I think this series has the poorest nobles. I mean they are all children of high nobles, not having much money should be enough to buy a commonors entire house
It's a light-hearted story, so I don't expect it to be dense with economic theory, but maybe their wealth is tied up in assets?
Also, it might be something like "your estate makes X amount of money per annuum, but a proper noble lifestyle is damn expensive, so you invest in important and/or higly visible places, leaving little for kids free spending."
There might be some who leave their estates to be managed, and just live in the capitol year-round, attending social events in the high society and such. In a case like that, a person could be far more cash-strapped, even in debt, but seem far wealthier than well-to-do merchants.
Then again, from what I've seen, the nobles in the story, at least the good guys, don't seem that decadent, so it may be teaching the kids a lesson about frugality and hardship, or something.