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At what age does the ‘libertarian’ suggest that it should be legal to choose to sell their body?

I don't know, 18 is usually the agreed upon age for adulthood.

You're not going to stop people from doing what they want to do. Prostitution might be morally repugnant to you, but to those involved it's their decision they're making, not yours. The best you can do is have the community set standards and let religious or non-profit groups intervene and give these women alternatives to prostitution.

I don't know, 18 is usually the agreed upon age for adulthood.

Not according to the Libertarian Party:

Children are human beings and, as such, have all the rights of human beings.
We recognize that children who have not reached maturity need guardians to secure their rights and to aid in the exercise of those rights. We hold that guardianship belongs to those who most love and value the child and his or her development, normally the parents and never the state.
We oppose all laws that empower government officials to seize children and make them "wards of the state" or, by means of child labor laws and compulsory education, to infringe on their freedom to work or learn as they choose. We oppose all legally created or sanctioned discrimination against (or in favor of) children, just as we oppose government discrimination directed at any other artificially defined sub-category of human beings. Specifically we oppose ordinances that outlaw adults-only apartment housing.
We also support the repeal of all laws establishing any category of crimes applicable to children for which adults would not be similarly vulnerable, such as curfew, smoking, and alcoholic beverage laws, and other status offenses. Similarly, we favor the repeal of "stubborn child" laws and laws establishing the category of "persons in need of supervision." We call for an end to the practice in many states of jailing children not accused of any crime. We seek the repeal of all "children's codes" or statutes which abridge due process protections for young people. We further favor the abolition of the juvenile court system, so that juveniles will be held fully responsible for their crimes.
Whenever parents or other guardians are unable or unwilling to care for their children, those guardians have the right to seek other persons who are willing to assume guardianship, and children have the right to seek other guardians who place a higher value on their lives. Accordingly, we oppose all laws that impede these processes, notably those restricting private adoption services or those forcing children to remain in the custody of their parents against their will.
Children should always have the right to establish their maturity by assuming administration and protection of their own rights, ending dependency upon their parents or other guardians and assuming all the responsibilities of adulthood.

To a hardcore LP type, economic independence = adulthood. Prostitution = economic independence in their twisted, morality free minds.

This agreed upon age; 18 for adulthood has been a big fat ongoing disaster; in more ways than this issue. No 18 year old is responsible enough to make the decision to become a whore. 21 should be the age. AMENDMENT XXVI was the start of this adult at 18 nonsense and is one of the many amendments that have had disastrous unforeseen consequences.