Theory of the second best

In economics, the theory of the second best concerns the situation when one or more optimality conditions cannot be satisfied. The economists Richard Lipsey and Kelvin Lancaster showed in 1956, that if one optimality condition in an economic model cannot be satisfied, it is possible that the next-best solution involves changing other variables away from the values that would otherwise be optimal. Politically, the theory implies that if it is infeasible to remove a particular market distortion, introducing a second (or more) market distortion in an interdependent market may partially counteract the first, and lead to a more efficient outcome.
Implications.
In an economy with some uncorrectable market failure in one sector, actions to correct market failures in another related sector with the intent of increasing economic efficiency may actually decrease overall economic efficiency. In theory, at least, it may be better to let two market imperfections cancel each other out rather than making an effort to fix either one. Thus, it may be optimal for the government to intervene in a way that is contrary to usual policy. This suggests that economists need to study the details of the situation before jumping to the theory-based conclusion that an improvement in market perfection in one area implies a global improvement in efficiency.
Application.
Even though the theory of the second best was developed for the Walrasian general equilibrium system, it also applies to partial equilibrium cases. For example, consider a mining monopoly that is also a polluter: mining leads to tailings being dumped in the river and deadly dust in the workers’ lungs. Suppose in addition that there is nothing at all that can be done about the pollution without also reducing production. However, the government is able to break up the monopoly.
The problem here is that increasing competition in this market is likely to increase production (since monopolists restrict production). Because pollution is highly associated with production, pollution will most likely increase. Thus, it is not clear that eliminating the monopoly increases overall welfare. Gains from trade in the mined mineral will increase, but externalities from pollution will increase as well, possibly outweighing the gains from trade.