The market doesn't control the supply; the supply rate is fixed on a declining scale with a cap. The bitcoin system was not designed to be stable, but to be a deflationary currency. The more people use it, the more it is worth relative to other currencies. At least in the short to medium term, anyways.
But it isn't necessarily deflationary. As evidenced over the past few days, bitcoins can be quite inflationary.
With gold, as it's price goes down, people stop mining it, and importantly, less of it is produced.
With bitcoin, the network just keeps spitting out coins at a constant rate
(at least for the first 4 years).
This means there is no reliable lower limit on the cost of mining bitcoins, besides difficulty 1. If the price of bitcoin goes down, quite perversely, it becomes cheaper to mine bitcoins. This causes the price to go down further.
The system I suggest is more like gold, which I think would result in steady long term deflation in real terms.