[Non-Sequitur]

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.

[Just another Joe]

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.

Exactly!
Number one, you take away the slaves and (A) has no money to buy said machine.
Number two, it still takes someone to run the machine.
Number three, machines don't make themselves.

It's still a matter of the econmical results of slavery, not the slavery itself.
I go back to my giant sloth in a cage example.