Plenty of people (economists and non) adhere to the idea that "markets work" and allow the idea guide their voting practices, policies and economic activities. Well, after a year of microeconomic theory coursework, I can trace the fundamental sources for the idea. I will attempt to explain The First Fundamental Theorem of Welfare Economics (yes, the number matters) in English. The theorem says that if we have a competitive equilibrium (a combination of the right prices and allocations for goods that allows the market to clear without excess demand for any good), then we have a state of Pareto efficiency (a socially-good distribution where everyone is well-off). Note my previous rantings about Pareto efficiency. This idea, that an equilibrium is also socially good, implies that there is no need to intervene in the market; it will produce efficient allocations to all consumers based on individual demand and this allocation will be an optimal distribution for all.
One thing most people do not know about this theorem is that it requires perfect information (everyone knows all prices at all times), perfect competition (infinitely many buyers and sellers, no barriers to entry), complete divisibility of goods (I can buy 1.432 chairs), strictly increasing utility (everyone always wants more of everything) and no interpersonal utility comparisons (you're not allowed to notice that you're better off than homeless people). Further, while this theorem claims that all competitive equilibria are Pareto efficient, it never actually guarantees that any equilibira exist in the first place.
On the other hand, we have The Second Fundamental Theorem of Welfare Economics, the twin theorem with an uglier proof. This one actually says the exact opposite. If there is a Pareto efficient allocation (socially-good distribution where everyone is well-off), then this allocation can be a competitive equilibrium with the right amount of redistribution. In other words, a desirable and optimal distribution of goods can be reached through redistribution of the endowments. The idea here is that we should always intervene with the market; we should keep reallocating resources until we have reached some socially-good distribution. Of course, the idea of redistribution is difficult to implement and regulate in practice (think subsidies and taxation) and the assumptions of this theorem are just as strict. We have the same assumptions as the First Welfare Theorem, and additionally that utility is a quasi-concave function (I am struggling with how to translate concavity into English-- econ friends?).
So while this explanation may earn me some points on the interpretation of welfare theorems on the exam (after state and prove), it also provides a space to reflect on the little known theoretical underpinnings of the idea that markets work.
A massive amount of credit goes to my professors, study group and classmates for this post. And of course, MWG and Varian too.