Excludability is the ability of producers to detect and prevent uncompensating consumption of their products. Rivalry is the inability of multiple consumers to consume the same good. A public good is defined as a non-rival non-excludable good, such as national defense. Because public goods are not excludable, they get under-produced. The pricing system cannot force consumers to reveal their demand for purely non-excludable goods, and so cannot force producers to meet that demand.
The evidence for under-production of public goods is so overwhelming that, as anarcholibertarian professor Walter Block admits about the resulting justification for state intervention, "virtually all economists accept this argument. There is not a single mainstream text dealing with the subject which demurs from it." For standard treatments, see e.g.
- Ch. 11 Public Goods and Common Resources in Principles of Economics by Greg Mankiw (Harvard economist fired as Chairman of White House Council of Economics for defending outsourcing).;
- The Free Rider Problem in the Stanford Encyclopedia of Philosophy;
- Public Goods and Externalities in the Concise Encyclopedia of Economics by Tyler Cowan (libertarian economist at GMU, co-blogger at Marginal Revolution).
Underproduction of public goods is inevitable in the presence of 1) the ability to free-ride (i.e. non-excludable goods) and 2) rational self-interest. How could it possibly be otherwise? It's simply arguing by assertion to define the optimal amount of production as whatever happens to get produced. Even Geoanarchist Fred Foldvary in Public Goods and Private Communities doesn't deny that underproduction can happen. (He instead describes some very clever ways to bundle public goods with land holdings in private communities, but to me they seem either unrealistic or nearly indistinguishable from properly-decentralized statism with secession rights.)
The free-rider problem would exist even if 100% of the people had the same utility function. It's not a question of sticking it to the tiny minority. It's primarily a question of preventing defections by rational self-interested agents in the hypothesized majority who by defecting would gain the entire value of their share while seeing e.g. national defense diminish only infinitesimally. Of course, we have no truth serum with which to identify the tiny minority, and so when the empirical evidence tells us that a large supermajority support a public good, force-initiation is used to prevent free-riding. (Remember, every rational self-interested agent will claim to be in the tiny minority if doing so will exempt him from the tax, so we can't rely on self-report or market behavior to identify the tiny minority.)
"Mutual coercion mutually agreed upon" is like signing a contract saying "I'll keep my front lawn mowed as long as everybody else on our street does so too." The only difference is that public goods demonstrate the possibility of a class of agreements that are similarly Pareto-efficient — i.e. that make everybody involved better off without making anyone worse off — but that will never get made under market anarchy because of free riding and the inability of markets to make people fully reveal their preferences regarding non-excludable goods.
The existence of such market failures is essentially indisputable. The only question is whether and how we can know enough about people's preferences to institute tax-financed public goods that while not strictly Pareto-efficient are still highly Kaldor-Hicks efficient. That is, they make so many people so much better off that, if everyone's preferences were knowable, the few made worse off could be easily compensated by the rest. Minarchists claim that such trade-offs are morally justifiable only for "pure" public goods aimed at protecting life and liberty, like national defense and universal access to the justice system.
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