Central banks intervene on FOREX exchange all the time to stablize the exchange rate of their currency. A good example is the exchange rate between Swiss franc and euro, it stayed in a very narrow range during summer 2012 because of this kind of action
Bitcoiners advocate free market, but if one large entity have enough fiat money reserve, he can manipulate the price and cause large price swing, like we saw last year in china (Chinese have huge fiat money reserve). Because majority of the coins were hoarded, the number of coins circulating on exchanges are small and vulnerable to price manipulation
And, even when each coin worth millions, majority of coins would still be hoarded, thus the outflow of any small amount of those hoarded coins could cause large price swing on exchanges
So, some kind of collective price stabilizing mechanism could be established to reduce volatility. It is a networked society, if everyone is informed and act the same way, it should be as efficient as central bank's action
You can limit the downside risk, but you can never limit the upside risk, because you can have large fiat money reserve but impossible to have large bitcoin reserve, so large price swing to the upside would still happen
If there are enough amount of bitcoin supporters, and they reach such an agreement with enough fiat money reserve, then they can guarantee the lowest possible exchange rate. For example, bitcoin is guaranteed to be above $400 if their collective fiat money reserve is larger than 5.09 billion (12.7 million coins mined so far)
Considering the dynamics, the required fiat money reserve is much less, since the price is decided by the daily coin supply/demand. Supply is around 5000 to 20000 coins, and the daily purchase of 5-20 million USD will guarantee a price of $1000, requiring only 5-20 USD per day from each bitcoiner, if there are one million of them
This is very useful: Most of the people wonder who is backing bitcoin, and they are afraid that a currency without any backing will crash to zero one day. Now here is a simple answer: Millions of bitcoiners back bitcoin. Bitcoin is people's money, so people back it, instead of central banks or governments. Once people know that bitcoin is backed by millions of bitcoiners with a large fiat money reserve, their acceptance and confidence about bitcoin will greatly improve
Comparing with this method, the merchants who are accepting bitcoin actually don't back bitcoin, since they usually convert the coin to get fiat money. Only those merchant who exclusively accepting bitcoin and never convert them back to fiat is backing bitcoin with his goods/services. That is a long term goal, but might never be reached
It seems MV=PQ formula can show that bitcoin will increase in value with more economy activity, but that only apply to a money which is the only money in that economy. Until there are many bitcoin-only businesses, the demand to get a bitcoin for transaction is minimum (for fiat money it is maximum), so the increase in bitcoin acceptance from merchants will not cause an increase in demand of bitcoin, thus will not help to stabilize its value
The question is how to reach a consensus among millions of bitcoin supporters to step into exchange and buy coins when it fall below a certain threshhold (average mining cost for example). I guess currently the most motivated people are those mining rig manufacturers and mining farm operators, a higher exchange rate will definitely help their business. For other people there is less motivation. Maybe eventually we will have an industry association to collectively guarantee the lowest exchange rate of bitcoin. Without some kind of coordinated action, each single of them will not dare to provide any backing, unlike a central bank who can take action any time
Anyway, with backing, the final uncertainty on bitcoin is gone. It is ready for some serious business