Answer to Question #275338 in Microeconomics for Rashed

Question

According to the study of the Ministry of

Health the price elasticity of demand of

cigarettes is -0,2. And people purchase about 500 million cigarettes

each year.

a. If the tax on cigarettes were increased enough to raise the

price of cigarettes by 50 percent, what would be the effect

on the quantity cigarettes demanded? Show your work

explicitly.

b. Is raising the tax on cigarettes a more effective way to reduce

smoking, if the demand of cigarettes is elastic or if it is

inelastic? Briefly explain and justify your answer with

diagrams.

Answer 1

(A)

Elasticity of demand = % Change in quantity demanded / % Change in Price

 

% Change in Price = 50%

 

-0.2 = % Change in quantity demanded/50

 

Therefore, % Change in quantity demanded = -10%

 

Therefore, quantity of cigarettes demanded would fall by 10%

 

New quantity demanded = 0.9 × 500 = 450 million.

(B)

Raising a tax is more effective to reduce the quantity demanded of cigarettes when the demand is elastic since, elastic demand has a flatter demand curve which reduces quantity by a greater percentage for the same increase in the price level whereas inelastic demand has a steeper demand curve which decreases quantity by a lesser percentage for the same increase in the price level.

 

Let the tax raise the price of cigarettes from p to p' such that p' = p + t. The effect of the tax on the demand curves is shown below -

 

As can be seen from the figure for the same increase in the price level the decrease in quantity Q1, Q2 is greater in case the demand is elastic.