Question

Please compose three full paragraphs (one page single spaced) with any graphical or technical analysis as appropriate for each question 4) Suppose the legislature was considering an increase in the tax on cigarettes of 50 cents per pack. Assume the current price of a pack of cigarettes of $4.00, and sales in your state are five million packs per year. The estimated short-run elasticity of demand for cigarettes at the current price and quantity is 0.4. The long-run elasticity of demand (one year or longer) is 0.75.

a) Calculate and explain how much additional revenue the government can expect to receive in the first year (assuming no growth in the number of people smoking)? How much will smoking be reduced by?

b) Calculate and explain how much additional revenue the government can expect to receive in the second year (assuming no growth in the number of people smoking)? How much will smoking be reduced by?

Answer 1

Government was considering an increase in the tax on cigarettes of 50 cents per pack. Current price of a pack of cigarettes of $4.00, and quantity demanded = 5 million packs per year. Short-run elasticity of demand = 0.4. The long-run elasticity of demand = 0.75.

a) With tax, the new price will be 4.50. This implies a percentage change of (4.50 - 4)*100/4 = 12.5%. With short run elasticity being -0.4, the % change in consumption = 12.5%*-0.4 = -5%. Hence quantity demanded of cigarettes falls by 5% to reach 5 million x (1 - 0.05) = 4.75 million packs per year. Smoking is reduced by 0.25 million or 250000 packs and additional revenue earned in the first year = (4.75*4.50 - 5*4) = 1.375 million

b) With tax, the new price will be 4.50. This implies a percentage change of (4.50 - 4)*100/4 = 12.5%. With long run elasticity being -0.75, the % change in consumption = 12.5%*-0.75 = -9.375%. Hence quantity demanded of cigarettes falls by 9.375% to reach 5 million x (1 - 0.09375) = 4.53125 million packs per year. Smoking is reduced by 0.48675 million packs or 486750 packs and additional revenue earned in the sugar year = (4.53125*4.50 - 5*4) = $390625