Deadweight Loss Calculator
Measure the welfare lost to a per-unit tax as the triangle between the trades that stop happening.
A $2.00 tax cuts quantity from 100 to 80 units (ΔQ = 20), destroying $20.00 of surplus. Tax revenue is $160.00.
Deadweight loss is the surplus destroyed when a tax stops mutually beneficial trades. It equals the triangle ½ × tax per unit × the drop in quantity. With a $2 tax that cuts quantity from 100 to 80 units, the loss is ½ × $2 × 20 = $20, while the tax raises $2 × 80 = $160 in revenue.
How a tax creates deadweight loss
A per-unit tax drives a wedge between the price buyers pay and the price sellers keep. At the equilibrium quantity every trade was worth doing — each buyer valued the unit more than it cost to make. Once the tax raises the buyer’s price and lowers the seller’s take, the units near the margin no longer clear: buyers who valued them just above cost, and sellers who could just cover cost, walk away. Those trades that no longer happen are the deadweight loss. The gain to each was small, but summed across the missing units it forms a triangle whose area the tax revenue can never recover — the value simply vanishes from the economy.
The loss is a triangle: its height is the per-unit tax and its base is the fall in quantity traded.
Worked example
A market clears at 100 units. A $2 per-unit tax pushes the quantity traded down to 80 units.
- 1 Find the drop in quantity. Subtract the quantity after the tax from the quantity before it: ΔQ = 100 − 80 = 20 units. These are the trades the tax prevents.
- 2 Set the triangle’s height. The height of the deadweight-loss triangle is the per-unit tax — here $2, the wedge between the buyer’s price and the seller’s price.
- 3 Apply the triangle-area formula. DWL = ½ × tax × ΔQ = ½ × $2 × 20 = $20. That is the surplus lost to trades that no longer occur.
- 4 Compute tax revenue for context. Revenue = tax × Q_after = $2 × 80 = $160. This transfers to the government rather than vanishing, so it is not part of the loss.
- 5 Compare the two. The government collects $160 while $20 of surplus disappears — the efficiency cost of raising that revenue with this tax.
Tax revenue vs deadweight loss, and the role of elasticity
Revenue is a transfer; deadweight loss is value destroyed. How much is lost depends on how much quantity responds to the tax.
| Concept | What it represents | Effect on the loss |
|---|---|---|
| Tax revenue (tax × Q_after) | Money moved from buyers and sellers to the government — a transfer, not a loss. | Larger when quantity barely falls; not counted in deadweight loss. |
| Deadweight loss (½ × tax × ΔQ) | Surplus from mutually beneficial trades that the tax prevents — value that disappears entirely. | Grows with the size of the tax and with the drop in quantity. |
| Elastic supply or demand | Buyers or sellers respond strongly to the price change, so quantity falls a lot. | Large ΔQ → large deadweight loss. |
| Inelastic supply or demand | Quantity barely changes when the tax shifts the price. | Small ΔQ → small deadweight loss, so more revenue per unit of loss. |
Reading the result
Revenue is not a loss. The tax revenue is a transfer from buyers and sellers to the government — someone still has that money. Only the deadweight-loss triangle is value that no one captures, which is why economists judge a tax’s efficiency by the loss, not the revenue.
The loss rises faster than the tax. Doubling the tax roughly doubles ΔQ as well, so the triangle — being ½ × tax × ΔQ — grows with the square of the tax rate. Small taxes are cheap in welfare terms; large ones are disproportionately costly.
Elasticity drives everything. Because ΔQ is the base of the triangle, taxing goods with inelastic demand or supply (few substitutes, hard to avoid) destroys the least surplus. That is the standard efficiency argument behind taxing staples and addictive goods more heavily than easily-substituted luxuries.