QS = 40p
where Q is the number of packs of cigarettes per year (in millions!), and p is the price per pack.
a. Compute the market equilibrium price and quantity.
b. Calculate the price elasticities of each curve at the equilibrium price/quantity.
c. California imposes a tax on cigarettes of $0.90 per pack. Suppliers pay this tax to the government. Compute the after-tax price and quantity. How much do suppliers receive net of tax (per pack)?
d. Demand for cigarettes is generally more elastic over longer periods of time as consumers have more time to kick the habit. What does this imply about the tax incidence in the long run as compared to the short run?
a. Set the supply and demand equal:
150 – 20p = 40p
Solving for p:
p* = 2.5
Q* = 100
So the price is $2.50 per pack and 100 million packs of cigarettes sold.
b. The slope of the demand equation is:
dQD/dp = -20
The elasticity of demand is therefore
ED = -20 (2.5/100 ) = -0.5
The slope of the supply equation is:
dQS/dp = 40
The elasticity of supply is then:
ES = 40 (2.5/100 ) = 1.0
c. The supply with the tax becomes:
QS = 40(p – 0.90 )
The new equilibrium is where
40(p – 0.90 ) = 150 – 20p
60p = 180
p* = 3.10
The quantity is:
Q* = 150 – 20 (3.10 ) = 88
The price sellers earn net of tax (per pack) is 3.10 – 0.90 = $2.20.
d. The more elastic the demand curve is, the less of the burden falls on consumers. So over a longer period of time, the burden on consumers ($0.60 ) will move towards the suppliers. Price will fall from $3.10 as consumers quit smoking.