Deadweight Loss Calculator
Calculate the deadweight loss (allocative inefficiency) caused by a price floor, price ceiling, tax, or subsidy. Deadweight loss is the loss of economic surplus to society that is not captured by any party.
How to use this tool
- Enter change in price (δp) and change in quantity (δq) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your deadweight loss and the full breakdown beneath it.
⚠ This tool provides general estimates for education only and is not financial, tax or legal advice. Figures may not reflect your situation — verify with a qualified professional.
Formula
Deadweight Loss = ½ × ΔP × ΔQ
Where ΔP is the change in price caused by the distortion (tax, price control, etc.) and ΔQ is the resulting change (reduction) in the quantity traded. This formula computes the area of the welfare-loss triangle on a supply-demand diagram.
How it works
Deadweight loss represents the reduction in total economic surplus — consumer surplus plus producer surplus — that results from market inefficiencies such as taxes, subsidies, price floors, or price ceilings. On a standard supply-and-demand diagram it appears as a triangle between the supply curve, the demand curve, and the distorted equilibrium. The formula (½ × ΔP × ΔQ) calculates the area of that triangle. The magnitude depends on the size of the price distortion and the price elasticities of supply and demand.
Worked example
Tax-Induced Deadweight Loss
- A government imposes a $4-per-unit tax on a good. As a result, the quantity traded falls by 200 units from the competitive equilibrium.
- The deadweight loss is the area of the welfare triangle: DWL = ½ × ΔP × ΔQ.
- Substitute: DWL = ½ × $4 × 200 units.
- Calculate: DWL = ½ × 800 = $400.
The deadweight loss is $400, representing economic value destroyed by the tax that neither the government nor buyers or sellers receive.
Common mistakes to avoid
- Calculating deadweight loss as delta_P x delta_Q rather than 0.5 x delta_P x delta_Q, doubling the actual welfare loss by computing a rectangle instead of the correct triangle.
- Applying the linear triangle formula when supply or demand curves are non-linear; the formula is an approximation valid only under linear supply and demand.
- Confusing deadweight loss with the tax revenue or surplus transfer -- DWL is only the portion of lost surplus that no party captures, not the full price-quantity distortion.
Key terms
- What causes deadweight loss?
- Deadweight loss is caused by anything that prevents a market from reaching its competitive equilibrium: taxes, subsidies, price floors (minimum prices), price ceilings (maximum prices), and monopoly pricing.
- Who bears the deadweight loss?
- Nobody receives it — that's what makes it a 'loss.' It represents mutually beneficial trades that would have occurred in a free market but do not occur because of the distortion.
- How does elasticity affect deadweight loss?
- More elastic supply or demand means quantity responds more to price changes, creating a larger DWL for any given price distortion. Inelastic markets produce smaller deadweight losses.
- Is deadweight loss the same as tax revenue?
- No. Tax revenue is the rectangle of tax × quantity sold; deadweight loss is the additional triangle of lost surplus beyond that, representing trades that no longer occur.
Frequently asked questions
- What causes deadweight loss?
- Any market distortion that prevents trades at the competitive equilibrium creates deadweight loss. Common sources include per-unit taxes, price floors (minimum wage above equilibrium), price ceilings (rent control), and monopoly pricing.
- Who bears the deadweight loss?
- No one. That is why it is called a loss. It represents surplus that would exist at competitive equilibrium but is destroyed because mutually beneficial trades no longer occur. Tax revenue transfers surplus to the government; DWL is surplus destroyed on top of that transfer.
- How does price elasticity affect the size of deadweight loss?
- More elastic supply and demand produce a larger quantity change from a given price distortion, creating a larger DWL triangle. Inelastic goods (necessities, addictive products) have smaller DWL from a given tax.