How It Works
Measure how far the tax pushes the traded quantity down by subtracting the after-tax quantity from the before-tax quantity.
Deadweight Loss = ½ × Tax per Unit × (Quantity before − Quantity after)
- Recognize that the lost surplus forms a triangle whose height is the tax wedge and whose base is that drop in quantity.
- Take half of the tax times the quantity reduction to get the area of that triangle, the deadweight loss no one captures.
- Separately multiply the tax by the units still traded to find tax revenue, the part of the wedge that the government does collect.
Worked Example
Suppose a $4 per-unit tax cuts trade from 100 units to 80 units.
Quantity reduction
100 − 80 = 20 units
Deadweight loss
½ × $4 × 20 = $40
Tax revenue
$4 × 80 = $320
The $4 tax shrinks trade by 20 units and destroys $40 of surplus that no one captures, on top of the $320 collected in tax.
Understanding Deadweight Loss
Transfer versus loss
The single most important idea here is that a tax does two very different things at once, and only one of them is a loss. On the units that still trade, the tax simply moves money from buyers and sellers to the government — surplus changes hands but does not disappear, so it is a transfer. On the units that stop trading, something is genuinely destroyed: trades that both parties would have valued no longer happen, and the surplus they would have generated vanishes for everyone. That destroyed surplus is deadweight loss. The decomposition table beside this calculator draws the line explicitly, separating the wedge that becomes revenue from the wedge that becomes pure waste.
Why the loss is the lost trades
A market is efficient at its competitive equilibrium because every trade whose value to the buyer exceeds its cost to the seller actually takes place. A tax wedge breaks that: it raises the price buyers pay and lowers the price sellers receive, so trades whose value sat between the two now look unprofitable to at least one side and are abandoned — even though, ignoring the tax, they were still mutually beneficial. Deadweight loss is the total value of exactly these forgone-but-worthwhile trades. It is why economists call the wedge distortionary: it does not just redistribute, it shrinks the pie by discouraging transactions that should have happened.
Why doubling a tax can quadruple the loss
Deadweight loss grows with the square of the tax, not in proportion to it, and the triangle geometry shows why. Raising the tax stretches the triangle taller (a bigger wedge) and, because more trades become uneconomic, wider (a bigger quantity reduction). Two dimensions grow together, so the area roughly squares. The practical lesson is that a series of small taxes is usually far less damaging than one large tax raising the same revenue, and that the marginal efficiency cost of taxation rises sharply as rates climb. Intuition calibrated on small levies badly understates the cost of steep ones.
Elasticity decides who and how much
How big the loss is depends on how responsive the two sides are to price — their elasticity. If buyers and sellers barely change quantity when price moves (inelastic), almost no trades are lost and the triangle is small; a tax on such a good raises revenue cheaply. If they respond strongly (elastic), the same tax wipes out many trades and the loss balloons. Elasticity also governs incidence: the more inelastic side — the one less able to walk away — bears the larger share of the burden. This is the logic behind taxing necessities and addictive goods, which are inelastic, when the goal is revenue with minimal distortion.
Beyond taxes: the same triangle everywhere
Per-unit taxes are the textbook case, but the same wedge-and-triangle logic measures the cost of many interventions. A binding price ceiling or floor holds quantity below the efficient level and opens an identical deadweight-loss triangle. A monopolist restricting output to raise price creates one without any tax at all. Tariffs and quotas do it at the border. One important exception runs the other way: when a market already misfires because of an externality — pollution, congestion — a corrective tax can move it toward the efficient quantity and reduce deadweight loss rather than create it. The triangle is a general tool for scoring any departure from the competitive quantity, in either direction.
Where it fits in microeconomics
Deadweight loss is the capstone of basic welfare analysis, tying together consumer surplus, producer surplus, and market equilibrium. It is the standard way economists quantify the efficiency cost of taxes, subsidies, price ceilings, price floors, tariffs, and monopoly pricing. Because it isolates pure waste from mere redistribution, it lets the revenue, fairness, and efficiency of a policy be weighed separately — the core trade-off at the heart of public economics.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.