Deadweight Loss Calculator
Enter the equilibrium price and quantity, then the new price and quantity after a tax, subsidy, price ceiling, or price floor. The calculator uses the standard triangle formula to find the deadweight loss and shows how consumer surplus and producer surplus shift. All results update instantly as you type.
What is deadweight loss?
Deadweight loss (DWL) is the loss of economic efficiency that occurs when a market fails to reach its competitive equilibrium. In a free, unregulated market, prices settle where supply meets demand. At that equilibrium, every mutually beneficial trade takes place, and total social welfare (the sum of consumer surplus and producer surplus) is maximised. When an external factor forces price or quantity away from equilibrium, some potentially beneficial transactions no longer happen. The value of those lost trades is the deadweight loss: wealth that is destroyed rather than redistributed.
The DWL triangle and the formula
On a standard supply-and-demand diagram, deadweight loss appears as a triangle. The two sides of the triangle are the price gap (the vertical distance between the original and new price) and the quantity gap (the horizontal distance between the original and new quantity). Because both supply and demand curves are assumed to be straight lines near equilibrium, the lost welfare area is a right triangle: DWL = 0.5 x (P1 - P0) x (Q0 - Q1). Here P0 and Q0 are the equilibrium price and quantity, and P1 and Q1 are the price and quantity after the intervention. The factor of one-half comes from the triangle area formula. Larger price or quantity gaps mean a bigger triangle and a larger welfare loss.
Causes: taxes, subsidies, and price controls
The four most common sources of deadweight loss are per-unit taxes, subsidies, price ceilings, and price floors. A tax on a good drives a wedge between what buyers pay and what sellers receive, pushing the market away from equilibrium and reducing the quantity traded. A subsidy has the mirror effect: it lowers the price buyers pay and raises the price sellers receive, pushing quantity above the efficient level so that goods are produced whose cost exceeds their value to consumers. A price ceiling (such as rent control) caps prices below equilibrium, creating a shortage and cutting off trades that would otherwise have occurred. A price floor (such as the minimum wage applied to low-skill labour markets) sets a minimum price above equilibrium, creating a surplus. In each case the quantity exchanged ends up different from what the market would freely choose, and the area of the resulting triangle measures the value of the trades that do not happen.
Elasticity and the size of deadweight loss
The size of deadweight loss depends critically on how elastic supply and demand are. When demand is very inelastic (buyers need the good regardless of price, such as insulin), a large price change causes only a tiny quantity drop, so the DWL triangle is narrow. When demand is highly elastic (buyers switch easily to substitutes), even a small price increase causes a large fall in quantity, producing a wide triangle and a large welfare loss. The same logic applies to the supply side. This is why economists argue that taxes should, where possible, be placed on goods with inelastic demand or supply: the tax raises revenue while creating a smaller DWL triangle. Conversely, subsidies and price controls on elastic markets cause the largest welfare losses.
Common causes of deadweight loss
| Intervention | Effect on price | Effect on quantity | Burden | Size of DWL |
|---|---|---|---|---|
| Tax on buyers | Rises for buyers | Falls | Shared by buyers and sellers | Grows with elasticity |
| Tax on sellers | Rises for buyers | Falls | Shared by buyers and sellers | Grows with elasticity |
| Subsidy | Falls for buyers | Rises beyond optimum | Taxpayers | Grows with elasticity |
| Price ceiling | Below equilibrium | Falls (shortage) | Sellers | Depends on gap size |
| Price floor | Above equilibrium | Falls (surplus) | Buyers | Depends on gap size |
| Monopoly pricing | Above marginal cost | Below competitive level | Consumers | Depends on market power |
Summary of how different market interventions create deadweight loss and who bears the burden.
Frequently asked questions
What is the deadweight loss formula?
DWL = 0.5 x |P1 - P0| x |Q0 - Q1|, where P0 is the equilibrium price, Q0 is the equilibrium quantity, P1 is the price after the intervention, and Q1 is the quantity traded after the intervention. This is the area of the triangle formed between the original and new price-quantity combinations on a supply-demand diagram.
What causes deadweight loss?
Any factor that pushes a market away from its equilibrium price and quantity creates deadweight loss. Common causes include per-unit taxes (which wedge buyer and seller prices apart), subsidies (which push quantity above the efficient level), price ceilings (which set a maximum price below equilibrium, causing shortages), price floors (which set a minimum price above equilibrium, causing surpluses), and monopoly pricing (where the firm restricts output to charge above marginal cost).
Is deadweight loss always bad?
Not necessarily. Deadweight loss from a Pigouvian tax (a tax set equal to the external cost of a negative externality such as pollution) can be socially desirable because it corrects a pre-existing market failure. In that case the DWL from the tax is offset or exceeded by the gain from reducing the externality. Similarly, a subsidy can correct an under-provision of goods with positive externalities (like vaccines). The DWL calculation here assumes the market was at its social optimum before the intervention; if it was not, the intervention may increase overall welfare despite creating a DWL triangle in the narrow sense.
How does elasticity affect deadweight loss?
More elastic markets produce larger deadweight losses for the same price wedge. When demand or supply is very elastic, a small forced change in price causes a large change in quantity, making the triangle tall and wide. When demand or supply is very inelastic, the quantity barely changes even for a large price wedge, so the triangle is narrow. This is why taxes on necessities (inelastic demand) produce less DWL per dollar of revenue than taxes on luxuries or easily substituted goods.
What is the difference between deadweight loss and producer/consumer surplus?
Consumer surplus is the extra value buyers receive above what they pay; producer surplus is the extra revenue sellers receive above their minimum acceptable price. Together they form total social welfare. An intervention like a tax redistributes some of these surpluses to the government as revenue, but does not destroy them. The deadweight loss is the portion of surplus that disappears entirely because beneficial trades that would have happened at equilibrium no longer occur. It is destroyed value, not transferred value.