The first fundamental theorem of welfare economics is often misunderstood, especially by technical economists. Briefly, the theorem says that a market outcome is efficient (Pareto-optimal). The theorem, as proven with great mathematical beauty by Arrow and Debreu, requires a number of reasonably strong assumptions such as very large numbers of buyers and sellers who have perfect rationality and perfect information.
Since the conditions required for the theorem’s proof are unlikely to hold in the real world it’s common for people to reverse the theorem to suggest that markets cannot be efficient. Thus Rodrik says:
The First Fundamental Theorem of Welfare Economics is proof, in view of its long list of prerequisites, that market outcome can be improved by well-designed interventions.
Now what is wrong with this is very simple. The First Theorem gives sufficient conditions for a market to be efficient it does not give necessary conditions.
Thus, as a matter of logic, the fact that the theorem’s conditions are not satisfied does not prove that market outcomes can be improved, even by "well-designed" interventions.
As an empirical matter, the difference between the sufficient and necessary conditions turns out to be quite large. We know from Vernon Smith’s work, for example, that markets can be competitive with only a handful of traders; nor do the traders have to be perfectly rational. In fact, markets can be very efficient with zero-intelligence traders.
Perhaps even more importantly technical economists seem to think that the First Theorem is the ultimate expression of "the invisible hand" or what makes markets good but in fact the First Theorem is but a pinched and limited expression of the virtues of markets. The First Theorem, for example, says nothing about innovation, experimentation, or the discovery process. Nor does the First Theorem say anything about markets and political philosophy. You will not learn from the First Theorem that markets are not simply a "mechanism," markets are peaceful exchange.
To be clear, I am correcting a misuse of the First Theorem. I am not asserting that markets are always perfectly efficient. But really what kind of standard is perfect efficiency anyway? The internal combustion engine isn’t even close to being perfectly efficient but my car gets me to work every day, is fun to drive and gives me the freedom of the open road.