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| Corporations cannot lawfully force individuals to do anything. |
No, but they have other means. If equilibrium wage is $2 per hour, then you either accept it or starve. Strictly speaking, the government can't force you to do anything, either, because you have a choice to break a law and go to prison, just like you have a choice to decline a meager wage and starve.
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| Monopolies and cartels are always government creations. |
This is simply false; counterexamples include Microsoft and Standard Oil. Governments sometimes choose to create monopolies on certain conditions because the free market is inefficient at providing infrastructure and basically every public good.
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| This begs the question, "Where does private space end and public space begin?" I would say that the market is also private space, in terms of privately held property (that is, property that has a specific owner(s)). |
Not precisely; while property is of course part of the private space, its exchange in a modern society is not. Unlike private space exchanges such as sex, it is deniable and can cause the formation of groups that deny people certain things required for a decent quality of life, such as a living wage. Remember that property rights are useless if the market deprives you of the ability to use them.