How this calculator works
A tax, a price floor, a monopoly price or another distortion moves a market away from the price and quantity where supply meets demand. Some buyers and sellers who would both have gained from a trade no longer trade, and the value of those lost trades is the deadweight loss. On a supply and demand diagram it is the triangle between the old and new quantities, with height equal to the price change and base equal to the quantity change, so the area is half that product. The estimate assumes straight-line supply and demand and ignores administrative costs, compliance costs and any benefit from the revenue raised. Those effects need a separate accounting.
Formula
Deadweight loss = 0.5 × |new price - original price| × |original quantity - new quantity|. Solving for a price assumes the usual case where the new price is higher and the new quantity lower: original price = new price - 2 × loss / quantity change, and new price = original price + 2 × loss / quantity change.
Worked example
A price rising from $10 to $12 while quantity falls from 100 to 90 leaves a triangle of 0.5 × $2 × 10 = $10. The price change is $2 and the quantity change is -10.
Advertisement
Frequently asked questions
Does deadweight loss include the tax revenue?
No. The tax revenue is a transfer from buyers and sellers to the government, not a lost resource. Only the trades that no longer happen count as deadweight loss, though the cost of collecting and complying with the tax is a separate efficiency cost.
Why divide by two?
The loss is a triangle, not a rectangle. Its area is half the base times the height, so half the quantity change times the price change. Using the full product would double-count the lost trades.
Is deadweight loss always a triangle?
Only when supply and demand are approximately straight lines over the range involved. With curved curves the true loss is the area between them, which the triangle approximates for small changes.