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.
Helping the individual economic status is helping also the world economy. When the financial situation of a certain person is good or in bad, well it can affect also the status of the economic level of a certain country as well. A that is based on my observation in our country.