The Texas State Library and Archives Commission produced a study of the economic impact of public libraries in Texas using data from the 2015 fiscal year. This study was lead by Dr. James Jarrett, Senior Research Scientist of the Bureau of Business Research, IC² Institute, The University of Texas at Austin. The economic modeling was performed by Brian Lewandowski, Associate Director of the Business Research Division, Leeds School of Business, University of Colorado Boulder.
The short version is that Texas communities gain an average of $4.64 in benefits for every $1.00 invested in their public library. The full text of the press release is at https://www.tsl.texas.gov/news/2017/roi2017. A video announcement may be viewed at https://www.facebook.com/tslac/videos/1301309966558685.