How to Calculate Deadweight Loss

Sales taxes can create deadweight loss.
Sales taxes can create deadweight loss. (Image: Noel Hendrickson/Digital Vision/Getty Images)

Deadweight loss is a measure of economic inefficiency. It arises when the cost of making one more item -- the marginal item -- exceeds the benefit that item provides. This can happen when import quotas restrict supply, raising prices. Taxes and market interventions can also create deadweight loss. To calculate the size of the loss, you must compare prices with and without the source of the inefficiency.

Follow the Formula

Deadweight loss increases when a state imposes a sales tax. To measure the effect, create a chart showing the price (P) and quantity (Q) for a common product. Let's say intersecting curves on the chart show the price of milk (P1) based upon an efficient quantity (Q1) of supply that exactly satisfies demand. Now, adjust the price curve for the higher sales tax where P2 equals P1 plus tax. The new curve intersects the quantity curve at Q2. The formula to determine the deadweight loss is one-half the difference of Q2 and Q1 times the difference of P2 and P1.

Spilled Milk

Suppose P1 for milk is $3 a gallon and P2 is $3.20 a gallon. Reduced demand lowers the quantity produced in the state from 100,000 gallons per day to 95,000 gallons a day. The deadweight loss is 0.5 times ($3.20 - $3.00) times (100,000 - 95,000), or $500 a day for the entire state. That works out to $182,500 for a full year and more than $9.1 million on a 50-state basis.

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