Practice
Per-unit taxes and deadweight loss
What a per-unit tax does to the price buyers pay, the price sellers keep, the quantity, tax revenue and deadweight loss.
The skill
A per-unit tax collected from sellers shifts supply up by the amount of the tax at every quantity, so buyers pay more and fewer units are traded. Find the new quantity where demand meets the shifted supply. The buyer price is on demand at that quantity, and sellers keep that price minus the tax. Deadweight loss is the triangle between the curves from the new quantity back to the old one. Whichever side has the less elastic curve bears more of the tax, no matter who sends the money to the government.
A worked example
In a competitive market for concert tickets, demand is Qd = 204 − 5P and supply is Qs = −30 + 4P, where P is the price in dollars and Q is the number of tickets per week.
The government places a tax of $9 on each ticket sold, collected from sellers.
What is the deadweight loss from the tax, in dollars? Round to two decimal places.
Solution
- Before the tax: P = 26, Q = 74.
- Sellers now need $9 more at every quantity, so they supply Qs = −30 + 4(Pb − 9) at a buyer price Pb. Setting it equal to demand gives Pb = 30 and Q = 54.
- Sellers keep Pb − 9 = 21.
- Tax revenue = $9 × 54 = $486.
- Deadweight loss is the triangle between the curves from 54 to 74: ½ × 9 × 20 = $90.
- Buyers pay 4 of the $9 through the higher price, 44.4% of it; the side with the less elastic curve bears more.
Answer: 90