How to Calculate Deadweight Loss (DWL)
To calculate deadweight loss (DWL), find the triangle between supply and demand from the efficient to the actual quantity: DWL = ½ × |ΔQ| × price wedge.
Full guide: What deadweight loss is, with graphs
On the AP exam: AP Micro 2.8 Government Intervention in Markets, AP Micro 6.2 Externalities and AP Micro 6.4 Government Intervention Effects
The Deadweight Loss formula
Worked example: Deadweight Loss
A $4 per-unit tax reduces quantity from 100 to 80. DWL = ½ × (100 − 80) × $4 = ½ × 20 × 4 = $40.
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.
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 is the DWL formula?
DWL = ½ × base × height, the area of the triangle between the demand and supply curves over the units that no longer trade. The base is the drop in quantity from the efficient level, and the height is the price wedge at the actual quantity, such as a per-unit tax. A $4 tax that cuts quantity from 100 to 80 gives DWL = ½ × 20 × $4 = $40.
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.
How do you calculate deadweight loss for a price ceiling?
Use the same triangle, with the height measured as the gap between the demand curve and the supply curve at the quantity actually traded. If a ceiling cuts quantity from 50 to 30, and at 30 units buyers value the good at $14 while sellers need only $6, DWL = ½ × (50 − 30) × ($14 − $6) = ½ × 20 × $8 = $80. A price floor works the same way, except buyers rather than sellers limit the quantity traded.
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
Related calculators
Last updated