Buy Up Meaning

(idiomatic, transitive) To buy whatever is available of something.

Example:   The marshland was bought up by a housing company.‎
2013 June 8, “Obama goes troll-hunting”, The Economist, volume 407, number 8839, page 55:
  According to this saga of intellectual-property misanthropy, these creatures [patent trolls] roam the business world, buying up patents and then using them to demand extravagant payouts from companies they accuse of infringing them. Often, their victims pay up rather than face the costs of a legal battle.