How deadweight loss works
Put a $2 tax on a good and two things happen. Every unit still traded hands $2 to the government — that money is a transfer, moved from buyers and sellers to the treasury but not destroyed. The damage comes from the units no longer traded: with the tax wedged between the price buyers pay and the price sellers keep, some trades that buyers valued above the sellers' cost stop clearing that hurdle and simply vanish. The surplus those trades would have created goes to no one. That vanished value is the deadweight loss, drawn as the triangle Arnold Harberger made famous in his 1954 study of monopoly welfare costs — which is why economists still call these "Harberger triangles."
The formulas
DWL = ½ × t × (Q₀ − Q₁)
buyer share = Es ÷ (|Ed| + Es)
seller share = |Ed| ÷ (|Ed| + Es)
where t is the per-unit tax (or, generally, the wedge between the buyers' and sellers' prices), Q₀ the quantity traded before the distortion, and Q₁ after. Tax revenue ist × Q₁. The incidence shares use the magnitudes of the price elasticities of demand (Ed) and supply (Es): the more inelastic side bears more of the tax.
Worked example
Take the default scenario: a $2.00 per-unit tax cuts the quantity traded from 1000 to 800 units. Here is the triangle, step by step:
| Step | Amount |
|---|---|
| Trades lost to the tax1000 units traded before − 800 after | 200 units (20%) |
| × Price wedgea per-unit tax is exactly the wedge between what buyers pay and sellers keep | $2.00 |
| × ½the first lost trade was worth nearly the full wedge, the last nearly nothing — on average, half | 0.5 |
| = Deadweight loss½ × $2.00 × 200 — surplus destroyed, collected by no one | $200.00 |
| Tax revenue (a transfer, not a loss)$2.00 × 800 units still traded | $1,600.00 |
Computed with this calculator's default settings — open the tool above and you'll see the same numbers, then swap in your own tax and quantities.
Incidence: the inelastic side pays
A law can say "sellers remit this tax," but economics decides who actually pays. Sellers facing price-sensitive customers cannot pass much of a tax along without losing them, so the burden stays on the sellers; sellers of something buyers cannot do without pass nearly all of it forward. The same elasticities that set the incidence split also set the size of the loss: when both sides are inelastic, quantity barely falls, the triangle is thin, and the tax mostly raises revenue instead of destroying surplus. That is exactly why excise taxes cluster on fuel, tobacco, and alcohol.
Deadweight loss is measured in the same currency as the surplus it destroys — see how that surplus arises with theconsumer & producer surplus calculator, estimate how strongly quantity responds to price with theprice elasticity of demand calculator, or work out what a tax adds to a checkout total with thesales tax calculator.
Frequently asked questions
What is deadweight loss?
Deadweight loss is the total surplus a market loses when something stops mutually beneficial trades from happening. A tax, price ceiling, or quota drives a wedge between what buyers pay and what sellers receive, so some trades that were worth more to buyers than they cost sellers no longer occur. The value those missing trades would have created goes to no one — not to buyers, not to sellers, not to the government. That vanished value is the deadweight loss, and on a supply-and-demand diagram it appears as the famous triangle between the curves.
Who really bears a tax — buyers or sellers?
Not necessarily whoever writes the check. Tax incidence depends on elasticity: the side of the market that can adjust less bears more of the burden. If demand is inelastic (buyers cannot easily cut back or switch), sellers pass most of the tax on as a higher price and buyers bear it. If supply is inelastic, sellers absorb it. The standard shares are buyer share = Es ÷ (|Ed| + Es) and seller share = |Ed| ÷ (|Ed| + Es) — tick the elasticity option in the calculator to see the split.
Why is the loss a triangle?
Because the lost trades are not all equally valuable. The trade lost right at the old equilibrium created almost no surplus — the buyer valued it only a hair above the seller's cost — while the last trade choked off by the full wedge created surplus worth nearly the entire wedge. With straight-line demand and supply curves, the lost surplus per trade rises linearly from zero up to the wedge, so the total is the area of a triangle: one-half times the wedge times the number of lost trades. That is why the formula carries the ½.
Do subsidies create deadweight loss too?
Yes — from the opposite direction. A subsidy pushes quantity past the efficient equilibrium, inducing trades where the resource cost of producing a unit exceeds what any buyer actually values it at. The excess cost on those over-produced units is deadweight loss, again a triangle, this time on the far side of equilibrium. The subsidy checks themselves are a transfer from taxpayers to buyers and sellers, but the over-production is pure waste. Anything that moves quantity away from equilibrium — up or down — destroys surplus.
When is a tax's deadweight loss small?
When quantity barely responds — that is, in inelastic markets. Deadweight loss comes from lost trades, so if a tax on gasoline or cigarettes hardly changes the quantity bought, the triangle is thin and most of the tax simply becomes revenue. It also matters that DWL grows with roughly the square of the tax rate: doubling a tax widens the wedge and lengthens the lost-quantity base at the same time, about quadrupling the loss. This is the Ramsey intuition behind efficient taxation: raise revenue with low rates on broad, inelastic bases rather than high rates on narrow, elastic ones.
Sources
- OpenStax, Principles of Economics 3e — Demand, Supply, and Efficiency (consumer surplus, producer surplus, and deadweight loss)
- OpenStax, Principles of Economics 3e — Elasticity and Pricing (elasticity and tax incidence)
The official figures this page quotes are drawn from the primary sources above — check them (or a qualified professional) before relying on a result.
Disclaimer: This calculator is foreducation and illustration only. The ½ × wedge × ΔQ triangle assumes linear demand and supply near the equilibrium and no other market failures; real-world welfare estimates account for curve shapes, pre-existing distortions, and externalities. Results are a textbook calculation, not a policy analysis, and nothing here is tax, financial, or investment advice.