The doctrine of fair use allows unauthorized copying of original works of art, music, and literature for limited purposes like criticism, research, and education, based on the rationale that copyright holders would consent to such uses if bargaining were possible. This paper develops the first formal analysis of fair use in an effort to derive the efficient legal standard for applying the doctrine. The model interprets copies and originals as differentiated products and defines fair use as a threshold separating permissible copying from infringement. Application of the analysis to several key cases (including the recent Napster case) shows that this interpretation is consistent with actual legal reasoning. The analysis also underscores the role of technology in shaping the efficient scope of fair use.