An entity wants to do an action that causes a negative externality. The action is taxed at the precise amount of externality, causing a socially optimal amount of the action. So far, so good.
The difficult problem is redistributing the tax revenues to compensate those negatively affected by the externality. Moral hazard arises as the victims may choose not to take other actions themselves to minimize their negative effect. Adverse selection arises when those who have the most to gain from compensation become, or remain, members of the victim class. Corruption arises whenever there is a resource to be allocated.
A seemingly somewhat attractive solution is not to attempt to compensate the victims at all: the socially optimal amount of action has been induced, and that's good enough; contribute the tax revenue to the general fund. However, I think the difficulty theoretically remains: in order to calculate the optimal tax rate, in order to calculate the value of the negative externality, we must determine who the victims are and how much they are hurt.
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