Formula

Optimal Pigouvian Tax Formula

To achieve a Pareto-efficient outcome in a market with a negative externality, the optimal Pigouvian tax rate, denoted as x∗x^*, should be set precisely equal to the marginal external cost (Ce′C'_{e}) evaluated at the Pareto-efficient level of output (Q∗Q^*). The formula is expressed as x∗=Ce′(Q∗)x^* = C'_{e}(Q^*). Imposing this specific tax rate incentivizes producers to voluntarily adjust their production to the socially optimal quantity, Q∗Q^*.

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Updated 2026-06-25

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