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).
Samuelson's paper did not fully explicate the modern quadripartite theory of private/public/club/common goods, let alone formalize all the kinds of market failure inherit in that analysis. There was important work related to this both before and after 1954:
- The 1939 generalization of Pareto optimality by Kaldor and Hicks to launch modern welfare economics;
- The 1950 formalization of the Prisoner's Dilemma and the subsequent avalanche of developments in game theory;
- Arrow's 1951 impossibility theorem, leading to Sen's 1970 liberal paradox;
- The 1953 discovery of the Allais paradox, and many subsequent discoveries about bounded rationality and cognitive bias and the development of Prospect Theory by Tversky and Khaneman in 1979;
- Tiebout's 1956 theorem about the optimal local provision of public goods;
- Coase's 1959 proof that markets can handle negative externalities only in the absence of transaction costs;
- The 1962 creation of public choice theory by Buchanan and Tullock; and
- Arrow's 1963 formalization of the problem of asymmetric information.