Compute deadweight loss (excess burden) from a per-unit tax using linear demand & supply curves. Visualize the tax wedge, consumer/producer burden, and the Harberger triangle.
Deadweight loss (DWL) represents the efficiency cost of a market distortion — commonly a tax, subsidy, price ceiling, or floor. When a per-unit tax is imposed, it creates a wedge between the price consumers pay and the price producers receive, reducing the equilibrium quantity below the socially optimal level. The lost consumer and producer surplus that is not transferred to government revenue constitutes the excess burden or Harberger triangle. This calculator uses linear supply/demand curves to compute DWL precisely.
Deadweight Loss = ½ × t × (Q₀ − Qₜ)
where t = per-unit tax, Q₀ = original quantity, Qₜ = quantity after tax.
Formula derivation: DWL = ½ × tax × change in quantity, reflecting the triangular area between the demand and supply curves from the new quantity to the original equilibrium.
The tool reconstructs linear demand: P = a - b·Q (b = demand slope absolute), and linear supply: P = c + d·Q (d = supply slope). Given initial equilibrium (P₀, Q₀) and slopes, intercepts are derived uniquely. After tax t: Pd = Ps + t; solving yields new quantity Qₜ, consumer price Pd, producer price Ps. Tax revenue = t·Qₜ, consumer burden = (Pd - P₀)·Qₜ, producer burden = (P₀ - Ps)·Qₜ. The deadweight loss is always non-negative and increases with the square of the tax rate.
The size of DWL depends on price elasticities of demand and supply. More elastic curves → larger deadweight loss because quantity responds strongly to the tax wedge, creating a larger reduction in trade. Inelastic markets (e.g., essential goods) yield smaller DWL but higher tax revenue per unit. The calculator visually shows how the tax wedge shifts the equilibrium.
| Market Type | Demand / Supply Elasticity | Deadweight Loss | Tax Incidence |
|---|---|---|---|
| Cigarettes (short-run) | Inelastic demand, elastic supply | Moderate | Mostly on consumers |
| Luxury yachts | Elastic demand, elastic supply | High | Shared based on relative slopes |
| Labor (payroll tax) | Relatively inelastic supply & demand | Low-to-moderate | Depends on elasticities |
| Gasoline (short-term) | Inelastic both sides | Small | Mostly on consumers |
Many cities impose a $0.01–0.02 per ounce tax. Using conservative estimates: initial price $1.80 per 20oz bottle, Q₀ = 500 units/day, demand slope 0.008, supply slope 0.005, tax $0.40 per bottle. DWL calculation shows a moderate loss compared to revenue, but health benefits may offset. The graph illustrates the reduction in consumption and the efficiency cost. Our tool enables “what-if” policy analysis.
On the graph, the blue line is demand, orange line supply. After tax, the effective supply curve shifts upward by the tax amount (illustrated as a dashed line). The area between the demand and supply curves from Qₜ to Q₀ is shaded in red — that is the deadweight loss. The green rectangle between Pd and Ps over quantity Qₜ represents government tax revenue. The graph automatically scales to fit the relevant price and quantity ranges.