Public goods, group size, and the degree of rivalry

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It is well established that the provision of a pure public good is increasing in group size if the good is normal. What I show is that if the good exhibits even a small degree of rivalry, then the individual level of consumption of the public good falls to zero in a large group. Thus, a strong version of Olson’s large group hypothesis applies to anything other than a pure public good. While individual consumption of the public good goes to zero in a large group, there is not a monotonicity result. If it is initially small, an increase in the group size may lead to an increase in the individual consumption of the public good.