Principles of Microeconomics / Unit 4 MIC 0327 worked example, 60 to 90 seconds
Computing a Tax's Deadweight Loss
The idea
With straight-line curves, the deadweight loss is a triangle with the tax as its height and the lost quantity as its base. First find the quantity before the tax and the quantity after. Second, subtract to get the lost quantity. Third, take one half of the tax times the lost quantity. Revenue sits beside it: the tax times the after-tax quantity. Together they account for everything the tax took from surplus, and the surplus buyers and sellers keep is what remains.
In practice
Worked example: bottled juice traded twelve thousand bottles a week at three dollars. A one-dollar tax moves buyers to three seventy and sellers to two seventy, and the quantity falls to nine thousand. The lost quantity is three thousand, so the deadweight loss is one half times one dollar times three thousand, fifteen hundred dollars a week. Revenue is one dollar times nine thousand, nine thousand dollars. Buyers and sellers together lost ten thousand five hundred dollars of surplus, of which nine thousand reached the government.
Where people slip
The base is the change in quantity, not the after-tax quantity; using nine thousand as the base overstates the loss threefold. And the loss is not the revenue: revenue is a transfer that still exists, while the triangle is value that no longer exists anywhere.
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