|
Economics 121 B & C |
Quiz 4 - Answers |
October 3, 1997 |
|
Prof. A. D. Becker |
|
|
A recent economic study predicts that a $0.25 per pack increase in the price of cigarettes will reduce teen smoking by 20% and adult smoking by only 5%. The average retail price of cigarettes is currently $1.75.
Estimate and interpret the elasticity of demand for cigarettes by teen smokers and again for adult smokers.
|
Teen Demand |
Adult Demand |
|
|
Elasticity estimate |
-1.4 |
-.35 |
|
Elasticity interpretation |
Elastic |
Inelastic |
The percent change in price is (0.25/1.75)% = 14.29% (or 1/7th). So, the elasticity of teen demand is -20%/(1/7) = -1.4 and the elasticity of adult demand is -5%/(1/7) = -0.35.
The overall elasticity of demand for cigarettes at the retail level (adult + teen) is -0.5 (h = -0.5) and the elasticity of supply is 3 (e = 3). How much of a tax will be needed to get the retail price to rise by $0.25?
Remember that the buyers' and sellers' shares of a tax are:
The buyers' share is all we need and it is (3/(3 + |-0.5|)) = 6/7 or 0.857. The increase in retail price is the amount the buyers pay so the tax amount, T, multiplied by the buyers' share, 6/7, should be $0.25:
(6/7) T = $0.25
T = $0.25 (7/6)
T = $0.2917 (or T = 0.29166666… = 29 1/6¢)