The economic value of public libraries has been studied in different contexts. For the researcher who is looking to support a building project, the economic value of libraries may need to be shared with your community to build support.
In 2010, the economic value of academic libraries report was released by M. Oakleaf of the iSchool at Syracuse University. This is a good place to look if you are developing a building plan and need to align support on campus.
If you are looking for a video that discusses why libraries matter – John Grisham on the Value of Libraries and Librarians –