Question

Suppose the demand curve for a good is given by QD = 10 - 2P and the supply curve is given by QS = -2 + P.

a) (4 points) Find the equilibrium price and quantity in the absence of any government intervention.

b) (6 points) Now suppose the government imposes a tax of t = 3. Find the new equilibrium price at

which the good is sold in the market and the quantity of the good sold. What is the net price (net

of taxes) that sellers receive?

c) (5 points) How much of the burden of the tax is borne by the buyers and how much is borne by

the sellers? Why is the burden of the tax asymmetric? (In the sense that one party bears more of the burden)

Answer 1

(a) Equating QD and QS,

10 - 2P = - 2 + P

3P = 12

P = 4

Q = - 2 + 4 = 2

(b) Assuming tax is imposed on sellers, the tax will reduce the effective price received by sellers by 3 at every output level, shifting supply curve leftward at every output level. New supply function becomes

QS = - 2 + P - 3 = - 5 + P

Equating with QD,

10 - 2P = - 5 + P

3P = 15

P = 5 (Price paid by buyers)

Price received by sellers = 5 - 3 = 2

Q = - 5 + 5 = 0

(c) Out of total tax of 3,

Tax burden of buyers = After-tax price paid by buyers - Pre-tax price = 5 - 4 = 1

Tax burden of sellers = Pre-tax price - After-tax price received by sellers = 4 - 2 = 2 (= Total tax - Tax burden of buyers)

In this case, sellers bear higher tax burden because supply is relatively inelastic compared to demand.