Question

Consider a case where the initial price of a pack of cigarette is $1.50 per pack and the quantity sold and bought is 200,000 packs per day. Assuming an elasticity of demand of -0.85 and elasticity of supply of 2.5,

1. Calculate the tax revenue and excess burden if the excise tax on each pack of cigarette is $1.50.
2. Suppose the elasticity of demand is -0.45 and the elasticity of supply is 1.05, what is the incidence of the tax on (i) the consumers (ii) the producer
3. What is the new tax revenue and excess burden?

Answer 1

A) elasticity of demand=(∆Q/∆p)*(p/q)

-0.85*200,000/1.5=(∆Q/∆p)

∆qd/∆p=-340,000/3

Elasticity of supply=(∆qs/∆p)*(p/qs)

∆qs/∆p=2.5*200,000/1.5=1,000,000/3

The new supply price of 200,000 is 1.5+1.5=3

But at p=3 ,qd=200,000-340,000*1.5/3=30,000

So there is a surplus in the market ,price need to reduced,.to reach new EQUILIBRIUM

Let reduction in price=x

Reduction in price increase quantity demanded and decrease quantity supplied

30,000+x*340,000/3( demand)=200,000-x*1,000,000/3(supply)

90,000+340,000x=600,000-1,000,000x

1,340,000=510,000

X=510,000/1,340,000=0.38

New equilibrium price=3-0.38=2.62new equilibrium quantity=30,000+0.38*340,000/3=220,000/3

Tax revenue=1.5*220,000/3=110,000

Excess burden=1/2*tax*change in quantity=1/2*1.5*(200,000-220,000/3)=0.5*1.5*(600,000-220,000)/3=0.5*380,000/2=380,000/4=95,000

B)

-0.45*200,000/1.5=∆qd/∆p

∆qd/∆p=-60,000

1.05*200,000/1.5=∆qs/∆p

∆qs/∆p=140,000

The new supply price of 200,000=1.5+1.5=3

But at p=3 ,qd=200,000-1.5*60,000=110,000

So at p=3 ,there is a surplus,so price need to be reduced to reach equilibrium.

Let x the reduction in price

110,000+x*60,000=200,000-x*140,000

200,000x=90,000

X=90,000/200,000=0.45

New equilibrium price=3-0.45=2.55

New equilibrium quantity=110,000+0.45*60,000=137,000

Tax incidence on consumer=new equilibrium price- initial equilibrium price=2.55-1.5=1.05

Tax incidence on producers=tax - tax incidence on CONSUMER=1.5-1.05=0.45

C) tax revenue=1.5*137,000=205,500

Excess burden ( deadweight loss)=1/2*1.5*(200,000-137000)=0.5*1.5*63,000=47,250