Inside the modern mainstream economic literature of welfare economics there are two main branches, named the “old” and the “new welfare economics”, respectively, but either one having troubles with their foundational premises. The “old” welfare economics tried to turn upside down the laissez-faire conclusions of the Classic School(s), based on the marginalist utility theory introduced by the marginalist revolution. If utility could be interpersonally compared, it was argued, the decreasing marginal utility implies a welfare gain as a result, among other Government interventions, of income distribution from the rich to the poor. But this argument was quickly dismissed, showing that the subjectivity of value makes utility interpersonal comparisons impossible. The well-known Pareto rule stops the economists from claiming social welfare increase following state intervention, because it makes some people better off and some worse off. The “new” welfare economics tried to build a case for Government intervention, even in the Pareto framework. Its supporters tried hard to „adapt” this otherwise strict Pareto rule, attempting two approaches: to make the rule common, including it in the general equilibrium framework (which led to the development of the social welfare function and the “market failure” concept) and to introduce the ”compensation principle” (which soon led to the development of the concepts of “potential compensation” and “political rules” for defining consent).
In this line of reasoning, it is said that public goods, as a form of market failure, should be provided by the public sector (the State) in order to improve the aggregate welfare.
But the public goods existence can be easily dismissed because there is not such a good that is purely non-rival in consumption and because it cannot be soundly inferred from the fact that the market doesn’t provide it (the entrepreneurs’ decision, based on profitability calculations), then the market fails and state provision of that becomes necessary. Ludwig von Mises, the "dean" of the subjectivist-marginalist Austrian School of Economics, rigourously explained the way in which ordinal utility can somehow lie at the base of cardinal value judgements: transforming the preferences of different individuals, that, strictly speaking, are impossible to compare, into a common measurement unit, money, the market provides the foundation for economic calculation. It was left to Murray N. Rothbard, maybe the most prodigious disciples of Mises\\\'s, to reconstruct welfare economics, starting from Mises foundations, based on two value free elements: demonstrated preferences and private property. Only a social system where individual unanimous consent is given can generate the highest benefit for society, and the free market is the illustration of such a social system, thus weakening the case for the state-made public good.