What Deadweight Loss Actually Measures
Deadweight loss is the value of trades that stop happening once something pushes a market away from its equilibrium price. Before the distortion, 1,000 buyers valued the good above what it cost to make. After it, only 800 of those trades clear. The 200 vanished units each had a buyer whose willingness to pay exceeded the seller's marginal cost, so every one of them destroyed real surplus that neither side can recover.
A tax payment is different in kind. When buyers pay $10 more per unit, that $10 x 800 units = $8,000 flows to the government and still buys roads or schools — a transfer, a moved pile of money rather than a burned one. Buyers and sellers lose $9,000 of surplus in total, of which $8,000 reappears as revenue. Only the missing $1,000 triangle counts as deadweight loss, because nobody on any side of the market receives it.
Arnold Harberger put numbers on this idea in his 1954 and 1964 studies of US tax distortions, and the triangle computed here still carries his name. If you want the buyer-side piece of total surplus broken out on its own, the consumer surplus calculator measures the area under the demand curve and above the market price.
The Triangle Formula and Where It Comes From
The formula is DWL = 0.5 x change in price x change in quantity. With the default inputs the price rises from $50 to $60 and quantity falls from 1,000 to 800, so DWL = 0.5 x $10 x 200 = $1,000. Enter your own two price-quantity pairs and the calculator handles the absolute values, so a subsidy that lowers price works exactly the same way as a tax that raises it.
The 0.5 factor comes from linear demand and supply. The first foregone unit near Q = 800 loses almost the full $10 wedge, the last one near Q = 1,000 loses almost nothing because the curves meet there, and the average foregone unit loses half the wedge. Triangle area equals half the base times the height, with the quantity change as the base and the price wedge as the height.
Real curves bend, so the triangle is exact only for straight lines or small wedges. For a large tax with curved demand, the true loss differs from the triangle estimate by the area between the curve and its chord, which is usually second-order in size. Practitioners report the triangle anyway, because two prices and two quantities are the numbers you can actually observe in data.
How a Tax Drives the Wedge
A $10 per-unit tax charged to sellers shifts the supply curve up by $10. Buyers end up paying $60, sellers keep $50 after remitting the tax, and the market clears at 800 units instead of 1,000. The vertical distance between what buyers pay and what sellers keep is the wedge in the formula, and it appears identically if the tax is legally charged to buyers instead of sellers.
Statutory incidence and economic incidence are separate questions. Whoever is less elastic absorbs more of the tax, regardless of who writes the check — payroll taxes split roughly evenly between workers and firms in most empirical studies for exactly this reason. The deadweight loss itself does not care who remits; it depends only on the size of the wedge and the quantity of trade lost.
If you model the seller side of the market, remember that the short-run supply curve is the marginal cost curve above the shutdown point, which comes out of variable costs. The AVC calculator works out average variable cost per unit from your cost inputs, and the average fixed cost calculator covers the fixed-cost side, which never affects marginal supply decisions.
Elasticity Sets the Size of the Loss
The same $10 wedge destroys very different amounts of value depending on how responsive quantity is. Gasoline demand has a short-run elasticity near -0.1, so a $10 wedge barely moves gallons sold and the triangle stays thin. Restaurant meals or vacations, with elasticities beyond -1.0 in absolute value, shrink quantity sharply and the triangle fattens in proportion to the lost units.
This is the logic behind the Ramsey rule: raise revenue from the bases that respond least, because the excess burden per dollar collected scales with elasticity. A tax that destroys $1,000 of surplus while raising $8,000, as in the default result, burns 12.5 cents per dollar raised. Taxes on sharply inelastic bases like cigarettes can push that ratio under 10 cents at low rates.
Elasticities are measurable, and cross-market responses matter when substitutes exist. The cross price elasticity calculator estimates how the quantity of one good reacts to a change in another good's price, which tells you whether a tax leaks into substitute markets and opens a second triangle there.
Price Ceilings and Floors
A binding price ceiling, such as rent control set below market rent, caps the price under the $50 equilibrium. Quantity supplied slides down the supply curve, say to 800 units, while buyers still want 1,200, and a shortage of 400 units appears. The welfare geometry is the same as a tax: a triangle between the curves over the 200 lost units, priced by the same 0.5 x wedge x quantity-gap formula.
Floors mirror the damage from the demand side. A minimum price above equilibrium — agricultural price supports, or a high minimum wage in a competitive labor market — pushes quantity demanded down the demand curve while suppliers would gladly produce more. Unsold output, layoffs, or discarded inventory replace the shortage, and the triangle formula prices the distortion identically.
Ceilings add a second cost the triangle misses: the units that do trade may go to buyers who value them least, because rationing by queue, lottery, or connections replaces rationing by price. Glaeser and Luttmer estimated in 2003 that this misallocation destroyed additional value equal to a meaningful share of the direct triangle in New York's rent-controlled housing stock.
Monopoly Markup as a Private Tax
A monopolist restricts output until marginal revenue equals marginal cost, then charges the price read off the demand curve at that quantity. The default numbers read like a monopoly case: price rises from $50 to $60 while quantity drops from 1,000 to 800, and the gap between price and marginal cost is exactly the wedge in the DWL formula.
The rectangle between the two prices over the 800 surviving units is profit the monopolist takes from buyers — a transfer, the same way tax revenue is. The triangle over the lost 200 units is pure loss. This split is why economists score monopoly harm by the triangle while antitrust fights usually center on the profit rectangle and who keeps it.
You can size the wedge before running the numbers here by using the Lerner index, which links the price-cost margin to demand elasticity. The markup calculator converts cost and selling price into a percentage markup, and the accounting profit calculator totals the profit rectangle once you have per-unit margins and volume.
Tariffs and Trade Barriers
An import tariff raises the domestic price above the world price by the tariff amount. Domestic consumption falls, which is the consumption distortion, and domestic production climbs up a steeper marginal cost curve, which is the production distortion. The two triangles together form the classic tariff deadweight loss drawn in every international trade textbook.
For a small open economy, the tariff is a pure loss: the government collects tariff revenue as a transfer, but both triangles are destroyed value, and the world price does not move. Large economies can partly shift world prices in their favor, so a terms-of-trade gain offsets some of the triangles — the root of the optimal-tariff argument and of the retaliation risk that usually follows it.
Import quotas replicate the triangle without government revenue, since the markup becomes quota rent captured by license holders. If you compare landed costs across borders or evaluate tariff pass-through in a foreign currency, the cross exchange rate calculator converts between currency pairs through a common base rate.
Reading Your Result and What to Do With It
Divide the loss by the transfer to get cents destroyed per dollar moved: $1,000 of deadweight loss against $8,000 of tax revenue gives 12.5 cents per dollar raised, which is moderate by real-world standards. Estimates for broad US taxes generally land between 20 and 50 cents per marginal dollar, with narrower bases like capital taxation sometimes exceeding a dollar at the margin.
Small wedges do almost no damage, because the loss is second-order in the wedge size — doubling a small tax roughly quadruples the triangle. If your quantity gap is zero, the tool returns a $0 loss: a price change with no quantity response is a pure transfer, and no surplus is destroyed at all. This is the analytical case for tolerating mild distortions while resisting large ones.
Check unit consistency before trusting any output: the price gap and the quantities must refer to the same time period and the same unit count. The price per unit calculator turns bulk costs into per-unit prices for the price fields, and a break even calculator helps you test whether the post-wedge quantity still covers fixed costs.