To calculate deadweight loss with a price floor, use the triangle formula: DWL = ½ × (Qequilibrium − Qnew demand) × (Pfloor − Psupply at new demand). That gives you the area of the triangle on a supply-and-demand graph representing the value destroyed by the intervention. You need four numbers from the market’s supply and demand equations, and the arithmetic takes a few lines once you have them.
First, Confirm the Floor Is Binding
A price floor only distorts the market when it sits above the equilibrium price. A floor at or below equilibrium changes nothing because the market already clears at a higher price on its own. Economists call a floor that actually forces the price up a “binding” floor. If the floor is below equilibrium, the deadweight loss is zero and there is nothing to calculate.
When a floor is binding, it pushes the price above what buyers would normally pay. Buyers purchase fewer units, and sellers want to produce more. The federal minimum wage is the textbook example. Under the Fair Labor Standards Act, the federal floor sits at $7.25 per hour, a rate unchanged since 2009.1Office of the Law Revision Counsel. 29 USC 206 – Minimum Wage In any labor market where the equilibrium wage would naturally settle below $7.25, that statutory rate is binding and produces the same kind of surplus and deadweight loss the formula captures.
The Four Numbers You Need
Every price-floor deadweight loss calculation requires exactly four values. Miss one and you cannot draw the triangle.
Equilibrium Price and Quantity
Set the supply equation equal to the demand equation and solve for price. That intersection is the market’s natural resting point before any intervention. Plug the equilibrium price back into either equation to get the equilibrium quantity. These two values anchor the right-hand corner of the deadweight loss triangle.
Quantity Demanded at the Floor Price
Take the mandated floor price and substitute it into the demand equation. Because the floor sits above equilibrium, buyers want fewer units. This smaller quantity demanded is the number of transactions that actually occur under the floor. Sellers may want to produce more at the higher price, but only the amount buyers are willing to purchase gets traded.
The Supply Price at the New Quantity
This is the variable people most often forget. Plug the new quantity demanded into the supply equation and solve for price. The result tells you the lowest price sellers would have accepted to produce that reduced quantity. It represents the marginal cost of the last unit that actually gets sold. On the graph, this point sits on the supply curve directly below the floor price at the new quantity demanded, forming the bottom corner of the triangle.
A Worked Example
Suppose a market has these linear supply and demand equations:
- Demand: Qd = 100 − 4P
- Supply: Qs = −20 + 4P
The government imposes a price floor of $20.
Step 1: Find Equilibrium
Set quantity demanded equal to quantity supplied and solve for P:
100 − 4P = −20 + 4P
120 = 8P
P = $15
Plug $15 back into either equation to get equilibrium quantity:
Qd = 100 − 4(15) = 40 units
The market naturally settles at $15 and 40 units. The $20 floor sits above $15, so it is binding.
Step 2: Find Quantity Demanded at the Floor
Substitute $20 into the demand equation:
Qd = 100 − 4(20) = 20 units
Buyers will only purchase 20 units at $20. That is a drop of 20 units from equilibrium.
Step 3: Find the Supply Price at the New Quantity
Plug 20 units into the supply equation and solve for P:
20 = −20 + 4P
40 = 4P
P = $10
Sellers would have accepted as little as $10 to produce those 20 units. The floor forces buyers to pay $20 instead.
Step 4: Calculate the Triangle
You now have both dimensions:
- Horizontal distance (quantity reduction): 40 − 20 = 20 units
- Vertical distance (price wedge): $20 − $10 = $10
Apply the formula:
DWL = ½ × 20 × $10 = $100
That $100 is economic value that vanished. It did not shift from buyers to sellers or vice versa. It simply ceased to exist because 20 mutually beneficial transactions no longer happen.
What the Triangle Looks Like on the Graph
On a standard supply-and-demand diagram, the deadweight loss triangle sits between the supply curve, the demand curve, and a vertical line drawn from the equilibrium quantity down to the new quantity demanded. Its three corners are the original equilibrium point where the curves cross, the point on the demand curve at the new quantity (which sits at the floor price), and the point on the supply curve at the new quantity (the lower supply price you calculated). Everything inside that triangle is value from trades that would have benefited both buyer and seller but no longer occur.
The triangle does not include the surplus units that sellers want to produce but cannot sell. Those unsold units create their own problems, but they do not factor into the deadweight loss calculation because those transactions never would have occurred at the floor price anyway. The triangle captures only the trades that would have happened at prices between the supply cost and what buyers were willing to pay, and now cannot happen because the floor prohibits any transaction below the mandated price.
Mistakes That Produce the Wrong Number
The math is simpler than it looks, but a few errors come up constantly.
- Using quantity supplied instead of quantity demanded at the floor. Sellers want to produce more than buyers will purchase, but the quantity that actually trades is the quantity demanded. Using the supply quantity inflates the triangle.
- Forgetting to find the supply price at the new quantity. Some people subtract the equilibrium price from the floor price for the vertical distance. That is wrong. The vertical dimension runs from the floor price down to the supply curve at the new quantity, not down to the old equilibrium. The supply price at the reduced quantity is usually lower than the equilibrium price.
- Calculating the full rectangle instead of the triangle. The lost-transaction zone is triangular because the supply and demand curves slope toward each other. Multiplying base by height without dividing by two doubles the actual loss.
- Treating a non-binding floor as binding. If the imposed price is at or below equilibrium, the market ignores it. Compare the floor price to the equilibrium price first. If the floor is not higher, stop. Deadweight loss is zero.
Where the Formula’s Reach Ends
The triangle formula works cleanly with linear supply and demand equations, which is what most coursework and policy analysis uses. Real markets rarely produce perfectly straight lines, but linear approximation is standard practice for estimating welfare losses within a reasonable range of the equilibrium. For small price distortions, the error from assuming linearity is negligible.
The calculation gets messier in markets with additional intervention layered on top of the floor. Agricultural price supports, for instance, often come bundled with government purchases of the surplus, storage programs, and export subsidies. The basic triangle still captures the core inefficiency from the price distortion, but the full social cost includes whatever the government spends buying, storing, or disposing of goods that cannot find buyers at the mandated price. The formula will not capture those fiscal costs on its own.
The minimum wage context adds its own wrinkle. Surplus labor means unemployed people rather than goods sitting in a warehouse. The triangle measures the value of employment matches that no longer happen, but it does not capture secondary effects like reduced on-the-job training, informal wage theft, or shifts to contract work that skirts the floor. The formula gives a precise number for the primary efficiency loss, which is useful for comparison and policy debate, but it reads as a floor on the total social cost rather than a ceiling.