In economics externalities are the effects of one’s action on third parties. An externality can be positive or negative, and in general the occurrence of externalities is unintended. Negative externalities are those effects which cause harm upon (non-consenting) third parties.
Because of the harm principle the government is justified to create regulation to reduce the amount of negative externalities. There are several ways to do so. First the government can prohibit or restrict certain activities. Secondly the government can discourage certain activities.
One method to discourage certain activities is to impose a tax on such activities. The idea is that by making undesirable activities more expensive, people will either limit such activities or to abstain completely from it.
The first question is how much tax should be levied. There are several things to be considered: the cost of enforcement, the effective deterrent and the compensation of harm caused.
Every tax has to be enforced, and tax enforcement is not for free. Ideally the revenues of a tax should be larger than the costs to collect it. Once we know what it takes to enforce a pigouvian tax, we could determine the minimal tax liability.
A possible problem, however, might be that this minimal liability, does not actually deter people from performing undesirable activities. This because the benefits they can gain, outweigh their tax liabilities. Hence the tax should be large enough to cancel any net benefit. On the other hand, this second minimum could be lower than the costs of enforcement.
Another way to look at the height of tax liability, is to take the cost of compensating negative externalities into account. For instance if water wells have been polluted, there are costs involved in restoring the water wells. On the maxim “the polluter will pay”, it’s reasonable to charge those who have polluted with this costs.
On the other hand, pigouvian taxes are meant to prevent the occurrence of negative externalities. Economically, the costs saved by this prevention should be counted as a benefit. Consequently, it does not actually matter if the revenues raised by a pigouvian tax does not cover the costs of its enforcement, as long as this tax succeed in reducing negative externalities.
Also the success of a pigouvian tax should not be measured in terms of revenues generated, but in terms of harm reduced. In a best case scenario a pigouvian tax will generate zero revenue, because everyone quits producing negative externalities. A pigouvian tax should not be imposed solely for the purpose of raising public revenue. Nevertheless the revenues raised in this way, should be used for public causes.