On models with an uncongestible public good and a continuum of consumers

This short note shows that models with an uncongestible or mildly congestible public good and a (non-atomic) continuum of consumers have an interesting but unfortunate property. Only an infinite level of public good provision in the continuum economy can be approximated by feasible public good levels in a sequence of economies with finite populations. We discuss the theoretical and practical problems this creates for familiar models that employ a continuum of consumers and a finite level of an uncongestible public good.