Consider public policy aimed at smoking.
a. Studies indicate that the price elasticity of demand for cigarettes is about 0.3. If a pack of cigarettes currently costs $5 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 that teenagers have a higher price elasticity of demand than adults. Why might this be true?
a. To calculate how much the government should increase the price of cigarettes to reduce smoking by 20 percent, we can use the concept of price elasticity of demand. Price elasticity of demand measures the responsiveness of quantity demanded to a change in price.
The formula for price elasticity of demand is as follows:
Price elasticity of demand = Percentage change in quantity demanded / Percentage change in price
In this case, we are given that the price elasticity of demand for cigarettes is 0.3. Let's assume the initial quantity demanded is 100 (for the sake of simplicity).
To reduce smoking by 20 percent, we need to reduce the quantity demanded by 20. So, the new quantity demanded would be 100 - (20% of 100) = 80.
The percentage change in quantity demanded is (80 - 100) / 100 * 100 = -20%.
Now, we can use the price elasticity formula to find the percentage change in price:
0.3 = -20% / Percentage change in price
We can solve this equation by cross-multiplying:
Percentage change in price = -20% / 0.3
Percentage change in price = -66.67%
Finally, to calculate the increase in price, we multiply the current price by the percentage change in price:
Increase in price = $5 * (-66.67%) = -$3.33 (approximately)
Therefore, the government should increase the price of cigarettes by approximately $3.33 to reduce smoking by 20 percent.
b. The long-term impact of a permanent increase in the price of cigarettes on smoking depends on several factors, including consumer behavior and habit formation. However, in general, the policy is likely to have a larger effect on smoking 5 years from now compared to 1 year from now.
When the price of cigarettes increases, it may take some time for individuals to adjust their behavior and reduce or quit smoking. In the short term, some smokers may continue to purchase cigarettes despite the price increase. However, as time goes by, individuals may find it increasingly difficult to afford and justify the higher cost of cigarettes. Moreover, over a longer duration, the habit-forming nature of smoking may weaken as individuals experience the health and financial consequences associated with their smoking habit. Therefore, the impact of the policy is generally expected to be greater after 5 years compared to just 1 year.
c. Teenagers often have a higher price elasticity of demand for cigarettes than adults. This means that teenagers are more responsive to changes in the price of cigarettes compared to adults. There are several reasons why this might be true:
1. Limited financial resources: Teenagers generally have lower incomes or allowances compared to adults. As a result, they may be more sensitive to price changes and may need to cut back on their spending when cigarette prices increase.
2. Lack of addiction: Many teenagers are occasional smokers or experimenting with smoking. They are less likely to be addicted to cigarettes compared to long-term adult smokers. Therefore, teenagers may find it easier to quit or reduce smoking in response to price increases.
3. Health concerns and greater risk aversion: Teenagers may be more aware of the negative health effects of smoking and may be more likely to respond to anti-smoking campaigns or public health messages. They may be more willing to make lifestyle changes and avoid smoking if the price increases.
4. Peer pressure and social norms: Teenagers are often more influenced by social factors, including their friends and social circles. If there is a social stigma associated with smoking or if public opinion turns against smoking, teenagers may be more inclined to change their behavior in response to price increases.
Overall, these factors contribute to teenagers having a higher price elasticity of demand for cigarettes compared to adults.