Inmates are products, not consumers. Consumers would be governments, and they would in theory over time select those administration companies that would offer the best correction facilities for the lowest price.
However, I am actually making the point against that. Privatization of that area makes no sense at all. I might have phrased that in a way that works against the central point of my argument, but the idea is that no, there is no competition that could possibly justify privatizing the corrections sector.
Why would you think that? It's not like consumers get to pick their prisons.