Of course, we don't know. But I can take my best guess.
If you ask me, it could very well happen on a single-digit price value, so I'll wildly guess <8. I base that on the possibility that the relatively sized inflow of overconfident speculators seems to decrease, which would cause the situation to behave like a classical price bubble. But with all the chaos, it's really hard to make out a "real" price, I could be wrong to an order of magnitude.
The price gets stable when the majority of incompetent speculators lost enough money to give control back to classical speculators. Real speculators make money from margins and stabilize price; insane speculators lose money and cause fluctuations.
The important point is: the smaller the inflow of newcomers compared to market size, the more stable the price will become, because bad speculators will burn out their resources over time. Give it at least a few months; Bitcoin is still brand new.
What do you mean with the term incompetent speculator? I started with Bitcoin about 2 weeks ago. I really liked the idea and started mining but had to realize that it is really not profitable. So I bought some bitcoins from MtGox. I didn't have any experience with shares except some things from my degree in finance. Of course nothing really applies to Bitcoin
Still, after buying some Bitcoins, I more than doubled the money i put into MtGox without any experience in that area. Why do you think the same doesn't apply to many other "newbies"?