1. Peter Barnes:
"Pigou, a colleague of Keynes’ at Cambridge, was the first economist to focus on the market’s failure to incorporate external costs such as pollution. This is capitalism’s Tragic Flaw #1 that is responsible for climate change, among other serious ills. The essence of it is that, because markets charge nothing for pollution, companies pollute far more than they would if markets charged a substantial price.
Pigou’s remedy was for government to estimate the costs that are externalized—let’s say the costs of pollution—and to tax polluting activities enough to reduce them. Though Pigou’s fix would work through markets, it isn’t entirely a market fix because it requires government to calculate external costs, and impose appropriate taxes and collect them. This supposes an adept and enlightened government, free from the sway of externalizing industries—a supposition that’s hard to make these days." (http://www.kosmosjournal.org/article/economics-for-the-anthropocene/)
2. From the Wikipedia:
"A Pigovian tax (also spelled Pigouvian tax) is a tax levied on a market activity to correct the market outcome, if there are negative externalities associated with the market activity. In the presence of negative externalities, the social cost of a market activity would exceed the private cost of the activity. In such a case, the market outcome is not efficient, and the market would tend to over-supply the product. If a Pigovian tax equal to the negative externality is imposed, the market outcome would be reduced to the efficient amount.
In the presence of positive externalities (public benefits from a market activity), the market would tend to under-supply the product. Similar logic would suggest the creation of Pigovian subsidies to increase the market activity.
Pigovian taxes are named after economist Arthur Pigou who also developed the concept of economic externalities. William Baumol was instrumental in framing Pigou's work in modern economics." (http://en.wikipedia.org/wiki/Pigovian_tax)