The lost value is a triangle between the supply and demand curves
A per-unit tax raises the price buyers pay and lowers what sellers keep. Trade shrinks by ΔQ, and the gap the tax opens is ΔP. The deadweight loss is the area of the triangle those two spans form — half of base times height. This is value that would have been created but no longer is, on top of whatever the government collects in revenue.
Where ΔQ comes from — elasticity does the work
You rarely know the drop in quantity directly. Elasticity converts the tax into that drop: the more responsive demand is, the more trade the same tax kills.
- Inelastic goods lose little. A tax on staples like bread or salt (elasticity near −0.3) barely changes how much people buy, so the triangle is thin.
- Elastic goods lose a lot. A tax on a good with easy substitutes (elasticity near −2) drives buyers away, so the same tax rate destroys several times more trade.
- The tax squared. Since ΔP and ΔQ both rise with the tax, a small tax wastes almost nothing while a large one wastes far more than in proportion.
Roughly how the loss scales with elasticity
| Good | Demand elasticity | Relative deadweight loss |
|---|---|---|
| Staple (salt, bread) | −0.3 | small |
| Typical consumer good | −1.0 | moderate |
| Good with substitutes | −1.5 | large |
| Luxury / discretionary | −2.5 | very large |
At the same tax rate, the loss rises in step with elasticity — which is why economists call taxes on inelastic goods "efficient": they raise revenue while wasting the least.
Common questions
What is deadweight loss in simple terms?
It is the value of the trades that stop happening once a tax or price control gets in the way. Some buyers drop out because the price rose, some sellers drop out because their take fell, and the deals those two sides would have made are simply lost. Nobody collects that value, not even the government.
Why is deadweight loss called the Harberger triangle?
Arnold Harberger showed in 1954 that the loss appears as a triangle on a supply-and-demand chart, wedged between the two curves over the quantity that trade drops by. Its area is one half times the base times the height, which is where the formula comes from.
Does a bigger tax cause proportionally more deadweight loss?
No, it grows faster than that. Because both the price change and the quantity change scale with the tax, the loss scales with the tax squared. Doubling the tax roughly quadruples the deadweight loss.
