Is the deadweight loss the same as the tax revenue?

No, and mixing them up is the classic mistake. Tax revenue is a transfer: buyers and sellers hand it to the government, but it still exists and gets spent. Deadweight loss is different — it is the surplus on trades the tax prevented entirely. Nobody collects it. It is pure loss to society.

How do you calculate the deadweight loss of a tax?

It is the area of the triangle between the supply and demand curves over the units no longer traded: DWL = 1{2} × t × (Q^* - Qt), where t is the tax per unit, Q^* is the original quantity, and Qt is the smaller quantity after the tax.

Does it matter whether the tax is placed on buyers or sellers?

No. Whether the law collects the tax from buyers or from sellers, the same wedge opens between the two prices, the quantity falls to the same level, and the deadweight loss is identical. Who legally pays does not change the economics.

When is the deadweight loss bigger?

When supply or demand is more elastic. If buyers or sellers respond strongly to the price change, the quantity drops a lot, so many trades are lost and the triangle is large. Taxing something with very inelastic demand — a necessity people buy regardless — shrinks quantity little and wastes less.

Can a tax ever avoid deadweight loss?

Almost only when quantity does not move — perfectly inelastic supply or demand. A lump-sum tax (a fixed charge that does not depend on how much you buy or sell) also avoids it, because it does not change the price of any trade and so distorts no decisions.

Why does a per-unit tax create deadweight loss?

Short answer: a tax drives a wedge between what buyers pay and what sellers keep. That wedge shrinks the quantity traded. Some deals that would have made both sides better off no longer happen — and the value they would have created just disappears. That vanished value is the deadweight loss.

The mechanism in four steps

Without a tax, the market settles where supply meets demand. Every unit up to that point is worth more to a buyer than it costs a seller, so all the worthwhile trades happen.
A per-unit tax of $t$ means buyers pay a higher price and sellers receive a lower one, with the gap equal to the tax: $P_{b} - P_{s} = t$ .
Facing a higher price, buyers want less; facing a lower one, sellers offer less. The quantity traded falls from $Q^{*}$ to a smaller $Q_{t}$ .
For the units between $Q_{t}$ and $Q^{*}$ , the buyer still values the good above the seller's cost — but the tax makes the trade unprofitable, so it never happens. The lost surplus is the deadweight loss.

Worked example

Demand is $P = 100 - Q$ and supply is $P = 20 + Q$ . The government puts a 20-dollar tax on each unit.

No tax: $100 - Q = 20 + Q \Rightarrow Q^{*} = 40$ at a price of 60 dollars.

With the tax, the demand price minus the supply price must equal 20: $(100 - Q) - (20 + Q) = 20$

Solve: $80 - 2 Q = 20 \Rightarrow Q_{t} = 30$ . Buyers pay $P_{b} = 70$ , sellers keep $P_{s} = 50$ .

Deadweight loss: $\frac{1}{2} \times 20 \times (40 - 30) = 100$ dollars.

Tax revenue: $20 \times 30 = 600$ dollars — a transfer, not a loss.

The quantity fell from 40 to 30. The government collects 600 dollars, which still exists and gets spent. The extra 100 dollars, though, is gone for good — it is the surplus on the ten trades that the tax choked off.

Where the lost 100 dollars goes

Take the 31st unit. A buyer values it at $100 - 31 = 69$ dollars; a seller can make it for $20 + 31 = 51$ dollars. There are 18 dollars of surplus sitting there for the taking. But the 20-dollar tax is bigger than that 18, so no price makes the trade work. It does not happen, and the 18 dollars evaporate. Add up that vanished surplus across units 31 to 40 and you get the 100-dollar triangle.

Common misconception

“The deadweight loss is the tax the government takes.” No. The revenue is a transfer — it moves from buyers and sellers to the government but is not destroyed. Deadweight loss is the surplus on trades that the tax stopped from ever happening. Nobody ends up with it. That is what makes it a true loss.

Frequently asked questions

Why does a per-unit tax create deadweight loss?: The tax opens a gap between the price buyers pay and the price sellers keep, so the quantity traded falls below the efficient level. For the units no longer traded, the buyer valued the good more than it cost the seller to make — those were mutually beneficial trades. The surplus they would have created simply disappears, and that vanished surplus is the deadweight loss.
Is the deadweight loss the same as the tax revenue?: No, and mixing them up is the classic mistake. Tax revenue is a transfer: buyers and sellers hand it to the government, but it still exists and gets spent. Deadweight loss is different — it is the surplus on trades the tax prevented entirely. Nobody collects it. It is pure loss to society.
How do you calculate the deadweight loss of a tax?: It is the area of the triangle between the supply and demand curves over the units no longer traded: $DWL = \frac{1}{2} \times t \times (Q^{*} - Q_{t})$ , where $t$ is the tax per unit, $Q^{*}$ is the original quantity, and $Q_{t}$ is the smaller quantity after the tax.
Does it matter whether the tax is placed on buyers or sellers?: No. Whether the law collects the tax from buyers or from sellers, the same wedge opens between the two prices, the quantity falls to the same level, and the deadweight loss is identical. Who legally pays does not change the economics.
When is the deadweight loss bigger?: When supply or demand is more elastic. If buyers or sellers respond strongly to the price change, the quantity drops a lot, so many trades are lost and the triangle is large. Taxing something with very inelastic demand — a necessity people buy regardless — shrinks quantity little and wastes less.
Can a tax ever avoid deadweight loss?: Almost only when quantity does not move — perfectly inelastic supply or demand. A lump-sum tax (a fixed charge that does not depend on how much you buy or sell) also avoids it, because it does not change the price of any trade and so distorts no decisions.

See the tax wedge and the triangle on a graph

Enter the tax into Econ Academy's deadweight-loss calculator, or drag the curves on the supply-and-demand graph to watch the triangle grow.

Open the deadweight-loss calculator Try the supply-and-demand graph

Why monopolies create deadweight loss →Consumer and producer surplus calculator →

The mechanism in four steps

Worked example

Where the lost 100 dollars goes

Common misconception

Frequently asked questions

Related