# Deadweight loss due to taxation

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## Definition

Deadweight loss due to taxation refers to a form of deadweight loss that occurs due to taxation. Essentially, when the size of the tax amount exceeds the economic surplus from the transaction, the activity does not occur in the presence of taxation.

## Computation of deadweight loss: example of sales tax in a competitive market

Consider an example of a competitive market where a sales tax is introduced. The introduction of the sales tax causes a decrease in the pre-tax price, an increase in the post-tax price, and a decline in quantity traded. In particular, consumers whose reservation price is between the price in a world without taxes and the new post-tax price are priced out of the market. Similarly, producers whose reservation price is between the new pre-tax price and the price in a world without taxes are priced out of the market. Even if no individual consumer or producer is priced out, the quantity they consume or produce may reduce due to the higher price.

Geometrically, the deadweight loss is represented by the area of a [[Harberger triangle whose vertices are the equilibrium no-tax (price,quantity) pair, the pre-tax (price,quantity) pair and the post-tax (price,quantity pair). In the diagram below, it is the sum of the areas E and F. The region E represents the loss in consumer surplus and the region F represents the loss in producer surplus.

Note that the actual loss to producers and consumers is greater than the deadweight loss. The original producer surplus was C + D + F, the new producer surplus is D. The producer surplus therefore goes down by C + F. However, the region C is simply redistributed to government, and therefore does not count as deadweight loss (note that what the government does with the money is excluded from the discussion here). Similarly, consumer surplus goes down from A + B + E to A, so the loss in consumer surplus is B + E. However, the region B is simply redistributed to government, and therefore does not count as deadweight loss.