We analyze the effect of a large group on an impure public goods model
with lotteries.
We show that as populations get large, and with selfish preferences, the
level of contributions
converges to the one given by voluntary contributions. With altruistic
preferences (of the warm glow
type), the contributions converge to a level strictly higher than those
given by voluntary contributions,
even though in general they do not yield first-best levels.
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