I suppose the idea behind 'The US making money' (meaning the US government?) Would be that it could save money in some situations. Not sure if that's true, but it is often true when governments decide to contract work out to private companies. I'm sure it is not true in some cases also.
Was curious as to how big the private prison industry was, and according to this in 2013 there was 8.4% of the US prison population held in privately run prisons
"Statistics from the
U.S. Department of Justice show that, as of 2013, there were 133,000 state and federal prisoners housed in privately owned prisons in the U.S., constituting 8.4% of the overall U.S. prison population"
https://en.wikipedia.org/wiki/Private_prison
So given that number, the common idea that the US prison population is so high in large part due to private prisons really wouldn't make sense. I can see the incentive of a private prison company wanting more business (more prisoners) but I can't see it being significant enough a factor in the grand scheme of things.