The standard theory that the first-best tax on pollution is equal to marginal environmental damages has been extended in two directions. First, many polluting activities are difficult to tax because they are not market transactions, and so recent papers have shown that the same effects can be...

This paper builds two simple general equilibrium models to demonstrate the equivalence between the Pigovian tax and the combination of a presumptive tax and an environmental subsidy. A presumptive tax is a tax that is imposed under the presumption that all production uses a dirty technology or...