Assume that the price elasticity of demand for cigarettes is 0.4. If a pack of cigarettes currently costs \$6 and the government aims to decrease smoking by 20 percent, by how much should it increase the price?

• A. \$1.20
• B. \$2.40
• C. \$3.00
• D. \$4.80

Answer: (C)

Verified step by step guidance

1. Understand the concept of price elasticity of demand, which measures how much the quantity demanded of a good responds to a change in the price of that good. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.
2. Identify the given values: the price elasticity of demand (E_d) is 0.4, the initial price (P_0) is \$6, and the desired percentage decrease in quantity demanded is 20%.
3. Use the formula for price elasticity of demand: E_d = (percentage change in quantity demanded) / (percentage change in price). Rearrange this formula to solve for the percentage change in price: percentage change in price = (percentage change in quantity demanded) / E_d.
4. Substitute the known values into the rearranged formula: percentage change in price = (-20%) / 0.4. Note that the percentage change in quantity demanded is negative because it is a decrease.
5. Calculate the new price by applying the percentage change in price to the initial price. The new price can be found using the formula: new price = initial price * (1 + percentage change in price).