Nolanverse Joker question

How does Joker being the sole inmate in Arkham (like stated in The Dark Knight Rises novelization) even work?

Do they keep a staff there just to feed Joker, clean Joker, and ensure he doesn’t escape? Arkham still has a water bill just for one inmate?

Is there a portion of the city’s budget dedicated to assuring the welfare of the Joker lol? How do they justify that to taxpayers?