Studies indicate that the price elasticity of demand for cigarettes is about
0.4. If a pack of cigarettes currently costs $4 and the government wants to
reduce smoking by 20 per cent, by how much should it increase the price?
Show your calculations.
(b) If the local government permanently increases the price of cigarettes, will the policy have a larger effect on smoking one year from now or five years from now?
(c) Studies find that teenagers have a higher price elasticity than do adults. Why might this be true?
Formula is:
P2-P1
_________
(P2+P1)/2
I got some of the calulation:
Percentage change in P=
.20 Quantity/.4 Price Elasticity of Demand = 0.5
P2-4
_______ = 0.5
(P2+4)/2
How can I resolve this ecuation?
To calculate the increase in price needed to reduce smoking by 20%, we first need to determine the price elasticity of demand formula:
Price Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)
Given that the price elasticity of demand for cigarettes is 0.4 and the government wants to reduce smoking by 20% (% Change in Quantity Demanded), we want to find the corresponding % Change in Price.
0.4 = (-20% / % Change in Price)
To solve for % Change in Price, we rearrange the formula:
% Change in Price = -20% / 0.4
% Change in Price = -50%
Now, to calculate the increase in price, we multiply the current price ($4) by the % Change in Price (-50%):
Increase in Price = $4 * (-50%)
Increase in Price = -$2
Therefore, the government should increase the price of cigarettes by $2 in order to reduce smoking by 20%.
(b) The policy of increasing the price of cigarettes will have a larger effect on smoking five years from now. This is because price elasticity of demand tends to increase over time. As people become more aware of the health risks and financial impact of smoking, they are likely to become more sensitive to price changes. Therefore, the longer a price increase is maintained, the greater the reduction in smoking that is expected to occur.
(c) Teenagers may have a higher price elasticity than adults for various reasons. One possible reason is that teenagers have less disposable income compared to adults, making them more sensitive to price changes. Additionally, teenagers may be more influenced by social and peer pressures, and increasing the price of cigarettes could make it less affordable or less socially acceptable to smoke. Teenagers are also more likely to be influenced by marketing and advertising efforts, which can affect their perceptions of smoking and related prices. Overall, these factors contribute to higher price elasticity among teenagers compared to adults.
(a) To reduce smoking by 20%, we need to determine the percentage increase in price that will lead to a 20% decrease in demand. We can use the price elasticity formula:
Percentage change in quantity demanded = (Price elasticity of demand) * (Percentage change in price)
Given:
Price elasticity of demand = 0.4
Percentage change in quantity demanded = -20%
Let's calculate the percentage change in price:
-20% = (0.4) * (Percentage change in price)
Solving for the percentage change in price:
Percentage change in price = -20% / 0.4
Percentage change in price = -50%
To increase the price enough to reduce smoking by 20%, the government should increase the price by 50%.
Current price of cigarettes: $4
Increase in price needed: 50% of $4
Increase in price = 0.5 * $4
Increase in price = $2
Therefore, the government should increase the price of cigarettes by $2.
(b) The policy will likely have a larger effect on smoking five years from now. This is because the price elasticity of demand measures the responsiveness of quantity demanded to price changes.
In the short term, people may have a harder time adjusting their habits and may not immediately quit smoking when prices increase. However, over time, they may become more sensitive to the price changes and start cutting down or quitting smoking altogether.
(c) Teenagers may have a higher price elasticity than adults due to the following reasons:
1. Limited income: Teenagers typically have limited financial resources and depend on their allowance or part-time jobs. As a result, even small changes in the price of cigarettes can have a significant impact on their ability to afford them.
2. Peer pressure and social norms: Teenagers are more susceptible to peer influence and social norms, including the perception of smoking as "cool" or rebellious behavior. However, if the price of cigarettes increases, it may make it less financially feasible or socially acceptable for teenagers to continue smoking.
3. Long-term health concerns: Teenagers may have a higher price elasticity because they are more aware of the long-term health risks associated with smoking. Therefore, they may be more responsive to price changes as they prioritize their health and financial concerns.
Overall, teenagers have different socioeconomic factors, psychological influences, and health concerns, which may contribute to their higher price elasticity compared to adults.