This paper investigates to what extent the seminal contribution of Samuelson has been or not incorporated by the theories of general equilibrium and mechanism design in their analysis of optimal public good provision, and more generally of optimal public policy. Our conclusion is that, far from taking up the challenges raised by Samuelson's contribution, both paradigms lead to the negative conclusion of the impossibility of a fully decentralized optimal public goods provision through market or market-like institutions, without giving a key for (re)defining the role of state in market economies.General equilibrium, Lindahl-Foley equilibrium, Wicksell-Foley public competitive equilibrium, private provision equilibrium, mechanism design, free-rider problem, incentive compatibility, principal-agent models,