Public good provision with participation costs

Esteban and Ray develop a model with an increasing marginal cost of contribution, and overturn the Olson hypothesis that large groups cannot provide themselves with a rival public good. In contrast, Pecorino and Temimi incorporate fixed but avoidable participation costs into this framework, and conclude that public good provision must fall to zero in large groups if the degree of rivalry is high. However, they argue that the public good will continue to be provided in large groups when the degree of rivalry is sufficiently low. We show that this latter conclusion is incorrect. Specifically, suppose that there is rivalry “in the limit,” so, as group size grows, the per‐person benefit from any fixed total level of contribution falls to zero. Then, as group size grows, the payoff an individual receives from a public good, both when she contributes to it and when she does not, can each grow without bound in the absence of participation costs. However, the difference between these payoffs necessarily goes to zero. Thus, in a sufficiently large group, agents will not be willing to incur the participation costs. The same result also applies to the Morgan lottery mechanism.