But what about economics? To sustain the achieved standard of life we need that tight hierarchical integration between people (ironically called division of labor) which most anarchists loathe as much as they are afraid of... 
Would you do business with someone who used slave labor?
If not, and the other people you do business with agreed this was bad, the slave owner would either need to stop owning slaves or go out of business
If so, and the other people you do business with agreed this was bad, you put yourself at risk of going out of business along with the slave owner
I have to confess that I can't say for sure if I would do business with the guys using slave labor (or some variety thereof) since I have never yet been there, but I definitely try to avoid people who knowingly sell stolen things...
But it doesn't actually matter if I in particular would do business with them or not. I personally know many people who would buy stolen things without ever thinking whether it's good or bad. I have absolutely no doubts these same people would deal in with someone using slave labor without much remorse about it. And I have to admit that some of them would even be happy to employ some slave labor if there is an opportunity
And they would do business between themselves whether I like it or not...