Deadweight loss calculator

The formulas

Worked example — a 10 dollar tax

Demand: $P=100-Q$. Supply: $P=20+Q$. Per-unit tax: $t=10$.

FAQ

What is deadweight loss?

Deadweight loss (DWL) is the reduction in total economic surplus caused by a market intervention or distortion that prevents mutually beneficial trades. Graphically, it is the triangle between the demand and supply curves over the range of units that would have been traded in the competitive equilibrium but are not traded under the distortion.

What is the formula for deadweight loss from a per-unit tax?

$DWL=\frac{1}{2}\times t\times (Q^{\ast }-Q_t)$, where $t$ is the per-unit tax, $Q^{\ast }$ is the competitive equilibrium quantity, and $Q_t$ is the quantity traded after the tax. The base of the triangle is the reduction in quantity and the height is the wedge the tax drives between what buyers pay and what sellers receive.

How does a price ceiling create deadweight loss?

A binding price ceiling (set below the equilibrium price) causes the quantity supplied to fall below the quantity demanded, producing a shortage. Trade happens only up to the quantity supplied at the ceiling price. The DWL is the triangle between demand and supply over the units that are no longer traded: $DWL=\frac{1}{2}\times (Q^{\ast }-Q_{\text{traded}})\times (P_d-P_s)$, where $P_d$ and $P_s$ are the demand and supply prices at $Q_{\text{traded}}$.

How does a price floor create deadweight loss?

A binding price floor (set above the equilibrium price) raises the price consumers face and reduces quantity demanded below the competitive equilibrium quantity. Producers are willing to supply more at the higher price, but they can only sell what consumers want at that price. The DWL is again a triangle over the lost units of trade, with the same formula as the ceiling case.

Who bears the burden of a per-unit tax?

Tax incidence depends on the relative elasticity of demand and supply. The side that is more inelastic bears a larger share of the tax. Statutory incidence — who formally pays the tax — does not affect economic incidence: a tax on buyers and an equivalent tax on sellers yield the same Qt, same price wedge, and same DWL.

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