a. The equilibrium price of alcohol before the tax can be found by setting the demand equal to the supply:
500,000 - 20,000P = 30,000P
50,000P = 500,000
P = $10 per gallon
So the price of alcohol before the tax is $10 per gallon.
b. After the tax is imposed, the new supply curve becomes:
Q = 30,000(P - $1)
Setting this equal to the demand curve, we get:
500,000 - 20,000P = 30,000(P - $1)
50,000P = 530,000
P = $10.60 per gallon
So the price of alcohol after the tax is $10.60 per gallon.
c. The tax revenue is equal to the tax per unit times the quantity sold:
Tax revenue = $1 per gallon x Quantity sold
The quantity sold after the tax is imposed is equal to the quantity supplied, which is:
Q = 30,000($10.60 - $1) = 255,000 gallons
So the tax revenue is:
Tax revenue = $1 per gallon x 255,000 gallons = $255,000
d. The excess burden (deadweight loss) of the tax is the loss of consumer and producer surplus due to the distortion of the market caused by the tax. It can be calculated as the area of the triangle between the original and new supply curves, and above the new demand curve.
The original equilibrium quantity is:
Q = 30,000($10) = 300,000 gallons
The new equilibrium quantity is:
Q = 255,000 gallons
The change in quantity is:
∆Q = 300,000 - 255,000 = 45,000 gallons
The change in price is:
∆P = $10.60 - $10 = $0.60 per gallon
The area of the triangle is:
(1/2) x ∆P x ∆Q = (1/2) x $0.60 per gallon x 45,000 gallons = $13,500
So the excess burden (deadweight loss) of the tax is $13,500.