Deadweight Loss Calculator
Enter the original and new price and the original and new quantity to see the deadweight loss, the triangle of total surplus that is lost.
Updated
Deadweight Loss Calculator
Our Deadweight Loss Calculator measures the value a market loses when a tax, price control, subsidy or monopoly pushes price and quantity away from the efficient equilibrium. Type the original price, the new price, the original quantity and the new quantity. It returns the deadweight loss as the area of the triangle between the two points, along with the change in price and quantity in units and percent. It is built for economics students checking homework, teachers preparing examples and analysts sizing the cost of a policy.
Quick answer
Deadweight loss is ½ × price change × quantity change: if the price moves from 100 to 120 and the quantity falls from 500 to 420, ½ × 20 × 80 = 800.
- Price change: new price − original price, taken as a positive number.
- Quantity change: new quantity − original quantity, taken as a positive number.
- Deadweight loss: half of price change × quantity change.
- No change in quantity: the deadweight loss is 0.
What Is Deadweight Loss?
Deadweight loss is the total surplus that disappears when a market trades less (or more) than the efficient quantity. Total surplus is the gain buyers get from paying less than they were willing to pay, plus the gain sellers get from receiving more than their cost.
At the free-market equilibrium every trade worth making takes place. When a tax or a price control cuts the quantity traded, some of those trades no longer happen. The gains from them are not handed to anyone else. They are simply lost, which is why economists call the loss "deadweight". It is also known as excess burden, welfare loss or the Harberger triangle.
Deadweight Loss Formula
ΔP = new price − original price
ΔQ = new quantity − original qty
- DWL: the deadweight loss, in money.
- ΔP: the change in price per unit.
- ΔQ: the change in the quantity traded.
The upright bars mean "ignore the sign": a fall of 80 units counts as 80. The formula is the area of a triangle, half of base times height, with the quantity change as the base and the price change as the height.
How to Calculate Deadweight Loss
A market sells 500 units at a price of 100. After a tax the price is 120 and sales fall to 420 units:
ΔQ = 420 − 500 = −80
DWL = ½ × 20 × 80
= 800
- Find the price change. 120 − 100 = 20.
- Find the quantity change. 420 − 500 = −80. Drop the minus sign to get 80.
- Multiply the two. 20 × 80 = 1,600.
- Halve the result. 1,600 ÷ 2 = 800.
The deadweight loss is 800. Sales fell by 16% while the price rose by 20%.
Deadweight Loss on a Graph
Supply and demand cross at the original quantity. At the new, lower quantity there is a gap between what buyers are willing to pay (the demand line) and what it costs sellers to supply (the supply line). That gap is ΔP. The triangle runs from the gap back to the crossing point, a distance of ΔQ, and its area is the surplus lost on the units that are no longer traded.
Which Prices and Quantities to Enter
- Original price and quantity: the market equilibrium before the change.
- New quantity: the amount traded after the tax, price control or other change.
- New price: chosen so that the price change equals the full gap at the new quantity.
For a tax, the gap is the tax per unit: the price buyers pay minus the price sellers keep. If a tax of 2 splits into buyers paying 1.20 more and sellers keeping 0.80 less, the height of the triangle is 2, not 1.20. Entering only the buyers' price rise would understate the loss.
Deadweight Loss Examples
A per-unit tax. A good sells 1,000 units at 10. A tax of 2 per unit opens a gap of 2 and sales fall to 850. Enter 10, 12, 1,000 and 850:
= 150
The tax raises 2 × 850 = 1,700 for the government and destroys a further 150 of surplus.
A price ceiling. Rent is capped at 40 where the market price was 50, and the number of flats offered falls from 200 to 160:
= 200
A price floor. A minimum price lifts the price from 8 to 10 and the quantity bought falls from 300 to 240:
= 60
What Causes Deadweight Loss?
| Cause | Effect on quantity |
|---|---|
| Tax | Falls |
| Price ceiling | Falls (less supplied) |
| Price floor | Falls (less bought) |
| Monopoly | Falls (output held back) |
| Quota | Falls (capped) |
| Subsidy | Rises above efficient |
In every case the quantity traded moves away from the efficient level. A subsidy is the odd one out: it causes too much trade, with units produced that cost more than buyers value them. The triangle then sits to the right of the crossing point, and the same formula applies.
