Pretty obvious that prisons exploit prisoners in unjustified ways to the benefit of private enterprises, fail to protect prisoners they are responsible for watching, etc.
Yes, that's correct, though it doesn't mean NY and NYC don't outsource/insource service at rates that're unreasonably by any measure either due to cost or failure to provide reasonable service.
For examples, funding for pensions assumes that the state will maintain a set population of prisoners - which to me seems at odds of what longer objectives should be.
_____
NYC spends $168,000 a year per prisoner according to the NY Times: http://mobile.nytimes.com/2013/08/24/nyregion/citys-annual-c...
Why We Let Prison Rape Go On http://mobile.nytimes.com/2015/04/18/opinion/why-we-let-pris...
Abussive Phone Rates https://www.prisonphonejustice.org
Etc.