is also no deadweight loss.

So if the goal in choosing whom to tax is to minimize deadweight loss, then taxes should be imposed on goods and services that have the most inelastic response—that is, goods and services for which consumers or producers will change their behavior the least in response to the tax. (Unless they have a tendency to revolt, of course.) And this lesson carries a flip-side: using a tax to purposely decrease the amount of a harmful activity, such as underage drinking, will have the most impact when that activity is elastically demanded or supplied.

ECONOMICS in Action: Taxing the Marlboro Man

Taxing the Marlboro Man

One of the most important excise taxes in the United States is the tax on cigarettes. The federal government imposes a tax of $1.01 a pack; state governments impose taxes that range from $0.17 cents a pack in Missouri to $4.35 a pack in New York; and many cities impose further taxes. In general, tax rates on cigarettes have increased over time, because more and more governments have seen them not just as a source of revenue but as a way to discourage smoking. But the rise in cigarette taxes has not been gradual. Usually, once a state government decides to raise cigarette taxes, it raises them a lot—which provides economists with useful data on what happens when there is a big tax increase.

Table 7-1 shows the results of big increases in cigarette taxes. In each case, sales fell, just as our analysis predicts. Although it’s theoretically possible for tax revenue to fall after such a large tax increase, in reality tax revenue rose in each case. That’s because cigarettes have a low price elasticity of demand.

State

Year

Increase in tax (per pack)

New state tax (per pack)

Change in quantity transacted

Change in tax revenue

Mississippi

2009

$0.50

$0.68

−22.8%

188.3%

Hawaii

2009

  0.60

  2.60

−11.3   

 14.5  

New Mexico

2010

 0.75 

 1.66

 −7.8   

 67.5  

Florida

2010

 1.00

  2.00

−27.8  

193.2  

Washington

2010

 1.00

 3.03

−20.5  

17.0 

Source: Orzechowski & Walker, Tax Burden on Tobacco. U.S. Alcohol and Tobacco Tax and Trade Bureau.
Table :

TABLE 7-1 Results of Increases in Cigarette Taxes

Quick Review

  • An excise tax generates tax revenue equal to the tax rate times the number of units of the good or service transacted but reduces consumer and producer surplus.

  • The government tax revenue collected is less than the loss in total surplus because the tax creates inefficiency by discouraging some mutually beneficial transactions.

  • The difference between the tax revenue from an excise tax and the reduction in total surplus is the deadweight loss from the tax. The total amount of inefficiency resulting from a tax is equal to the deadweight loss plus the administrative costs of the tax.

  • The larger the number of transactions prevented by a tax, the larger the deadweight loss. As a result, taxes on goods with a greater price elasticity of supply or demand, or both, generate higher deadweight losses. There is no deadweight loss when the number of transactions is unchanged by the tax.

7-2

  1. Question 7.6

    The accompanying table shows five consumers’ willingness to pay for one can of diet soda each as well as five producers’ costs of selling one can of diet soda each. Each consumer buys at most one can of soda; each producer sells at most one can of soda. The government asks your advice about the effects of an excise tax of $0.40 per can of diet soda. Assume that there are no administrative costs from the tax.

    Consumer

    Willingness to pay

    Producer

    Cost

    Ana

     $0.70

    Zhang

     $0.10

    Bernice

       0.60

    Yves

       0.20

    Chizuko

       0.50

    Xavier

       0.30

    Dagmar

       0.40

    Walter

       0.40

    Ella

       0.30

    Vern

       0.50

    1. Without the excise tax, what is the equilibrium price and the equilibrium quantity of soda transacted?

    2. The excise tax raises the price paid by consumers post-tax to $0.60 and lowers the price received by producers post-tax to $0.20. With the excise tax, what is the quantity of soda transacted?

    3. Without the excise tax, how much individual consumer surplus does each of the consumers gain? How much with the tax? How much total consumer surplus is lost as a result of the tax?

    4. Without the excise tax, how much individual producer surplus does each of the producers gain? How much with the tax? How much total producer surplus is lost as a result of the tax?

    5. How much government revenue does the excise tax create?

    6. What is the deadweight loss from the imposition of this excise tax?

  2. Question 7.7

    In each of the following cases, focus on the price elasticity of demand and use a diagram to illustrate the likely size—small or large—of the deadweight loss resulting from a tax. Explain your reasoning.

    1. Gasoline

    2. Milk chocolate bars

Solutions appear at back of book.