Question

Assume you work for the Virginia Department of Health. Your boss just came to you with one of his brilliant ideas to reduce smoking in the state. He just learned that raising the price of a good will reduce consumption of it, so he wants to impose a “sin” tax on cigarettes to reduce smoking by 1,000 packs per day. From your economic research unit, you know the inverse demand function for cigarettes P(cig)=10-4Q(cig) [paranethesis are subscripts] where P(cig) is the price of a pack of cigarettes in dollars and Qcig is the daily number of packs in thousands. A quick check at the Kwik-E-Mart tells you that the current price of cigarettes is $2 per pack.

a. Your boss said that the Republicans in the state legislator will only allow a new tax of $2 per pack to be levied, but he thinks doubling the price should be enough to achieve his goals. Explain to him why he’s wrong. As part of your explanation you should show how much a reduction in smoking, in percentage terms, would result from a 100% price increase.

b. But he argues that he achieved the same desired reduction in consumption of pink tennis balls (which contained known carcinogens), so surely it would work with cigarettes as well. Comparing and contrasting the characteristics of the two goods, explain to him why he’s wrong.

c. How high would the tax need to be to achieve his goal of a 1,000 pack reduction?

Answer 1

a) When the price is 2, the demand for cigarettes is 2000 units. If the tax rate is 2 per unit, the effective price is 4 per unit. This will lead to a demand of 1500 units of cigarettes. So, taxing at the rate of 2 per unit does not achieve the goal of 100 units.

b) He may be wrong because of the demand functions of both the goods. This might be the case that the demand for tennis balls was very price sensitive.

c) To achive the goal, we solve the following equation