Question

According to Professor Becker, by how much would cigarette prices have to rise to get a 20 percent reduction in smoking in Instructions: Enter your responses as a percentage rounded to one decimal place a. one year 50 percent b. three years_______percent

Answer 1

a. According to Professor Becker, cigarette prices would have to rise by 50 percent in one year to achieve a 20 percent reduction in smoking.

Step-by-step explanation:

a. Professor Becker suggests that a 20 percent reduction in smoking can be achieved by raising cigarette prices by 50 percent in one year. This relationship is based on the assumption that the price elasticity of demand for cigarettes is -0.4, a commonly used estimate in economic studies.

The formula for price elasticity of demand
`(\(E\))` is given by the percentage change in quantity demanded
`(\(\%\Delta Q\))` divided by the percentage change in price
`(\(\%\Delta P\))`:

`\[ E = (\%\Delta Q)/(\%\Delta P) \]`

In this case,
`\(E = -0.4\)`, and the percentage change in quantity demanded is set to -20 percent (a 20 percent reduction), allowing us to solve for the percentage change in price.

b. If the goal is to achieve a 20 percent reduction in smoking over three years, we can use the same elasticity of demand
`(\(E = -0.4\))`. The formula for the percentage change in price
`(\(\%\Delta P\))` can be rearranged as follows:

`\[ \%\Delta P = E * \%\Delta Q \]`

Substituting
`\(E = -0.4\) and \(\%\Delta Q = -20\)`, we can calculate the percentage change in price required over three years.

In conclusion, Professor Becker's suggestion is based on the concept of price elasticity of demand, where a 50 percent increase in cigarette prices in one year is anticipated to lead to a 20 percent reduction in smoking. Extending this analysis to three years involves applying the same elasticity estimate to calculate the required percentage change in price.