ON THE PRIVATE PROVISION OF PUBLIC GOODS

ON THE PRIVATE PROVISION OF PUBLIC GOODS

1986 | Theodore BERGSTROM, Lawrence BLUME and Hal VARIAN
The paper by Bergstrom, Blume, and Varian analyzes the non-cooperative provision of public goods. It shows that under weak assumptions, there is a unique Nash equilibrium in their model. Small wealth redistributions do not change the equilibrium amount of the public good, but larger redistributions can change the set of contributors and thus the equilibrium provision. The paper characterizes the properties and comparative statics of the equilibrium and analyzes how government provision of public goods affects private contributions. The authors consider a model with one public good, one private good, and n consumers. Each consumer consumes a private good and donates to the public good. The total supply of the public good is the sum of all donations. The utility function of each consumer depends on their private consumption and the total supply of the public good. The paper shows that a redistribution of income among contributors does not change the supply of the public good if it does not change the set of contributors. However, many applications involve redistributions that change the set of contributors or their wealth. The paper also discusses the importance of the "extensive margin" – the decision to contribute – compared to the "intensive margin" – the amount contributed. It shows that adjustments on the extensive margin are at least as important as those on the intensive margin. The usual practice of assuming interior solutions in comparative statics is misleading in this case, and a careful analysis of boundary cases is necessary. The paper presents a neutrality theorem, which states that a redistribution of income among contributors does not change the equilibrium amount of the public good if it does not change the set of contributors. This result is extended to multiple public goods. The paper also discusses the effect of government provision of public goods on private contributions, showing that government provision can "crowd out" private contributions, but the extent of this effect depends on the distribution of income. The paper concludes that the model provides a number of testable implications of the Nash hypothesis concerning the voluntary provision of public goods. It suggests that further research is needed to understand the effects of income inequality on the provision of public goods and to develop new methods using both experimental methods and traditional empirical data to test the Nash hypothesis.The paper by Bergstrom, Blume, and Varian analyzes the non-cooperative provision of public goods. It shows that under weak assumptions, there is a unique Nash equilibrium in their model. Small wealth redistributions do not change the equilibrium amount of the public good, but larger redistributions can change the set of contributors and thus the equilibrium provision. The paper characterizes the properties and comparative statics of the equilibrium and analyzes how government provision of public goods affects private contributions. The authors consider a model with one public good, one private good, and n consumers. Each consumer consumes a private good and donates to the public good. The total supply of the public good is the sum of all donations. The utility function of each consumer depends on their private consumption and the total supply of the public good. The paper shows that a redistribution of income among contributors does not change the supply of the public good if it does not change the set of contributors. However, many applications involve redistributions that change the set of contributors or their wealth. The paper also discusses the importance of the "extensive margin" – the decision to contribute – compared to the "intensive margin" – the amount contributed. It shows that adjustments on the extensive margin are at least as important as those on the intensive margin. The usual practice of assuming interior solutions in comparative statics is misleading in this case, and a careful analysis of boundary cases is necessary. The paper presents a neutrality theorem, which states that a redistribution of income among contributors does not change the equilibrium amount of the public good if it does not change the set of contributors. This result is extended to multiple public goods. The paper also discusses the effect of government provision of public goods on private contributions, showing that government provision can "crowd out" private contributions, but the extent of this effect depends on the distribution of income. The paper concludes that the model provides a number of testable implications of the Nash hypothesis concerning the voluntary provision of public goods. It suggests that further research is needed to understand the effects of income inequality on the provision of public goods and to develop new methods using both experimental methods and traditional empirical data to test the Nash hypothesis.
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