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. And would also weaken the claim that slavery was a 'dying institution'.
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?