Anarchy won't work for many reasons (at least not full blown anarchy). For starters, currency is non existent, meaning people won't work for other people, just individuals. This may not be a bad thing, but I'd say about 90 percent of the worlds population (at least more urban countries) would die off very soon due to starvation. Also, people would be killing everyone, as there's nothing negative about not doing it. You wouldn't want to have anything as people would just steal it. Like I said, this would happen for full blown Anarchism, not that market what ever... although, I don't think that would work either (assuming killing isn't punished in that system), as if you owned companies, the one that could kill the other quickest would win. However, if you can't kill without consequence, then I don't really consider it Anarchy. I don't mind private business though.
Personally, I have no idea why people are for anarchy. It would just lead to a lot of dieing... I guess if your slightly to moderately twisted in the head then you would be all for it.
Oh, and poor people would probably need to adapt less than those with more things, as there would be less of EVERYTHING. No one would work, so there would be no food. Homeless people would probably survive the longest in cities, as they're used to not having much food.
Yeah, I can't see this working out well...
By the way, let's not get communism mixed up with Mao-communism. They're very different. Regular communism is actually not a bad idea, but there's so much that wouldn't work with it that it will never happen (currency is needed for people to work at all). At least, I can't see it happening. I don't know everything about true communism, so my opinion isn't really valid here.