Endless studies could be written about it, since the topic is very complex and outcomes are pretty much impossible to predict. No wonder economists have such a bad reputation about forecasts :D. It's almost a question of religion. My gut feeling is the following:
Outside of an isolated economy, the bitcoin economy would be rapidly buried by other economies that can inflate their money supply at will. Even with boom and bust cycles, the bitcoin economy is unlikely to survive competing with a China like entity who will just fuel their own expansion with debt until the bitcoin economy is in the toilet.
In case of an isolated economy, it would eventually start to stagnate as cash becomes an appreciating asset that is better to hoard than invest. Taken ad absurdum, you'd end up with a completely dead economy with a small handful of hoarders sitting on all the cash. Of course, in the real world there'd have been a revolution long before, since people can't eat coins and eventually people would resort to barter and most likely a new fiat currency would emerge naturally.