Deadweight Loss Calculator
From the quantity change and price wedge caused by a tax or control, compute the deadweight loss: DWL = 0.5 x quantity change x price change (welfare triangle).
Input Data
Results
At a glance:Deadweight loss (DWL) is the welfare that consumers and producers lose, captured by no one, when a distortion (tax, control, monopoly) pushes volume below the optimal. Triangle approximation: DWL = ½ x quantity change x price wedge. Example: volume falls 10, wedge HK$4 → 0.5 x 10 x 4 = 20. The more elastic supply/demand, the larger the DWL for the same wedge. WARNING: linear-curve approximation; education only, not advice.
Formula
DWL = ½ × quantity change × price wedge (welfare triangle area).
More elastic supply/demand → larger DWL for the same wedge.
$$DWL = \tfrac{1}{2} \times \Delta Q \times \Delta P$$How to Use
- Enter the reduction in trade volume.
- Enter the price wedge between buyer and seller.
- View the deadweight loss.
FAQ
What is deadweight loss and why does it occur?
DWL (welfare net loss) measures the efficiency loss when a market deviates from the free-competitive optimum — the value that disappears and is captured by no one. In a well-functioning market, quantity and price reach an efficient equilibrium where all trades with 'buyer willingness ≥ seller cost' occur and total surplus is maximised. A distortion (tax, price cap/floor, subsidy, monopoly) shifts volume away from that optimum (usually down), so some mutually beneficial trades no longer happen. Their lost surplus — not consumer benefit, not producer profit, not government tax — is pure loss. That is the 'deadweight'. With a tax: the wedge between buyer-paid and seller-received prices cuts volume; the government collects a rectangle (tax revenue), but the triangle of lost trades is DWL — net loss nobody receives.
How is DWL calculated, and why a triangle?
On the standard graph, DWL is a triangle: area = 0.5 x base x height. This tool's form: DWL = 0.5 x quantity change x price wedge. 'Quantity change' is the base (how much volume fell from equilibrium); 'price wedge' is the height (the buyer-seller price gap, i.e. the tax). Why a triangle, not a rectangle? Near the original equilibrium, the lost trades have buyer-seller gaps near zero (tiny loss); farther away, the gap grows. Summing losses from zero to the max wedge gives a triangle. Example: tax cuts volume by 10 and creates a HK$4 wedge → DWL = 0.5 x 10 x 4 = 20. This is a linear-curve approximation; real curves may bend, but it gives a good estimate.
What is DWL's policy meaning, and how does elasticity affect it?
DWL is the key tool for a policy's 'efficiency cost' — a tax raises revenue but also distorts and cuts volume, creating DWL; good tax design minimises DWL for needed revenue (hence taxing inelastic goods like tobacco/fuel has lower efficiency loss). Same logic applies to price controls, subsidies, tariffs, monopoly. Elasticity rule: the MORE elastic supply/demand (more price-sensitive), the LARGER the DWL for the same distortion; the less elastic, the smaller. Intuition: sensitive buyers/sellers slash volume on a price change, killing many mutually beneficial trades (long base); insensitive ones barely reduce volume (small base). This explains why governments tax inelastic goods.
How is DWL different from tax revenue?
A tax creates two different effects. One is tax revenue (what government gets) — a rectangle = remaining volume x per-unit tax; this is a transfer (consumers/producers lose, government gains, society's total unchanged), NOT DWL. The other is DWL — a triangle = the trades that vanished (buyer value exceeded seller cost but didn't happen); nobody gets it (not even government, since the trade didn't occur). So revenue is 'transferred', DWL is 'evaporated'. Evaluating a tax's efficiency hinges on its DWL — smaller is better. Pair with the consumer-surplus calculator.
Besides taxes, what else causes DWL?
Any force pushing volume away from the free equilibrium creates DWL; tax is the classic case. Others: (1) price controls — a binding price ceiling (e.g. rent control) cuts supply below optimum; a price floor (e.g. minimum wage above equilibrium, price supports) creates surplus; both shrink volume; (2) quotas/quantity limits — cap trade below optimum; (3) monopoly/market power — a monopolist restricts output and raises price above the competitive optimum, profiting (transfer) but losing the compressed trades (DWL) — the economic rationale for antitrust; (4) subsidies — push volume ABOVE optimum, the extra high-cost/low-value trades are also DWL (opposite direction); (5) uncorrected externalities — negative (pollution) or positive (vaccines, education) externalities leave volume off the social optimum, creating DWL. DWL is the universal yardstick for the efficiency cost of market interventions and failures.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.