Why a Bigger Tax Hurts More Than Proportionally
With straight-line supply and demand, doubling a tax doubles both sides of the triangle, so the deadweight loss is four times as large. Take the tax example above and raise the tax from 2 to 4, so that sales fall by 300 instead of 150:
| Tax | ΔQ | DWL |
|---|---|---|
| 2 | 150 | 150 |
| 4 | 300 | 600 |
Tax revenue rises from 1,700 to only 4 × 700 = 2,800, while the loss quadruples. This is why economists tend to favour low rates on a broad base over high rates on a narrow one.
Elasticity and Deadweight Loss
How far quantity falls depends on how sensitive buyers and sellers are to price, which economists call elasticity.
- Elastic markets: a small price gap causes a large fall in quantity, so ΔQ and the deadweight loss are large.
- Inelastic markets: quantity barely moves, so the triangle is thin and the loss is small.
- Perfectly inelastic: quantity does not change at all and the deadweight loss is 0.
This is one reason taxes are often placed on goods such as fuel and tobacco, where demand changes little when the price rises.
What the Result Leaves Out
- Curved lines. The triangle is exact only when supply and demand are straight between the two points. For curved lines it is an estimate.
- Who bears the loss. The result is the total. It does not split the loss between buyers and sellers.
- Transfers. Tax revenue and gains passed from one side to the other are not losses and are not included.
- Side effects. A tax on a harmful good may reduce pollution or illness. Those benefits are outside this formula.
The result is for education and planning and is not economic or financial advice.
Key Terms
- Deadweight loss
- Total surplus lost when a market is away from its efficient quantity.
- Consumer surplus
- What buyers were willing to pay minus what they paid.
- Producer surplus
- What sellers received minus their cost of supplying.
- Equilibrium
- The price and quantity where supply equals demand.
- Tax wedge
- The gap between the price buyers pay and the price sellers keep.
- Elasticity
- How strongly quantity responds to a change in price.
How to Use the Deadweight Loss Calculator
- Enter the original price. Type the price per unit at the original equilibrium, such as 100.
- Enter the new price. Type the price per unit after the change, such as 120.
- Enter the original quantity. Type the number of units traded at the original price, such as 500.
- Enter the new quantity. Type the number of units traded after the change, such as 420.
- Read and copy the result. The deadweight loss appears as you type, with the working and the change in price and quantity in units and percent. Press Copy to copy it, or Clear or Esc to start again.
Example: a rent cap moves the price from 50 to 40 and the quantity from 200 to 160. The result is 200, from ½ × 10 × 40.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you calculate deadweight loss?
Subtract the original price from the new price, subtract the original quantity from the new quantity, ignore any minus signs, multiply the two changes and divide by 2.
What is the deadweight loss formula?
Deadweight loss = ½ × |ΔP| × |ΔQ|, where ΔP is the change in price and ΔQ is the change in quantity. It is the area of a triangle on a supply and demand graph.
What is the deadweight loss if the price rises from 100 to 120 and the quantity falls from 500 to 420?
It is 800. The price change is 20 and the quantity change is 80, so ½ × 20 × 80 = 800.
What does deadweight loss mean?
It is the value of trades that would have benefited both buyers and sellers but no longer happen. Nobody receives that value, so it is a pure loss to society.
What causes deadweight loss?
Anything that moves the quantity traded away from the efficient level: taxes, price ceilings, price floors, quotas, subsidies and monopoly pricing are the usual causes.
Why is deadweight loss a triangle?
Each unit that is no longer traded loses the gap between what a buyer would pay and what it costs to supply. That gap shrinks steadily to zero at the original quantity, which traces out a triangle.
Can deadweight loss be zero?
Yes. If the quantity traded does not change, for example when demand or supply is perfectly inelastic, the triangle has no width and the deadweight loss is 0.
Is tax revenue part of deadweight loss?
No. Tax revenue is a transfer from buyers and sellers to the government. Deadweight loss is the extra surplus that is lost on top of that and goes to nobody.
Is the Deadweight Loss Calculator free?
Yes. It is free to use, with no sign-up and no limit on how many times you use it.
Sources
- Wikipedia. Deadweight loss.
- Corporate Finance Institute. Deadweight Loss.
- OpenStax. Principles of Economics 3e, 3.5 Demand, Supply, and Efficiency.
- WallStreetMojo. Deadweight Loss.
- Wikipedia. Economic surplus.
- Wikipedia. Excess burden of taxation.
Try our Deadweight Loss Calculator to size the surplus lost to any tax, price cap or price floor.