An economic solution to the problem was evolved as early as in the 1920s by the well- known British economist Arthur Pigou in the form of pollution tax popularly known as Pigouvian tax. According to Pigou, the social damage or the social cost imposed by a firm by its pollution activity on society may be neutralised by imposing a pollution tax on the firm. The rate of the tax, according to him is equal to the marginal environmental cost or marginal social damage by the polluting firm on society.
We explain the situation in the below diagram where MCs, is the social marginal cost while MCp, is the private marginal cost of production of a good. As more output is produced, MCs, increases with the level of pollution. The demand for the pollution good is given by the demand curve DD' (representing marginal revenue curve, MR). As per market mechanism, the equilibrium output is q1 and price is P1 where MCp = MR. Socially optimum level of output, however, is q* and price P*, where MCS = MR. If the producer were made to pay for the social costs also, equilibrium output would have been at the level q*. We observe from below diagram that the difference between MCs, and MCp, at the socially optimum level output is 'ac'. In order to internalize the externalities Pigou suggests imposition of a tax t per unit of output where t = ac. Here it is assumed that pollution emitted per unit of output remains unchanged as level of output changes.
Diagram: Pigouvian Tax