Tag: Price elasticty of demand

(Photo from Zuma Press via the Wall Street Journal.)

When state and local governments impose taxes on sales of liquor, on cigarettes and other tobacco products, or on soda and other sweetened beverages, they typically have two objectives: (1) Discourage consumption of the taxed goods, and (2) raise revenue to pay for government services.  As we discuss in Chapter 6 of Microeconomics (also Economics, Chapter 6), these objectives can be at odds with each other. The tax revenue a government receives depends on both the size of the tax and the number of units sold. Therefore, the more successful a tax is in significantly reducing, say, sales of cigarettes, the less tax revenue the government receives from the tax.

As we discuss in Chapter 6, a tax on a good shifts the supply curve for the good up by the amount of the tax. (We think it’s intuitively easier to think of a tax as shifting up a supply curve, but analytically the effect on equilibrium is the same if we illustrate the effect of the tax by shifting down the demand curve for the taxed good by the amount of the tax.)  A tax will raise the equilibrium price consumers pay and reduce the equilibrium quantity of the taxed good that they buy. For a supply curve of a given price elasticity in the relevant range of prices, how much a tax increases equilibrium  price relative to how much it decreases equilibrium quantity is determined by the price elasticity of demand. 

The following figure illustrates these points. If a city implements a tax of $0.75 per 2-liter bottle of soda, the supply curve shifts up from S₁ to S₂. If demand is price elastic, the equilibrium price increases from $1.75 to $2.00, while the equilibrium quantity falls from 90,000 bottles per day to 70,000. If demand is price inelastic, the equilibrium price rises by more, but the equilibrium quantity falls by less. Therefore, a more price elastic demand curve is good news for objective (1) above—soda consumption falls by more—but bad news for the amount of tax revenue the government collects. When the demand for soda is price inelastic, the government collects tax revenue of $0.75 per bottle multiplied by 80,000 bottles, or $60,000 per day. When the demand for soda is price elastic, the government collects tax revenue of $0.75 per bottle multiplied by 70,000 bottles, or only $52,500 per day.

One further point: We would expect the amount of revenue the government earns from the tax to decline over time, holding constant other variables that might affect the market for the taxed good, . This conclusion follows from the fact that demand typically becomes more price elastic over time. In other words, when a tax is first imposed (or an existing tax is increased), consumers are likely to reduce purchases of the taxed good less in the short run than in the long run. This result can a problem for governments that make a commitment to use the tax revenues for a particular purpose.

A recent article in the Los Angeles Times highlighted this last point. In 1999, California voters passed Proposition 10, which increased the tax on cigarettes by $0.50 per pack, with similar tax increases on other tobacco products. The tax revenues were dedicated to funding “First 5” state government agencies, which are focused on providing services to children 5 years old and younger.  The article notes, as the above analysis would lead us to expect, that the additional revenue the state received from the tax increase was largest in the first year and has gradually declined since as the quantity of cigarettes and other tobacco products sold has fallen. (Note that over such a long period of time, other factors in addition to the effects of the tax have contributed to the decline in smoking in California.) As a result, the state and county governments have had to scramble to find additional sources of funds for the First 5 agencies. The article quotes Deborah Daro, a researcher at the University of Chicago, as noting: “It seemed like a brilliant solution—tax the sinners who are smoking to help newborns and their parents …. But then people stopped smoking, which from a public health perspective is great, but from a funding perspective for First 5—they don’t have another funding stream.”