# How to Calculate Deadweight Loss to Taxation

by Ryan Menezes ; Updated April 19, 2017In a free market, a product's price settles at an equilibrium between the buyer and the seller's interests. The free market price, and the quantity consumers buy at that price, maximizes economic surplus, a value encompassing benefits to both producers and consumers. Taxes artificially raise the product's price, reducing trade and hurting both parties. The government gains revenue from the tax, but deadweight loss measures the reduction in the economic surplus beyond any tax revenue. This loss may itself exceed tax revenue. Tax increases may even cut trade so sharply that tax revenues drop.

Estimate relationships for the number of units of the product consumers buy as prices change, and the number of units that producers sell as prices change. Graphically, these relationships form demand and supply curves. For example, assume consumers willingly buy a number of sausages equal to 10 minus the their price in dollars, and producers willingly sell a number of sausages exactly equal to their price in dollars. Under these conditions, sausages will reach an equilibrium price of $5, at which consumers will buy five of them.

Calculate the price of the product under the tax. For example, imagine that government levies a $1.50 tax on sausages. They will now cost $6.50 each.

Calculate the number of units that consumers will buy at the increased price. According to the relationship from Step 1, consumers will now buy 3.5 sausages.

Multiply the change in the product's price by the change in the number of units sold: ($6.50 - $5) × (5 - 3.5) = $2.25.

Divide the answer from Step 4 by two. Continuing the example: $2.25 ÷ 2 = $1.125, or about $1.13. This is the size of the deadweight loss due to the tax.

#### Tips

On a graph, deadweight loss is a triangular area; the price change is the triangle's base, and the quantity change is its height. Divide the figure from Step 4 by two to find deadweight loss because a triangle's area is half the product of its base and height.

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