Consumer welfare and market structure in a model of competition between open source and proprietary software

I consider a Vickrey-Salop model of spatial product differentiation with quasi-linear utility functions and contrast two modes of production, the proprietary model where entrepreneurs sell software to the users, and the open source model where users participate in software development. I show that the OS model of production may be more efficient from the point of view of welfare that the proprietary model, but that an OS industry is vulnerable to entry by entrepreneurs while a proprietary industry can resist entry by OS projects. A mixed industry where OS and proprietary development methods coexist may exhibit large OS projects cohabiting with more specialized proprietary projects, and is more efficient than the proprietary model of production from the point of view of welfare.