Edit: Is it possible to broadly categorize the ways in which market failures occur into relatively few categories? If so, what are they?
Any situation where markets fail to clear leads to market failure. Some common reasons for this are:
Externalities, or agents not being responsible for costs or benefits of their actions
Information assymetry, or agents operating with different information
- Irrationality, or agents doing random things for no reason
- Principal agent problems, where someone entrusted with others funds uses them wastefully
- Productive inefficiency, or firms failing to produce goods effectively given the allocated capital (think using Gatorade to water plants)
- Allocative inefficiency, where firms are not provided the appropriate capital
- Economies of scale, or the problem of capitalist firms failing to grow large enough to establish a service
- Destructive competition- eg, private militaries blowing each other up
- Shortsighted management of natural resources
- Moral hazard, adverse selection, and other problems in contract theory
I just wrote about this very thing. There are many misconceptions and incorrect information floating around about market failure.
The 3 types of market failures I identify are:
- Anti-competitive markets
- Suboptimal initial resource allocation
Almost all market failures come from externalities. This includes a very broad range of things including violence, fraud, and pollution.
Anti-competitive markets are basically natural monopolies. However, monopolies are very misunderstood beasts. There is reason to believe that monopolies don't generally cause significant deadweight losses, and its not clear whether monopolies have more or less ability and drive to innovate vs a competitive market. It seems likely that most monopolistic markets are economically worse than competitive markets, but it is far from clear that there is any realistic government alternative that can be expected to do better than the market in the long run.
Point 3 is basically the fact that everyone starts off with a different lot in life, and that some "lump-sum transfers" can improve society's total utility from a utilitarian point of view.
Market failure is a strong statement that requires more than simple inefficiency. A market failure is a systemic inefficiency that will prevent the system from ever reaching an optimal state.
Things that aren't market failures that you often see people claim:
- Information asymmetries and imperfect information
- Simple inefficient behavior by a company or companies
- "missing markets"
- Merit and demerit goods
- Time-inconsistent preference
- Factor immobility and geographic immobility
There are also several things usually talked about as market failures that are all just special cases of externalities:
- Principle-agent problem (aka conflict of interest or moral hazard)
- Public goods
And DJ Sim's answer above is particularly bad. He includes several things that are definitely not market failures that aren't even in the usual list of market failure myths:
- Productive inefficiency, allocative inefficiency, and mismanagement of resources are all basically identical, and none of them are market failures, just the failure of a particular person or company to be efficient.
- Economies of scale