To totally internalize an externality, a government can levy a tax related only to the physical quantity of pollution if

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If the economic damages associated with the pollution are the same across different locations, then a tax related only to the physical quantity of pollution can internalize the externality because it will incentivize polluters to reduce pollution to the socially optimal level. However, if the economic damages are different across different locations, a tax related only to physical quantity may not be enough to fully internalize the externality because it does not take into account the varying costs of pollution in different areas. If the economic damages are too large to be determined or the damages are zero, then a tax related to physical quantity may not be appropriate.

To Totally Internalize an Externality, a Government Can Levy a Tax