Question

Market demand and supply for a commodity are given by the following equations:
Demand: X = 30 – (1/3) P Supply: X = -2.5 + (1/2) P where X= quantity (units), and P=price per unit ($)

Suppose that the government is planning to impose a tax on this commodity and considering the following two options:

Option 1: A unit tax of $15

Option 2: An ad valorem tax of 20

What is the excess burden of each option?

Answer 1

Option 1.

New supply equation after tax= X=-2.5+0.5(P-15)= -2.5+0.5P-7.5= -10+0.5P

Excess burden=Deadweight loss= 0.5(48-33)(17-14)= 0.5*15*3= $22.5

Option 2.

Ad valorem tax= 20%

New supply equation: X=-2.5+(P-0.2P)

Deadweight loss=0.5(44.3-35.4)(17-15.2)=$8.01