Question

The market for a particular good is described by the following demand and supply equations respectively: QD = 448 – 3.5P and QS = 2.5P – 80. Consider that after much discussion among policymakers and following a final vote, the government implements a 20% ad valorem tax on sellers of the good. The market adjusts and is currently in equilibrium.

1. After the tax is implemented, what quantity of the good is traded?

2. What price do buyers pay?

3. What price do sellers receive?

4. After the tax is implemented, do consumers or producers face any tax burden? If so, then state who faces a higher burden, and what this implies about the group’s price elasticity relative to the other group’s price elasticity.

Answer 1

Let us calculate the equilibrium price before tax

Set QD=QS

448-3.5*P=2.5P-80

528=6P

P=$88

a)

Given

QD=448-3.5*P

New supply curve is given by

QS'=2.5P*(1-20%)-80

QS'=2.0P-80

Set QD=QS' for equilibrium

448-3.5P=2P-80

5.5P=528

P=96

QD=448-3.5P=448-3.5*96=112

QS'=2.0P-80=2*96-80=112

After tax, quantity traded=112

b)

Buyers' price=P=$96

c)

Price that seller's receive=P*(1-20%)=96*(1-20%)=$76.80

d)

After tax, price that sellers receive is less than what was before tax. So, producer surplus is reduced after tax.

Price that the buyers pay has increased after tax. So, there is a reduction in consumer surplus as well.

We can say that consumers and sellers both face the tax burden.

Tax burder faced by seller=Price that seller got before tax-Price that seller gets after tax

Tax burder faced by seller=88-76.8=$11.2 per unit sold

Tax burder faced by buyer=Price that buyers' pay after tax-Price that buyers' paid after tax

Tax burder faced by buyer=96-88=$8

Sellers face a higher tax burden.

We can say that buyers relatively more elastic.