Question

The accompanying diagram shows the market for cigarettes. The current equilibrium price per pack is \(\$ 4,\) and every day 40 million packs of cigarettes are sold. In order to recover some of the health care costs associated with smoking, the government imposes a tax of \(\$ 2\) per pack. This will raise the equilibrium price to \(\$ 5\) per pack and reduce the equilibrium quantity to 30 million packs. The economist working for the tobacco lobby claims that this tax will reduce consumer surplus for smokers by \(\$ 40\) million per day, since 40 million packs now cost \(\$ 1\) more per pack. The economist working for the lobby for sufferers of second-hand smoke argues that this is an enormous overestimate and that the reduction in consumer surplus will be only \(\$ 30\) million per day, since after the imposition of the tax only 30 million packs of cigarettes will be bought and each of these packs will now cost \(\$ 1\) more. They are both wrong. Why?

Short answer

Answer: The actual reduction in consumer surplus per day is \$10 million.

Step-by-step solution

Understanding consumer surplus

Consumer surplus is the difference between what consumers are willing to pay and what they actually pay for a good. In this case, we are looking at the change in consumer surplus before and after the government imposed the tax on cigarette packs.

Calculate consumer surplus before the tax

Before the tax, the equilibrium price per pack was \(\$ 4\) and there were 40 million packs sold per day. The total expenditure by the consumers on cigarettes can be calculated as \(4 \times 40 \, million = \$ 160\, million\) per day.

Calculate consumer surplus after the tax

After the tax, the equilibrium price per pack is \(\$ 5\) and there are 30 million packs sold per day. The total expenditure after the tax can be calculated as \(5 \times 30 \, million = \$ 150\, million\) per day.

Calculate the change in consumer surplus

The change in consumer surplus can be calculated by subtracting the consumer surplus after the tax from the consumer surplus before the tax: \(160\, million - 150\, million = \$ 10\, million\) per day.

Compare the change in consumer surplus with the economists' claims

Both economists are wrong because they both overestimated the reduction in consumer surplus. The economist working for the tobacco lobby claimed a reduction of \(\$ 40\, million\) per day, and the economist working for the lobby for sufferers of second-hand smoke claimed a reduction of \(\$ 30\, million\) per day. However, the actual reduction in consumer surplus is only \(\$ 10\, million\) per day.