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.
Countries can also benefit in a number of ways:
1) If the citizens of a country are making good money with their bitcoin investments, they will also pay more tax to the government. This will result in increased overall revenue for that country.
2) If more people become self dependent by investing in bitcoins, it reduces the work load of government. If these people do not earn anything, government has to spend huge amount of money as compensation package for these people.