A large and increasing share of economic activity in modern rich economies can be shown to lie outside what mainstream neoclassical economics itself says it can be applied to: according to neoclassical economics, such activities are unsuited to markets. Since World War II rich economies have de-industrialised, shifted to services. Since the 1970s neoclassical economics has come to dominate policy advice. This worldview justifies state interventions when there is remediable market failure, but it ignores irremediable market failure, where its theory says that markets cannot work efficiently (such as where there is joint production or own consumption). Servicisation, this article argues, has increased and is increasing the extent to which neoclassical economics is, in its own terms, ‘knowably ignorant’. This is because, where service provision is subject to irremediable market failure, neoclassical economics, in its own terms, is inapplicable. The GDP [Gross Domestic Product] share of sub-sectors serving diverse human needs, such as aged care and education, is large and rising. Such sub-sectors are dominated by joint production, manifest as diverse outputs (complex and inter-related changes in the welfare of their diverse clients). Setting aside questions of the wider ‘scientific’ validity of neoclassical theory, the article focuses on its assertion that markets cannot generate economically efficient outcomes in such activities. Arguing that the constrained optimisation of its conceptual world cannot happen in the case of joint production and own consumption of service outputs, neoclassical theory reports itself as unable to determine optimal resource allocation, and so by implication cannot fulfil its role as the foundational basis of state economic policy. Yet the literature shows that the coverage of this theoretical result is not publicised – it is ‘knowable’ but not widely known. The article concludes that, as neoclassical economics is foundational to contemporary state policy, both GDP data and neoclassical theory show that it, and markets, are knowably and increasingly inapplicable. Therefore, mainstream policy thinking continues to face an increasing ‘state of ignorance’, and the cognitive foundations of state policy are correspondingly weak.