Revisiting the ‘group-size paradox' in the private provision of a pure public good

In the presence of multiple varieties of a private good and a single pure public good, which is provided by the voluntary contribution of the individuals, Bag and Mondal (2014) shows that if the private and public goods are gross complement, the total amount of public good increases as the group size increases. But, if they are gross substitute, the relation between the two exhibits an inverted U pattern. In this paper, we assume a single variety of a private good and a pure public good. Our framework differs from that of Bag and Mondal (2014) in two aspects - all the individuals have general quasi- concave utility function instead of CES utility function, and the private good industry is competitive instead of monopolistic competitive. We show that if the two goods are gross substitute, the amount of public good increases with the group size under a unique sufficient condition which requires the labor demand in private good industry to be almost inelastic. But, if the two goods are gross complement, the relation is ambiguous. We also consider some possible extensions of the basic framework and intuitively discuss the relation between group size and level of provision of the public good.