This week “The Economist explains” is given over to economics. Today’s is the fourth in a series of six explainers on seminal ideas.

MARKETS are supposed to generate a magical state, where nobody could do better without somebody else doing worse. Awkwardly, they often fail. The reason is that those directly involved in a transaction are not the only ones affected by it. A drive into the centre of town, for example, creates congestion for everyone else; a company dumping waste into a river poisons the downstream drinking water; carbon emissions warm everyone’s planet. Economists have a special name for these extra costs: they are “externalities”. Unfettered market prices do not take them into account.

The economist famous for formalising the idea was called Arthur Pigou, a brilliant but scruffy Cambridge academic who wrote a seminal textbook that even he admitted was a tough read. He saw the effects of negative externalities at first hand. In London, smoke from chimneys blocked out sunlight for others, and he was particularly exercised by the problems of excessive alcohol consumption. He proposed a fix, in the form of “bounties and taxes”, which could restore market perfection. If the problem with untempered markets is that people ignore others when buying or producing stuff, a tax on social bads would discourage bad behaviour, and align what is best for individuals with what is best for society.

Once Pigou had provided governments with intellectual justification for meddling, the idea took the policy world by storm. Pigouvian taxes are now central to well-meaning governments’ toolkits. A tax placed on plastic bags in Ireland in 2002 cut their use by more than 90%. Three years after the British government introduced a charge on driving in central London in 2003, congestion had fallen by a quarter. Carbon taxes are currently applied in Finland, Denmark, Chile and Mexico. By using prices as signals, a tax should encourage people and companies to lower their carbon emissions more efficiently than a regulator could by diktat. If everyone faces the same tax, those who find it easiest to lower their emissions ought to lower them the most.

Pigou’s idea met resistance. In the 1960s Ronald Coase, an economist at the University of Chicago, criticised Pigou for his heavy-handedness. Rather than using the tax system to intervene, he said, governments should first establish whether existing institutions and laws could remedy failures instead. Corrective taxes come with caveats. Estimating the true extra social cost of something is more of an art than a science, so charges in practice are often infused with a certain amount of arbitrariness. (Cynics wonder whether they are simply a grab for extra cash.) Taxes generate losers, and with them comes tricky politics. Whether from powerful corporate interests or desperate constituents unable to cope with price rises, resistance raises awkward questions about who deserves the revenue raised. The idea of externalities is elegant in theory. But responding to them involves the real world, which is harder.