[quote=The Irish Tree]
...Then... who the fuck is paying for their room and board?
[/quote]

I'd figure that's what the pay from the missions the students do go to. I'd also imagine that they're funded by Sponsors like the local government, or whatever it is. It's a Public School, basically. A special Public School of high renown. It's not money that gets you in, it's ability, hence why Jaune needed to forge transcripts to enter; he lacked the skills to be eligible, while money wasn't a problem likely because it was never an issue in the first place.