Let’s Talk About Monopolies on Scarce Resources: A Ding In The Libertarian Armor?

Lets say that we all live in a free market Libertarian or Anarchist type of society. Joe Money-pants buys up all the mines in the United States that can extract a rare element. What do you do? Does that mean that Joe money pants can be the sole ruler of this market? Competition is not possible since Joe owns all the mines.

Perhaps there could be competition if research could be done to discover another way to manufacture something without the rare element. That could take a 1000 years.

What is the Libertarian answer to monopolies on scarce resources?