Question

3. Addiction: Taxation Issues: Consider the issue of cigarette taxation: Suppose the price elasticities for cigarettes by habitual smokers and potential smokers are -0.25 and -4.0. Ad- ditionally, suppose the relative share of habitual smokers in the population is m. The gov- ernment is considering levying a new 20% tax on cigarettes. Suppose the current price of cigarettes is $5, of which $1 is tax. (a) For each type of consumer, calculate the expected reduction in consumption resulting from the tax. Intuitively explain why the responses of these two groups will differ. (b) Given that m represents the population share of habitual users and 1-m represents the population share of potential users, calculate the change in tax revenue that will follow from the new tax3 (c) If the goal of the new tax is to increase tax revenues, for what values of m is this a successful tax? (d) Why might these types of taxes be considered regressive.

Answer 1

a) Price elasticity for habitual smokers = Percentage change in quantity demanded for cigarettes/Percentage change in price

or, -0.25 = Percentage change in quantity demanded for cigarettes/20%

or, Percentage change in quantity demanded for cigarettes = -0.25*20%

or, Percentage change in quantity demanded for cigarettes = -5%

Similarly, Price elasticity for potential smokers = Percentage change in quantity demanded for cigarettes/Percentage change in price

or, -4 = Percentage change in quantity demanded for cigarettes/20%

or, Percentage change in quantity demanded for cigarettes = -4*20%

or, Percentage change in quantity demanded for cigarettes = -80%

Thus, there is a much higher reduction in consumption of cigarettes for potential smokers in comparison to habitual smokers. The reason is the highly elastic demand curve for poential smokers and inelastic demand curve for habitual smokers.

b) With reduction in 5% consumption of cigarettes for habitual smokers, tax revenue falls from $m to $0.95m (where tax is $1).

However, with reduction in 80% consumption of cigarettes for potential smokers, tax revenue falls from $(1-m) to $0.2(1-m) (where tax is $1).

c) Now, tax revenue increases with a rise in price if demand curve is inelastic (for habitual smokers) whereas, tax revenue decreases with a rise in price if demand curve is elastic (for potential smokers)

If the goal is to increase in tax revenue, then,

for habitual smokers, increase in tax revenue must be positive

or, 0.95m-m >0

or, -0.5m>0

or, m must be negative which is not possible.

Again, for potential smokers, increase in tax revenue must be positive

or, 0.2(1-m) - (1-m) >0

or, -0.8+0.8m > 0

or, 0.8m >0.8

or, m > 1 (which is possible.

d) These kind of taxes can be considered regressive as they charge a high percentage on consumer's income.