Question

3.         

The U.S. Department of agriculture estimates that the elasticity of demand for cigarettes is 0.3 for adult smokers and 2.5 for teens and new smokers. Also the income elasticity of demand for cigarettes is estimated to be 0.5.

i.          Suppose the federal government, influenced by the health lobby, imposes a tax on cigarettes that raises the price by 15 percent. What effect will this have on the cigarette consumption of adult smokers? (4 points)

ii.         Suppose that it was estimated that this year there were 2 million teenage and new smokers. What would be the predicted number of new and teen smokers under the policy in (a)? (4 points)

Answer 1

Given:

Ed for adult smokers = 0.3

Ed for teens and new smokers = 2.5

Income elasticity = 0.5

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i) Tax causes % change in price by 15%

Now, Ed = % change in Qd / % change in P

Thus,

0.3 = % change in Qd / 0.15

% change in Qd = 0.045 = 4.5%

Consumption of cigarettes by adult smokers will fall by 4.5%

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ii) Tax causes % change in price by 15%

Now, Ed = % change in Qd / % change in P

Thus,

2.5 = % change in Qd / 0.15

% change in Qd = 0.375 = 37.5%

Consumption of cigarettes by teens and new smokers will fall by 37.5%

Earlier number = 2 million

New number = 2 x (1 - 0.375) = 1.25 million

The new number of teens and new smokers is 1.25 million