How does erudite contribute to the community

The faction produces most of the city's librarians, doctors, scientists, and teachers. They are responsible for keeping records of the city and the factions. All technological achievements that the factions benefit from came from Erudite minds, such as the advanced agrarian methods employed by the Amity and all of the simulation serums. Check this out for more detail:

https://divergent.fandom.com/wiki/Erudite#:~:text=They%20are%20responsible%20for%20keeping,all%20of%20the%20simulation%20serums.