Question

Assume that the State of Florida wants to reduce cigarette smoking by fifty percent (50%). A study found that own-price elasticity of demand for cigarette coefficient for Florida is 0.58. The current price per pack of cigarette in Florida is $5.00.
Question:

(a) How many percent tax (increase) will the State of Florida impose on a pack of cigarette to achieve the fifty percent (50%) reduction in cigarette smoking in Florida?

(b) What is the new, tax-inclusive price per a pack of cigarette in Florida?

Answer 1

(a) An increase in tax by 86.20% will result in the reduction of cigarette smoking in Florida by 50%.

To calculate this we will use the Price Elasticity of Demand formulae as mentioned below:

Price Elasticity of Demand = % change in demand / % change in price

Now in order to calculate the percentage of increase in price of cigarettes which will result in reduction in demand of the same by 50%, we will change the above formulae by dividing the percentage change in demand by price elasticity of demand, as shown below:

% change in demand / Price Elasticity of Demand = % change in price

50% / 0.58 = 86.20%

(b) The new, tax inclusive price per pack of cigarette in Florida is $9.31.

This can be calculate by multiplying the price per pack of cigarette by the % increase in price and then adding the same with the old price. As shown below:

5.00 x 86.20% = $4.31

New Price = $ 5.00 + $ 4.31 = $9.31

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