For a tax on a good, the deadweight loss is small when price elasticity of demand is low because of

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The deadweight loss is the loss of economic efficiency that occurs when the quantity of a good produced is not at the socially optimal level. When the price elasticity of demand is low, consumers are less responsive to changes in price, so the quantity demanded with the tax is closer to the efficient quantity of demand. Therefore, the difference between the efficient quantity of demand and the quantity demanded with the tax is small, resulting in a smaller deadweight loss.

For a Tax on a Good, the Deadweight Loss Is