Depletable externalities and pigouvian taxation

In their book Baumol and Oates “The Theory of Environmental Policy: Externalities, Public Outlays, and the Quality of Life,” Prentice-Hall, Englewood Cliffs, N.J. (1975).] argue that whether an externality is depletable (private) or undepletable (public) is the key characteristic in determining the optimal pricing pattern. They argue that unlike the undepletable case a negative depletable externality requires not only a charge or tax on the generator of the externality but a payment or compensation to the victim in order to achieve Pareto optimality. It is shown that the key characteristic determining whether compensation of victims is required for efficiency is not the depletability of the externality but whether the victim can costlessly control or limit the amount of the damaging substance received.