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Matching in the Kolm triangle: interiority and participation constraints of matching equilibria

Author

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  • Wolfgang Buchholz
  • Richard Cornes
  • Dirk Rübbelke

Abstract

Purpose - In this paper we show how the Kolm triangle method, which is a standard tool for visualizing allocations in a public good economy, can also be used to provide a diagrammatical exposition of matching mechanisms and their effects on public good supply and welfare. In particular, we describe, on the one hand, for which income distributions interior matching equilibria result, and on the other hand, for which income distributions the agents voluntarily participate in a matching mechanism. As a novel result, we especially show that the “participation zone” is larger than the “interiority zone” Design/methodology/approach - We employ the Kolm triangle approach, which has – compared to most other graphical methods for representing allocations in a public good economy – the advantage that it allows for showing the aggregate budget constraint, the levels of considered agents' private consumption, and the level of public good supply directly in the same diagram. Findings - The Kolm triangle method can be used to visualize important effects of matching in an elegant way, so basically the increase of public good supply through matching. The interiority of matching depends on the income distribution and especially, on how the “interiority zone” is shrinking when the matching rate increases. Moreover, we were able to delimit the “participation zone” in the Kolm triangle. An important and novel insight is that the participation zone is larger than the interiority zone, which means that also corner matching equilibria in which only one agent makes a positive flat contribution to the public good may make both considered agents better off. Research limitations/implications - Corner matching equilibria in which only one agent makes a positive flat contribution to the public good may improve all considered agents' welfare. How this welfare effect can be generalized to the case of different utility functions and matching rates will be an issue of future research. Practical implications - The examined matching mechanism finds application in many policy fields where public good undersupply is pending. International climate policy is one of these fields of application, for example. Originality/value - The Kolm triangle method has been particularly helpful to describe the Nash equilibrium in the case of non-cooperative public good provision and to compare this outcome with Pareto efficient public good allocations. Furthermore, the Kolm triangle approach facilitates the analysis of mechanisms for attaining an efficient public good allocation like the Lindahl equilibrium as well as the study of preconditions and limitations faced by such mechanisms. An important and novel insight of our study is that the participation zone is larger than the interiority zone.

Suggested Citation

  • Wolfgang Buchholz & Richard Cornes & Dirk Rübbelke, 2020. "Matching in the Kolm triangle: interiority and participation constraints of matching equilibria," Journal of Economic Studies, Emerald Group Publishing Limited, vol. 47(5), pages 1039-1050, April.
  • Handle: RePEc:eme:jespps:jes-06-2019-0254
    DOI: 10.1108/JES-06-2019-0254
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    1. Dirk T. G. Rübbelke, 2006. "Analysis of an international environmental matching agreement," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 8(1), pages 1-31, December.
    2. Andreoni, James & Bergstrom, Ted, 1996. "Do Government Subsidies Increase the Private Supply of Public Goods?," Public Choice, Springer, vol. 88(3-4), pages 295-308, September.
    3. Guttman, Joel M, 1978. "Understanding Collective Action: Matching Behavior," American Economic Review, American Economic Association, vol. 68(2), pages 251-255, May.
    4. Eduardo Ley, 1996. "On the private provision of public goods: a diagrammatic exposition," Investigaciones Economicas, Fundación SEPI, vol. 20(1), pages 105-123, January.
    5. Shibata, Hirofumi, 1971. "A Bargaining Model of the Pure Theory of Public Expenditure," Journal of Political Economy, University of Chicago Press, vol. 79(1), pages 1-29, Jan.-Feb..
    6. Julio Dávila & Jan Eeckhout & César Martinelli, 2009. "Bargaining over Public Goods," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 11(6), pages 927-945, December.
    7. Cornes,Richard & Sandler,Todd, 1996. "The Theory of Externalities, Public Goods, and Club Goods," Cambridge Books, Cambridge University Press, number 9780521477185, November.
    8. 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.
    9. Thomson, William, 1999. "Economies with Public Goods: An Elementary Geometric Exposition," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 1(1), pages 139-176.
    10. Richard Cornes & Roger Hartley, 2007. "Aggregative Public Good Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(2), pages 201-219, April.
    11. Buchholz, Wolfgang & Cornes, Richard & Rübbelke, Dirk, 2011. "Interior matching equilibria in a public good economy: An aggregative game approach," Journal of Public Economics, Elsevier, vol. 95(7), pages 639-645.
    12. Kirchsteiger, Georg & Puppe, Clemens, 1997. "On the possibility of efficient private provision of public goods through government subsidies," Journal of Public Economics, Elsevier, vol. 66(3), pages 489-504, December.
    13. Boadway, Robin & Pestieau, Pierre & Wildasin, David, 1989. "Tax-transfer policies and the voluntary provision of public goods," Journal of Public Economics, Elsevier, vol. 39(2), pages 157-176, July.
    14. William Thomson, 1999. "Economies with Public Goods: An Elementary Geometric Exposition," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 1(1), pages 139-176, January.
    15. Boadway, Robin & Song, Zhen & Tremblay, Jean-François, 2011. "The efficiency of voluntary pollution abatement when countries can commit," European Journal of Political Economy, Elsevier, vol. 27(2), pages 352-368, June.
    16. Marc Fleurbaey & Maurice Salles & John A. Weymark (ed.), 2011. "Social Ethics and Normative Economics," Studies in Choice and Welfare, Springer, number 978-3-642-17807-8, December.
    17. Boadway, Robin & Song, Zhen & Tremblay, Jean-Francois, 2007. "Commitment and matching contributions to public goods," Journal of Public Economics, Elsevier, vol. 91(9), pages 1664-1683, September.
    18. Matt Van Essen, 2015. "Bartering Games in the Kolm Triangle," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 17(3), pages 297-310, June.
    19. Danziger, Leif & Schnytzer, Adi, 1991. "Implementing the Lindahl voluntary-exchange mechanism," European Journal of Political Economy, Elsevier, vol. 7(1), pages 55-64, April.
    20. Chander, Parkash, 1993. "Dynamic Procedures and Incentives in Public Good Economies," Econometrica, Econometric Society, vol. 61(6), pages 1341-1354, November.
    21. Josef Falkinger & Johann K. Brunner, 1999. "Taxation in an economy with private provision of public goods," Review of Economic Design, Springer;Society for Economic Design, vol. 4(4), pages 357-379.
    22. Paul Healy, 2010. "Equilibrium participation in public goods allocations," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 27-50, March.
    23. Falkinger, Josef, 1996. "Efficient private provision of public goods by rewarding deviations from average," Journal of Public Economics, Elsevier, vol. 62(3), pages 413-422, November.
    24. Lipnowski, Irwin & Maital, Shlomo, 1983. "Voluntary provision of a pure public good as the game of `chicken'," Journal of Public Economics, Elsevier, vol. 20(3), pages 381-386, April.
    25. Tatsuyoshi Saijo & Takehiko Yamato, 2010. "Fundamental impossibility theorems on voluntary participation in the provision of non-excludable public goods," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 51-73, March.
    26. Bergstrom, Ted, 1989. "Love and Spaghetti, the Opportunity Cost of Virtue," Journal of Economic Perspectives, American Economic Association, vol. 3(2), pages 165-173, Spring.
    27. Schlesinger, Harris, 1989. "On the Analytics of Pure Public Good Provision," Public Finance = Finances publiques, , vol. 44(1), pages 102-109.
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    More about this item

    Keywords

    Public goods; Matching contributions; Pareto optimality; Kolm triangle; Aggregative games; C78; H41;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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