Ok, so this isn’t a true paradox, but it does illuminate the tension within the voluntary/coercive dualism which undergirds modern libertarianism.
The divide between market and state is synonymous with the divide between voluntary and coercive action, also called economic means and political means by Oppenheimer. Rothbard explains the unique coercive status of the state:
“All other persons and groups in society (except for acknowledged and sporadic criminals such as thieves and bank robbers) obtain their income voluntarily: either by selling goods and services to the consuming public, or by voluntary gift (e.g., membership in a club or association, bequest, or inheritance). Only the State obtains its revenue by coercion, by threatening dire penalties should the income not be forthcoming.”
But Rothbard recognizes that the state requires not only production off which to feed, but a certain level of ideological support. In the introduction to Boetie’s Discourse of Voluntary Servitude, Rothbard concedes that
“every tyranny must necessarily be grounded upon general popular acceptance. In short, the bulk of the people themselves, for whatever reason, acquiesce in their own subjection. If this were not the case, no tyranny, indeed no governmental rule, could long endure. Hence, a government does not have to be popularly elected to enjoy general public support; for general public support is in the very nature of all governments that endure, including the most oppressive of tyrannies. The tyrant is but one person, and could scarcely command the obedience of another person, much less of an entire country, if most of the subjects did not grant their obedience by their own consent (emphasis added).”
How is it that the state is an institution that is essentially voluntary and at the same time the embodiment of coercion, or the “organization of politcal means” in Oppenheimer’s words?
The solution that I think most libertarians hold is that while some (actually most) individuals support the state willingly, any given individual is still coercively subjected to the state regardless of their personal choice. While this effectively resolves any paradox, it also admittedly undermines the hardline dichotomy between market and state. The state is not qualitatively different from the market–at least not in the voluntary/coercive sense–but is instead quantitatively different.
I think this leads libertarian thought in one of two directions: either a rejection of ethical/moral content in favor of an economic approach (embodied in the non-Rothbardian Misesian project) or an embrace of the complexity and “thickness” which comes out of this insight (embodied in the left libertarian project).