I do not see bitcoin helping the world economy but rather it can help an individual economy. Obviously, every country will not legalise bitcoin but the individual economy that adopts bitcoin can push in a huge investment when bitcoin is down to get some accruing profit from investment when price go up. By such profit, the individual country can better her nation and her people by providing more social amenities, building projects, factories and employment.
Yeah, it all depends on individual. As the whole global economy is battling with their fiat system, we are safe in our own decentralized system and really, this would definitely open the eye of so many people right now with the way things are going to be changing in the long run. However, for country that may really accept the usage of bitcoin, it may really help the economy in general since everyone may end up doing pretty well without having to get screwed by fiat.
The entire world economy is sliding down basically because of all the government nonchalant policies that end up draining everything. Bitcoin would only come to the rescue if they accept the idea of decentralization, but of course, we already know that is not possible. So, at the end, only those who are smart enough to filter out the rubbish fiat system from the real thing will be able to do well in the system that is ridden with looming issues.