Open source software: Private provision of a public good

A simple model of open source software (as typified by the GNU-Linux operating system) is presented. Individual user-programmers decide whether to invest their own effort to develop a software enhancement that will become a public good if so developed. The effect of changing the population size of user-programmers is considered; finite and asymptotic results are given. Welfare results are presented. It is shown that whether development will increase when applications have a modular structure depends on whether the developer base exceeds a critical size. Potential explanations of several stylized facts are given, including why certain useful programs don't get written.