Question

2. The annual demand for liquor in a certain state is given by the following equation: QD = 500,000 – 20,000P

   where P is the price per gallon and QD is the quantity of gallons demanded per year. The supply of liquor is given by the equation:

   QS = 30,000P

   a.) Solve for the equilibrium annual quantity and price of liquor. Suppose that a $1.00- per-gallon tax is levied on the price of liquor received by sellers. Use both graphic and algebraic techniques to show the impact of the tax on market equilibrium. b)Calculate the excess burden of the tax, the amount of revenues collected, and the incidence of the tax between buyers and sellers.

Answer 1

a) Set QD=QS

500000-20000P = 30000P

500000 = 30000P+20000P

500000 = 50000P

P = 500000/50000 = 10

Q = 500000-20000*10 = 300000

After the tax, the supply curve becomes 30000(P-1)

New equilibrium price and quantity

500000-20000P = 30000P-30000

500000+30000 = 50000P

P = 10.6

Q = 500000-20000*10.6 = 288000

b) Excess burden of the tax = DWL = 0.5*(300000-288000)*1 = 12000

Tax revenue = 1*288000 = 288000

Tax incidence on the consumers = 10.6-10 = 0.6

Tax incidence on the producers = 10-9.6 = 0.4