Question

At the current price of 2.00/pack, 5,000 cartons of cigarettes are demanded per day in Trentville, ZA. 1000 cartons are sold to teenagers (it’s legal in Trentville) and the rest to adults. The price elasticity of demand for cigarettes is 2.5 for teens and 0.10 for adults. If a tax raises the price of cigarettes by $0.40/pack, a) How many cartons of cigarettes are sold per day to adults after the tax? b) How many cartons of cigarettes are sold per day to teenagers after the tax? c) What is the overall (for all consumers) price elasticity of demand for cigarettes?

Answer 1

When the price is 2.00/pack, Quantity demanded = 5,000 cartons. Quantity demanded by teenagers =1000 cartons quantity demanded to adults = 4000.

The price elasticity of demand for cigarettes for teens = 2.5. The price elasticity of demand for cigarettes for adults = 0.10.

There is an increase in the tax rate which has increased the price of cigarettes by $0.40/pack,

According to the rule of price elasticity of demand, ed = %∆Qd/%∆P. With different elasticities provided, find the change in quantity demanded separately by teens and adults

ed (teens) = %∆Qd/(0.40*100/2.00) ed (adults) = %∆Qd/(0.40*100/2.00)

-2.50 = %∆Qd/20% -0.10 = %∆Qd/20%

%∆Qd by teens = -50% %∆Qd by adults = -2%

Hence teens will now demand a total of 1000 - 1000*50% = 500 cartons and adults will demand 4000 - 4000*2% = 3920 cartons.

a) How many cartons of cigarettes are sold per day to adults after the tax?

3920

b) How many cartons of cigarettes are sold per day to teenagers after the tax?

500

c) What is the overall (for all consumers) price elasticity of demand for cigarettes?

We see that % change in price is (0.40*100/2.00) = 20%. Total consumption falls from 5000 cartons to (3920 + 500) = 4420 cartosn. Quantity demanded is reduced by (4420 - 5000)*100/5000 = -11.6%

Overall elasticiy = -11.6%/20% = -0.58