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Lindahl Equilibrium Versus Voluntary Contribution to a Public Good: The Role of the Income Distribution

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  • Wolfgang Buchholz
  • Richard Cornes
  • Wolfgang Peters

Abstract

Lindahl equilibria are often seen as an ideal outcome of cooperation in a public-goods economy. But it has also been observed that, if no transfer payments are possible, the Lindahl equilibrium may not be Pareto-superior to the Nash outcome of the voluntary-contribution game. We derive conditions under which agents (or countries in the case of an international public good) will prefer the Lindahl over the Nash solution. In particular we show that rich agents in general are better off in the Lindahl equilibrium than in the voluntary-contribution equilibrium. When the exogenously given income distribution is not skewed too much or the original economy is replicated sufficiently often, all agents will gain by the move from the Nash to the Lindahl outcome. The underlying effects are related to the famous exploitation of the rich by the poor countries occurring in Nash equilibrium (which follows from Warr neutrality) and the fact that the underprovision of the public good in Nash equilibrium is particularly serious in large economies. Finally, we tentatively discuss some potential applications concerning international cooperation on global public-good provision.

Suggested Citation

  • Wolfgang Buchholz & Richard Cornes & Wolfgang Peters, 2006. "Lindahl Equilibrium Versus Voluntary Contribution to a Public Good: The Role of the Income Distribution," FinanzArchiv: Public Finance Analysis, Mohr Siebeck, Tübingen, vol. 62(1), pages 28-49, March.
  • Handle: RePEc:mhr:finarc:urn:sici:0015-2218(200603)62:1_28:levvct_2.0.tx_2-3
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    References listed on IDEAS

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    1. Bergstrom, Ted C. & Blume, Larry & Varian, Hal, 1992. "Uniqueness of Nash equilibrium in private provision of public goods : An improved proof," Journal of Public Economics, Elsevier, vol. 49(3), pages 391-392, December.
    2. Althammer, Wilhelm & Buchholz, Wolfgang, 1993. "Lindahl-equilibria as the outcome of a non-cooperative game : A reconsideration," European Journal of Political Economy, Elsevier, vol. 9(3), pages 399-405, August.
    3. Bergstrom, Theodore & Blume, Lawrence & Varian, Hal, 1986. "On the private provision of public goods," Journal of Public Economics, Elsevier, vol. 29(1), pages 25-49, February.
    4. Bergstrom, Theodore C & Cornes, Richard C, 1983. "Independence of Allocative Efficiency from Distribution in the Theory of Public Goods," Econometrica, Econometric Society, vol. 51(6), pages 1753-1765, November.
    5. Andreoni, James, 1988. "Privately provided public goods in a large economy: The limits of altruism," Journal of Public Economics, Elsevier, vol. 35(1), pages 57-73, February.
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    Citations

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    Cited by:

    1. Karen Pittel & Dirk Rübbelke, 2012. "Transitions in the negotiations on climate change: from prisoner’s dilemma to chicken and beyond," International Environmental Agreements: Politics, Law and Economics, Springer, vol. 12(1), pages 23-39, March.
    2. Wolfgang Buchholz & Wolfgang Peters, 2008. "Equal sacrifice and fair burden-sharing in a public goods economy," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 15(4), pages 415-429, August.
    3. L.F.M. Groot & J. Swart, 2015. "From Nash to Lindahl in Climate Change Policy," Working Papers 15-01, Utrecht School of Economics.
    4. Wolfgang Buchholz & Richard Cornes & Wolfgang Peters, 2008. "Existence, uniqueness and some comparative statics for ratio and Lindahl equilibria," Journal of Economics, Springer, vol. 95(2), pages 167-177, November.

    More about this item

    Keywords

    public goods; Nash equilibria; Lindahl equilibria; international environmental agreements; Warr neutrality;

    JEL classification:

    • D3 - Microeconomics - - Distribution
    • H4 - Public Economics - - Publicly Provided Goods

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