How to Calculate Deadweight Loss
Deadweight loss is the welfare-loss triangle: ½ × base × height, where the base is the change in quantity and the height is the price wedge.
Formula
DWL = ½ × base × height = ½ × |Q_efficient − Q_actual| × (price wedge)
Steps
- 1Find the efficient quantity. The competitive equilibrium quantity where supply meets demand.
- 2Find the actual quantity. The quantity after a tax, price control, or monopoly.
- 3Measure base and height. Base = the difference in quantity; height = the gap between the demand price and supply price at the actual quantity (e.g., the per-unit tax).
- 4Compute the triangle. DWL = ½ × base × height.
Worked example
A $4 per-unit tax reduces quantity from 100 to 80. DWL = ½ × (100 − 80) × $4 = ½ × 20 × 4 = $40.
Frequently asked questions
What causes deadweight loss?
Anything that moves a market away from its efficient quantity: taxes, subsidies, price ceilings and floors, monopoly, tariffs/quotas, and externalities.
Why is deadweight loss a triangle?
It measures the lost gains from trades that no longer happen, which form a triangle between the supply and demand curves over the missing units.