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”
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.
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.
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.
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.
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.
The authors thank anonymous referees for their very helpful comments, which gave rise to a thorough revision and extension of the original version of the paper.
Buchholz, W., Cornes, R. and Rübbelke, D. (2020), "Matching in the Kolm triangle: interiority and participation constraints of matching equilibria", Journal of Economic Studies, Vol. 47 No. 5, pp. 1039-1050. https://doi.org/10.1108/JES-06-2019-0254
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