Efficiency and group size in the voluntary provision of public goods with threshold preference

Abstract

What is the optimal group size in the voluntary provision of public goods in a purely altruistic economy? The popular consensus on this fundamental question is that the free-rider problem worsens as the group size increases. This study provides a counterexample of the consensus by featuring plausible threshold preferences for certain typical public goods. Under these preferences, marginal utility hardly diminishes below a threshold level, but declines significantly in close proximity to the threshold and nearly drops to zero above the threshold. We find that threshold preferences significantly reduce inefficiency. We also show that if marginal costs increase, then the threshold preferences lead to a partly positive relationship between efficiency and group size, which allows us to detect the locally efficient group size. Moreover, the locally efficient group size is proportional to the slope of the marginal costs as well as the threshold of marginal utility.