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?

a. To calculate how much the price should be increased in order to reduce smoking by 20 percent, we need to use the price elasticity of demand formula:

Price elasticity of demand (E) = (% change in quantity demanded / % change in price)

In this case, we know that the price elasticity of demand for cigarettes is 0.4. We want to reduce smoking by 20 percent, which means the expected change in quantity demanded is -20% (-0.20).

Let's assume x is the percentage change in price:

0.4 = (-0.20 / x)

Solving for x:

0.4x = -0.20

x = -0.20 / 0.4

x = -0.50

So, the price should be increased by 50 percent to reduce smoking by 20 percent.

b. The long-term effect of the policy depends on the concept of price elasticity of demand. When the price of cigarettes is permanently increased, it will likely have a larger effect on smoking 1 year from now compared to 5 years from now. This is because, in the short run, people may not immediately adjust their behavior due to habit, addiction, or lack of alternatives. Over time, however, as the price remains high, people may seek alternatives, quit smoking, or reduce their cigarette consumption more significantly.

c. Teenagers generally have a higher price elasticity of demand for cigarettes compared to adults. There are a few reasons why this might be true:

1. Limited income: Teenagers typically have limited income, making them more sensitive to price changes. They may be less able to afford cigarettes when the price increases, compared to adults with higher incomes.

2. Peer pressure: Teenagers are more likely to be influenced by social factors, including peer pressure. If the price of cigarettes increases, it may discourage teenagers from starting or continuing smoking due to social pressure or wanting to fit in.

3. Health concerns: Teenagers may be more responsive to health campaigns and education about the negative effects of smoking. This awareness can make them more sensitive to price changes and more likely to reduce or quit smoking when the price of cigarettes increases.

These factors contribute to higher price elasticity among teenagers, making them more responsive to changes in cigarette prices compared to adults.