Question

Suppose the market supply and demand for a good is given by QP = 390 - 30P, and QS = 20P - 10, where Pis the price measured in dollars, QS is the quantity supplied, and QP is the quantity demanded. The government imposes a per-unit tax of $2. By how much will the quantity sold change because of the tax? What is the per-unit burden of tax on buyers? What is the per-unit burden of tax on sellers?

Answer 1

We have the following information

Demand = QD = 390 – 30P

Inverse demand: P = 13 – 0.033QD

Supply = QS = – 10 + 20P

Inverse supply: P = 0.5 + 0.05QS

For equilibrium we will equate the inverse demand and inverse supply equations

13 – 0.033Q = 0.5 + 0.05Q

Equilibrium quantity (Q) = 151

P = 13 – 0.033Q

Equilibrium price (P) = $8

Now, it is given that the government has imposed a tax of $2 per unit. So, the new supply equation will be

P = 0.5 + 0.05Q + 2

P = 2.5 + 0.05Q (new supply equation)

So, the tax will shift the supply curve upward to the left.

Equating the demand equation with the new supply equation

13 – 0.033Q = 2.5 + 0.05Q

Equilibrium quantity (Q) = 127

P = 13 – 0.033Q

Equilibrium price (P) = $9

Demand price = P = 13 – 0.033Q = $9.00

Supply price = P = 0.5 + 0.05Q = $6.85

Economic price incidence (EPI) on demanders = New Demand Price – Original Demand Price

EPI on demanders = 9.00 – 8.00 = 1

Economic price incidence (EPI) on suppliers = Original Supply Price – New Supply Price

EPI on demanders = 8.00 – 6.85 = 1.15