Private provision of public goods between families

We consider a two-stage voluntary provision model where individuals in a family contribute to a pure public good and/or a household public good, and the parent makes private transfers to her own child. We show not only that Warr's neutrality holds, regardless of the different timings of parent-to-child transfers, but also that there is a continuum of Nash equilibria which individuals' contributions and parental transfers are indeterminate, although the allocation of each's private consumption and total public good provision is uniquely determined. Furthermore, impure altruism or productivity difference in supplying public goods may not break our results above.