Question

3. A country which does not tax cigarettes is considering the introduction of a $0.40 per pack tax. The economic advisors to the country estimate the supply and demand curves for cigarettes as:

Q_D = 140,000 -25,000P      Q_s = 20,000 + 75,000P

Where Q = daily sales in packs of cigarettes, and P = price per pack.

The country has hired you to provide the following information regarding the cigarette market and the proposed tax.

1. What are the equilibrium values in the current environment with no tax?
2. What price and quantity would prevail after the imposition of the tax? What portion of the tax would be borne by buyers and sellers respectively?
3. Calculate the deadweight loss from the tax.
4. What tax revenue will be generated?

Answer 1

a)

Set QD=QS to determine equilibrium price

140000-25000P=20000+75000P

100000P=120000

P=$1.20 (equilibrium price)

QD=140000-25000P=140000-25000*1.2=110000

QS=20000+75000P=20000+75000*1.2=110000

Equilibrium quantity=QD=QS=110000

b)

In this case, New supply curve is given as

QS'=20000+75000*(P-0.40)=20000+75000P-30000=-10000+75000P

Set QD=QS' to determine equilibrium price

140000-25000P=-10000+75000P

100000P=150000

P'=$1.50 (equilibrium price after tax is imposed)

QD=140000-25000P=140000-25000*1.5=102500

QS'=-10000+75000P=-10000+75000*1.5=102500

Equilibrium quantity after tax is imposed=QD=QS'=102500

Tax borne by consumers=New equilibrium price-Initial equilibrium price

=1.50-1.20=$0.30

Tax borne by consumers in percent terms=0.30/0.40=75%

Price received by sellers after paying tax=1.50-1,40=$1.10

Tax borne by consumers=New equilibrium price after tax-Initial equilibrium price

=1.20-1.10=$0.10

Tax borne by sellers in percent terms=0.10/0.40=25%

c)

Dead weight loss=1/2*Per unit tax*(Change in equilibrium quantity)

Dead weight loss=1/2*0.40*(110000-102500)=$1500

d)

Tax revenue=New equilibrium quantity*per unit tax=102500*0.40=$41000