There was state run prison slavery before the institution of chattel slavery in North America, there was state slavery after it. Why wouldn't there be? The government always exempts itself from laws of that sort.

What was gross margin per average (because the cook picks no cotton) of your typical plantation?

I'd bet it's a whole lot less than the federal .gov's margin on someone in one of the 20+% brackets. State .govs are probably all over the place.

Hard to account for because the .gov "doesn't show a profit" in the same way that "we're totally a nonprofit <wink>" hospitals don't but should be a doable calculation.