Copyright infringement as user innovation

Copyright holders of major manga and anime in Japan have been ignoring copyright infringement by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d{\bar{o}}jinshi$$\end{document} (or doujinshi), a Japanese word referring to self-published works created predominately by amateurs. Many of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d{\bar{o}}jinshi$$\end{document} are derivative works of popular anime or manga but are sold without official permissions from the copyright holders. Thus, it is highly possible that the activity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d{\bar{o}}jinshi$$\end{document} creators violates Article 28 of the Copyright Law of Japan, which states the rights of original authors in the situation of exploitation by derivative works. We demonstrate that ignoring copyright infringement by a derivative creator can be optimal for the copyright holder based on an economic model that incorporates both positive and negative externalities of derivative work. We also demonstrate that when unauthorized use of the copyrighted work is optimal for the copyright holder, it is also optimal for social welfare although the opposite is not necessarily true.