Do Government Subsidies Increase the Private Supply of Public Goods?

We study three different models in which public goods are supplied by private contributions. In one of these models, tax-financed government subsidies to private contributions will definitely increase the equilibrium supply of public goods. In the other two models, government subsidies are neutralized by offsetting changes in private contributions. We explain why it is that these models lead to opposite conclusions and we argue on the basis of our first model that a government that wants to use taxes and subsidies to increase total provision of public goods will be able to do so. Indeed, our model yields a surprisingly decisive comparative statics result. If public goods and private goods are both normal goods, then increases in the subsidy rate necessarily increase the equilibrium supply of public goods. Do Government Subsidies Increase the Private Supply of Public Goods? James Andreoni and Ted Bergstrom Peter Warr (1983) discovered the remarkable fact that in a Nash-equilibrium model of voluntary public goods supply, small income redistributions among contributors to a public good are “neutralized” by changes in equilibrium private donations. Private consumption by individuals and the supply of public goods remain exactly the same as before redistribution. Warr (1982) also observed that small government contributions to a public good, paid for by arbitrary lump sum taxes on contributors, would be offset “dollar-for-dollar” by reductions in private contributions. The comparative statics of non-infinitesimal redistributions and of economies where some contributors may make zero contributions were examined by Bergstrom, Blume, and Varian (1986). They showed that redistribution is not, in general, neutral if the amount of income distributed away from any consumer exceeds his voluntary contribution to the public good. Russell Roberts (1987, 1991) suggested that if public goods are paid for by distortionary taxes, then efficiency would be improved by a “mixed system” in which the public good is supplied by private contributions that are (perhaps very heavily) subsidized by the government. While this idea seems appealing, it must somehow be reconciled with apparently contradictory results of Douglas Bernheim (1986), and of James Andreoni (1988), each of whom extended Warr’s result to show that seemingly distortionary taxes and subsidies may be “neutralized” by changes in private donations. This paper examines the neutrality results found by Andreoni and by Bernheim, and presents a new model in which increases in subsidy rates will necessarily increase the equilibrium supply of public goods. We show that in all of these models neutralization of tax-subsidy schemes is limited to “small” changes in tax obligations that do not exceed anyone’s voluntary contributions in the original equilibrium. Moreover, we argue that it is possible for governments to design “distortionary” tax-subsidy policies which can predictably increase the equilibrium total amount of contributions to a public good. 1. Game 1–A Model Where Government Subsidies are not Neutral Here and in subsequent sections, we follow the useful precedent set by Bernheim (1986) and Nett and Peters (1990) of describing the economy as a multi-stage game, with distinct stages in which government sets policy parameters, consumers choose actions, and the government collects taxes and provides public goods. The economy has n consumers, one private good and one pure public good. Preferences of consumer i are represented by a utility function, Ui(g, ci), where g is the amount of public This work was begun while the authors were both attending the Warwick Summer Research Workshop in Economics in July 1991. The authors are grateful to Clive Fraser of the University of Warwick for helpful comments.