Question

4. Consider public policy aimed at smoking.
a. Studies indicate that the price elasticity of demand for cigarettes is about 0.4. If a pack of cigarettes currently costs $2 and the government wants to reduce smoking by 20 percent, by how much should it increase the price?
b. If the government permanently increases the price of cigarettes, will the policy have a larger effect on smoking 1 year from now or 5 years from now?
c. Studies also find out that teenagers have a higher price elasticity that do adults. Why might this be true?

Answer 1

(a) Price elasticity of demand for cigarettes \(=0.4\)

i.e., \(\frac{\% \Delta \text { in quantity demanded }}{\% \Delta \text { in price }}=0.4\)

\(\frac{0.2}{\% \Delta \text { in price }}=0.4\)

\(\therefore \% \Delta\) in price \(=\frac{0.2}{0.4}=0.5\)

The government should increase the price by \(50 \%\)

Current cost \(=\$ 2\)

\(+\) Increase in price \((2 \times 50 \%)=\$ 1\)

New price \(=\$ 3\)

\(\therefore\) The government should increase the price of cigarettes by \(\$ 1\) and make the new price \(\$ 3 .\)

(b) If the government permanently increases the price of cigarettes, the policy will have a larger effect 5 years from now than 1 year from now. This is because, given the longer time, the public will find new alternatives to the smoking habit and the quantity of cigarettes demanded will fall substantially in the long run.

(c) Because teenagers do not have as much of an income as adults, they are likely to have a higher price elasticity of demand. Also, adults are more likely to be addicted to cigarettes, making

it more difficult to reduce their quantity demanded in response to a higher price.

Answer 2

Price elasticity of demand = 0.4

change in demand = 0.2

we have to find the change in price

Formula

Ed = change in demand / change in price

0.4 = 0.2 / change in price

change in price = 0.5 * 100 = 50%

current price =2$

add 50% in 2$

New price = 3$