Question

Suppose that the federal government is considering a new tax on cigarettes that is estimated to increase the retail price by $0.30 per pack. If the current price per pack is $8.60, use the regression in column (1) to predict the change in demand. What is the expected percentage change in cigarette demand?

Answer 1

To predict the change in demand due to a new tax on cigarettes, we can use the concept of price elasticity of demand. The expected percentage change in demand can be calculated using the price elasticity of demand and the percentage change in price.

Step-by-step explanation:

To predict the change in demand due to the new tax on cigarettes, 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. If a product has an elastic demand, a small change in price will result in a relatively large change in quantity demanded. On the other hand, if a product has an inelastic demand, a change in price will have a relatively small effect on quantity demanded.

In this case, we are given that the new tax on cigarettes is estimated to increase the retail price by $0.30 per pack. The current price per pack is $8.60. Using the regression in column (1), we can estimate the price elasticity of demand for cigarettes. We can then use this elasticity to calculate the expected percentage change in demand.

Let's assume that the price elasticity of demand for cigarettes is -0.5. This means that a 1% increase in price will result in a 0.5% decrease in quantity demanded. The percentage change in demand can be calculated by multiplying the percentage change in price by the price elasticity of demand:

Percentage change in demand = -0.5 × Percentage change in price

Given that the retail price per pack is estimated to increase by $0.30, we can calculate the percentage change in price:

Percentage change in price = (0.30 ÷ 8.60) × 100%

Plugging in the values, we can calculate the expected percentage change in demand:

Percentage change in demand = -0.5 × (0.30 ÷ 8.60) × 100%

Simplifying the calculation, the expected percentage change in demand is approximately -1.74%.

Answer 2

0.32 %

Step-by-step explanation:

Demand is the quantity that buyers are able & willing to buy, at a particular price & period of time. It is inversely related to price, as per law of demand.

Demand function is a regression equation that shows the relationship between dependent variable (demand) & independent variable (price)

Q = A - BP

where Q = Demand, A = Autonomous Demand, P = Price, B = Change in demand per unit change in price

Change in Quantity = B x Change in Price

Example : Considering Q = 50 - 0.5 P

Q {At previous P} = 50 - 0.5 (8.6) → = 50 - 4.3

= 45.7

Q {At new P} = 50 - 0.5(8.3) → = 50 - 4.15

= 45.85

Change in Quantity = 45.85 - 45.7 → = 0.15

Alternative Method : ΔQ = B x ΔP → = (0.30) x (0.5) → = 0.15

Percentage Change in Quantity = [Change IN Quantity / Old Quantity] x 100

[ΔQ/Q] x 100 → = [0.15 / 45.7] x 100 → = 0.32 %