1) The entire society would be based on a profit motive. Virtually nothing would be done that isn't motivated by personal profit. That means you can say bye bye to the environment among other things.

2) There would be nothing stopping monopolies from forming and thus the government would become whoever has the most money.

3) There would be no one to make sure the non-aggression principle and other such Anarcho-Capitalist bollocks is maintained because whoever has the most money would make the rules and do whatever they want.

4) There would be no law or police to defend and establish property rights and thus who owns what would be decided very often through the initiation of force.

5) The closest thing to police would be the armed thugs and extortionists working for the wealthy.

6) Eventually a super wealthy class would form and all the important land and resources would be owned by the one percent, thus the average person would have little to no economic freedom or property rights.

7) It would end up reverting back to croney capitalism and having a government and we'd be at square one.