The optimal Pigouvian tax is equal to the marginal social cost of pollution at the socially optimal quantity of pollution (assuming there are no private costs from pollution to the polluter).

Optimal Pigouvian Tax

A tax designed to correct the inefficiencies in a market that experiences externalities, set at a level that equates the marginal social cost of the externality with the marginal social benefit.

Socially Optimal

Pertains to a condition where resources are allocated in the most efficient manner from the perspective of society as a whole.

Pollution

The presence or introduction of harmful substances or contaminants into the natural environment, causing adverse effects.