Economists in business schools may be particularly fond of identifying markets where the necessary conditions are met, where many buyers and many sellers operate with very good information and very low transactions costs to trade well-defined commodities with enforced rights of ownership. These economists regularly produce studies demonstrating the efficiency of such markets (although even in this sphere, problems can obviously arise).
For other economists, especially those in public policy schools, the whole point of the first welfare theorem is very different. By clarifying the conditions under which markets are efficient, the theorem also identifies the conditions under which they are not. Private markets are perfectly efficient only if there are no public goods, no externalities, no monopoly buyers or sellers, no increasing returns to scale, no information problems, no transactions costs, no taxes, no common property, and no other distortions that come between the costs paid by buyers and the benefits received by sellers.
Therefore, we must focus on:
1) Public goods - the stability of the financial system itself.
2) Externalities - network effects, macroeconomic well being.
3) Large financial monopolies in certain markets, the government and central banks.
4) Increasing returns to scale and financial concentration.
5) Huge informational issues.
6) Other costs of involvement that lead to instiutional dominance.