Question

How is the neutrality of income redistribution in the private provision of pure public goods related to perfect crowding out of government provision?

Answer 1

The effect of income redistribution on the aggregate public good provision. For a complete network, the invariance result of Warr (1983) and Bergstrom, Blume, and Varian (1986), the so-called neutrality result, shows that income redistributions that preserve the set of contributors will have no e?ect on the aggregate public good provision or individual private good consumption. The following proposition provides a proof of the neutrality result based on network analysis of the private provision of public goods.

. Assume network normality and that g is the complete network. Then it holds that q^t-q^* = t

Proof. First, observe that, from the network normality assumption, it follows that both matrices I + AG and I A are invertible. Moreover, it holds that

Let u =  

then it holds that (I-A)^-1(I + AG) = I + u1^T . From the Sherman–Morrison formula,  it follows that

Hence, it follows

What is remarkable in the neutrality result is that, regardless of the form of the preferences, each consumer adjusts his public good provision by precisely the amount of the income transfer made to him, provided that the set of contributors remains unchanged.