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.
The Deadweight Loss formula
Calculator
Enter the efficient quantity, the actual quantity and the price wedge to get the DWL triangle.
The competitive equilibrium quantity, where supply meets demand.
The quantity after the tax, price control or monopoly.
The gap between the demand price and the supply price at the actual quantity, for example the per-unit tax.
The 20 units that no longer trade destroy $40 of total surplus, an average of $2 of lost gains on each one.
- Units no longer traded
- 20
- Tax revenue (wedge × units still traded)
- $320
The base of the triangle: mutually beneficial trades the distortion wipes out.
A transfer from buyers and sellers to the government, not a loss. This line only applies when the wedge is a per-unit tax.
How to calculate Deadweight Loss, step by step
- 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: Deadweight Loss
A $4 per-unit tax reduces quantity from 100 to 80. DWL = ½ × (100 − 80) × $4 = ½ × 20 × 4 = $40.
Where the triangle comes from
Take demand P = 100 − Q against supply P = 20 + Q. The market clears where 100 − Q = 20 + Q, so Q = 40 and P = 60. Now put a $10 per unit tax on producers, which lifts their supply curve to P = 30 + Q. The new quantity solves 100 − Q = 30 + Q, giving Q = 35.
Buyers now pay 100 − 35 = $65 and sellers keep 65 − 10 = $55. The government collects 10 × 35 = $350. The deadweight loss is the triangle over the five units that no longer trade: ½ × 5 × 10 = $25.
Notice what that $25 is and is not. It is not money anybody has: the $350 moved from buyers and sellers to the government, and nobody lost it. The $25 is value that simply stops existing, because five units worth more to buyers than they cost to make are no longer produced.
Who actually pays the tax
The same worked example answers the incidence question, which usually follows on the same free-response prompt. Before the tax the price was $60. Buyers now pay $65, so they carry $5 of the $10. Sellers now keep $55, so they carry the other $5.
The split came out even because demand and supply have the same steepness here. That is the general rule worth carrying: the side of the market that is less elastic pays more of the tax, because being less responsive means being less able to walk away. A tax on something with very inelastic demand, like cigarettes, falls almost entirely on buyers, and that is also why it raises a lot of revenue and destroys comparatively little surplus.
The two results are linked. The less elastic either side is, the smaller the fall in quantity, so the smaller the deadweight loss and the larger the revenue.
The same triangle under a different name
Deadweight loss is not a tax concept. It is the value of every mutually beneficial trade that does not happen, so the same ½ × base × height appears wherever quantity is pushed away from the efficient level.
Under a binding price ceiling, quantity falls to what sellers will supply at the capped price, and the triangle sits between the demand and supply curves over the missing units. Under a price floor, quantity falls to what buyers will buy at the raised price, and the triangle sits in the same place. A monopoly produces where marginal revenue meets marginal cost rather than where price meets marginal cost, so the triangle spans the units between the monopoly quantity and the competitive one. A negative externality has an efficient quantity below the market quantity, and the triangle spans the overproduced units.
The base is always the gap in quantity and the height is always the vertical gap between what a unit is worth and what it costs, measured at the quantity that actually trades.
Deadweight Loss 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.
Get AP Econ exam tips in your inbox
Occasional emails with study tips, new interactive graphs, and exam-season reminders. Free, no spam.
No spam. Unsubscribe anytime. Read our privacy policy.
Keep track of what you have studied
A free EconLearn account adds progress tracking, your quiz history, and achievements. Studying here is free either way, and there is nothing to pay for as a student.
Create a free accountAlready have one? Sign in
Last updated