I would like to see the statistics you use to support that. If true it would contradict most of what I have read on the subject.I don't have statistics close at hand but will see if I can dredge them up.
However, common sense plays part of a role here.
If you have two businessmen, one a slave owner (A), one not a slave owner (B), if (A) just minimally feeds, clothes, and shelters the slave does it not make sense that he will probably pay less to do that than (B) pays a free man to do the same thing?
Now if you have a machine that will do the same thing, NOW if (B) buys the machine he might pay less to do the same thing.
(A), however, is thinking, "Yeh, but that machine doesn't make more machines and my slaves do.", so he wants to keep the slaves.
I don't say this is what happened, but maybe a possibility of the thinking?
But then you would get into the issue of productivity and supervision. If your one slave needs an overseer to make sure that the work is done and the worker doesn't run away then that adds to your cost. How productive is the slave? It the free man is 50% again as productive then your cost per unit of work also decreases. No, slavery wasn't the most efficient form of business. The south depended on it because it was there, the slaves formed a large part of their personal wealth, and there was no other alternative in the form of free labor willing to do work that was seen as slave work. They were pretty much stuck with it.