Pigou tax

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A Pigou tax (subsidy) is a tax (subsidy) on an economic activity, equal to the marginal value of its negative (positive) externality. A Pigou tax is also called a Pigovian tax.

Arthur Pigou, in his 1920 book Economics of Welfare, defines the Pigou tax as follows:

"If the amount of investment in any industry was carried exactly to the point at which the value of the marginal social net product there is equal to the central value of marginal social net products, the national dividend, so far as that industry is concerned, would be maximised. Disregarding the possibility of multiple maximum positions, I propose, for convenience, to call the investment that would then be made in the industry the ideal investment and the output that would be obtained the ideal output.
Under conditions of simple competition, if in any industry the value of the marginal social net product of investment is greater than the value of the marginal private net product, this implies that the output obtained is less than the ideal output: if the value of the marginal social net product is less than the value of the marginal private net product, this implies that the output obtained is greater than the ideal output.
It follows that, under conditions of simple competition, for every industry in which the value of the marginal social net product is greater than that of the marginal private net product, there will be certain rates of bounty, the granting of which by the State would modify output in such a way as to make the value of the marginal social net product there more nearly equal to the value of the marginal social net product of resources in general, thus -- provided that the funds for the bounty can be raised by a mere transfer that does not inflict any indirect injury on production -- increasing the size of the national dividend and the sum of economic welfare; and there will be one rate of bounty, the granting of which would have the optimum effect in this respect.
In like manner, for every industry in which the value of the marginal social net product is less than that of the marginal private net product, there will be certain rates of tax, the imposition of which by the State would increase the size of the national dividend and increase economic welfare; and one rate of tax, which would have the optimum effect in this respect.
These conclusions, taken in conjunction with what has been said in the preceding paragraphs, create a presumption in favour of State bounties to industries in which conditions of decreasing supply price simpliciter are operating, and of State taxes upon industries in which conditions of increasing supply price from the standpoint of the community are operating."

Although we now think that a Pigou tax or subsidy (Pigou's "bounty") applies to an externality, Pigou had a much wider range of market imperfections in mind.

Francis Bator (1958 QJE) brings externalities and the internalization of externalities through what is now known as the Pigou tax into the modern era. Bator recalled that, in a Pareto optimum, the marginal rate of transformation should equal the social price ratio. The social price is the sum of the market price and the externality. In an unregulated market, the marginal rate of transformation equals the ratio of market prices, ignoring externalities. Market prices include taxation, however. If the taxes applied would equal the external costs at the margin, then the marginal rate of transformation equals the social price ratio. Efficiency is restored.

James Buchanan (1969 AER) recalls that an externality is an unintended and uncompensated impact on a third party. He therefore argues that a negative (positive) externality should be taxed (subsidized) and the victim (beneficiary) of the pollution (pollination) should be subsidized (taxed). William Baumol (1972 AER) shows that this is not the case. In order to restore the market to efficiency, it suffices to tax (subsidize) negative (positive) externalities. Compensation to (by) the victims (beneficiaries) is a lump-sum transfer of income. This may be deemed fair but, per the Second Welfare Theorem, it has nothing to do with efficiency.

Bator's simple prescription -- the Pigou tax should equal the marginal value of the externality -- does not hold in general. James Buchanan (1969 AER) demonstrates that it is suboptimal to impose a Pigou tax on a monopolist as this would further increase market power. The same argument holds for other forms of market power. Agnar Sandmo (1975 SJE) shows that, if there are pre-existing fiscal distortions, the Pigou tax should be corrected with the marginal cost of raising public funds. Dennis Carlton and Glenn Loury (1986 QJE) note that the Pigou tax is static and should be corrected for its dynamic effects. Taxes (subsidies) raise (lower) the average cost of doing business and so deter (attract) investment in the polluting (pollinating) sector. In some cases, no government intervention is needed: The Coase Theorem shows that externalities can sometimes be solved by negotiations between the affected parties.