Economics in fantasy worlds is usually not worth paying much attention to but TV is a huge and wealthy city sitting astride trade routes and between the wonderful Ogier construction and the AS's way of dealing with crime they clearly don't need to blow much cash on maintaining roads, police forces, standing armies, or medical concerns. They don't get a plague wandering through killing off vital workforce components and leaving orphans to be cared for. They also control the area around TV, which is left vague but impression I get is that their tax base parallels or exceeds any of the other nations, who also send them cash, and they doubtless have massive investments all over the place.

There's also the whole inflation/deflation thing. We see inflation going on even in book one and it only gets worse, but the AS have had centuries - and live centuries - to have been sucking precious metals out of circulation. Gold typically doesn't get lost, and its implied the population has been steadily decreasing for a long while even as mining doubtless continued. The tower - and other kingdoms and nobles - are shown to be serious hoarders. The AS post-Hawkwing might have decided there should be X gold per person in circulation, roughly, and simply slowly removed coins and dumped them in the tower basement. Then they have a reserve when the shit hits the fan but gold has no intrinsic value so when it dumps into the market in wads everything costs more. They clearly have sufficient income to maintain the sisters in good form regularly, TV alone could probably do that with cash to spare, so they've probably been hoarding the excess.

I'd actually go so far as to say that the AS, the kings, the banks, and all the nobles had so much gold sitting around their mansions and vaults that it exceeded what was in regular circulation as coins, and that when they started having to raise armies and buy food in serious quantities they began using that and flooding the market with gold, inflating the cost of everything.