How this instrument works
Deadweight loss is the piece of a market's total surplus that a tax, quota, price ceiling, or monopoly price destroys rather than merely moves around. When a per-unit tax or a binding price control drives a wedge between what a buyer pays and what a seller keeps, some trades that were worth making at the old price stop happening — a buyer who would gladly have paid $40 for a unit costing $32 to produce no longer finds the deal worthwhile once the wedge pushes the price past what either side will accept. That foregone trade benefited nobody; its value simply disappears from the economy.
The formula draws that loss as a triangle on the standard supply-and-demand diagram, and the shape explains the one-half. The unit right at the efficient quantity carried almost no surplus to begin with, so losing it costs almost nothing; the unit furthest into the shortfall carried close to the full price gap. Treating demand and supply as roughly straight lines over that narrow range makes the lost region a right triangle, and a triangle's area is half its base — the quantity choked off — times its height, the price gap at the reduced quantity.
That triangle is not the same figure as the money changing hands. A per-unit tax also raises revenue equal to the wedge times every unit still traded, a rectangle that transfers from buyers or sellers to the government rather than evaporating; a monopolist's markup above cost is profit it keeps, not a loss to anyone. The triangle this instrument returns excludes both transfers on purpose — it isolates only the trades that stopped happening, which is why economists call it the excess burden or the welfare cost of a distortion, separate from who wins or loses on the units still bought and sold.
- Enter Efficient (competitive) quantity — the amount that would trade at the market's undistorted, clearing price.
- Enter Actual (distorted) quantity — the smaller amount that actually trades once the tax, quota, or price control takes effect.
- Enter Price gap at the distorted quantity, $ — the vertical distance between what buyers pay and what sellers receive once the market has adjusted to that smaller quantity.
- Read Deadweight loss — the dollar value of surplus that neither buyer, seller, nor government collects, recomputed the instant any figure changes.
- If the field flags an ordering problem, check that the efficient quantity was entered as the larger of the two — a distortion can only shrink quantity traded, never raise it.
Worked example — a $15 wedge shrinks 1,000 units to 700
Set Efficient (competitive) quantity to 1,000 units, Actual (distorted) quantity to 700, and Price gap at the distorted quantity to $15 — the wedge a per-unit tax or a binding price control has driven between what buyers pay and what sellers keep once the market has settled at the smaller quantity. The instrument computes ½ × (1,000 − 700) × $15 = $2,250, the area of the triangle sitting between the demand and supply curves over the 300 units that no longer trade.
That $2,250 is not revenue and nobody banks it. If this wedge came from a per-unit tax, the government still collects real money on the 700 units that continue to trade — a separate rectangle, unaffected by this formula — while the $2,250 describes only the 300 units where a willing buyer and a willing seller could once have struck a deal worth more than it cost to make, and now cannot. Widen the price gap to $20 with the same quantities and the loss rises to $3,000; narrow the quantity shortfall to 100 units instead of 300 and, holding the $15 gap fixed, it falls to $750 — the triangle grows with either dimension.
Questions
Is deadweight loss the same thing as the tax revenue a government collects?
No — they sit on different parts of the same diagram. Revenue is a rectangle: the per-unit wedge multiplied by the quantity still traded, and it transfers from buyers or sellers to the government rather than vanishing. Deadweight loss is the triangle beyond that rectangle — the value of trades that would have cleared at the efficient quantity but no longer happen once the wedge makes them unprofitable for either side. Treating the two as one figure overstates or understates what a policy truly costs, since a transfer between parties is not a loss to the economy as a whole.
Who actually calculates a deadweight loss triangle, and for what decision?
Public-finance economists size the excess burden of a proposed excise tax against the revenue it is projected to raise, since a tax with a modest yield but a wide quantity effect can cost more in foregone trade than it collects. Antitrust economists apply the identical triangle to monopoly pricing, separating profit the firm captures — a transfer from consumers — from the units that never sell at all. Agricultural and trade economists run the same arithmetic on price supports, quotas, and tariffs to isolate the piece of a policy nobody, on either side, ever gets.
Why does the formula use one-half instead of the full rectangle?
Because the foregone trades do not all carry the same lost value. The unit sitting right at the efficient quantity was worth almost exactly what it cost to produce, so losing it costs almost nothing; the unit furthest into the shortfall carries close to the entire price gap. Treating supply and demand as roughly straight lines over that stretch makes the lost region a triangle, and a triangle's area is half its base times its height — half the quantity choked off times the full price gap, not the whole rectangle a linear reading might suggest.
What does it mean if the calculator flags my quantities?
It means the actual quantity was entered above the efficient one, an ordering that cannot describe a real distortion — a tax, quota, or binding price control only shrinks the quantity traded, never raises it past the competitive level. Check whether the two figures were swapped; the formula assumes the efficient quantity, the undistorted amount, is the larger of the pair.
Does a bigger deadweight loss always mean a worse policy?
Not by itself. This figure measures only the efficiency cost of a distortion, not everything a policy gets judged on. A minimum wage or a rent-control ordinance can carry a genuine efficiency triangle while still advancing a distributional goal, such as raising pay for low-wage workers or protecting sitting tenants, that this number never touches. It tells you which trades stopped happening and what they were worth; it does not weigh that against the reason the distortion exists.
Does the triangle formula hold for every size of distortion?
It is exact only when demand and supply run as straight lines across the stretch between the actual and efficient quantities — the standard textbook simplification. Real curves bend, so for a modest wedge the triangle sits close to the true lost area, but for a very large distortion spanning a strongly curved section of either curve, the actual shape departs from a clean triangle and this formula becomes an approximation rather than an exact accounting.
References
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.