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Absolute And Relative Measures Of Concentration Reconsidered

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  • Christian Marfels

Abstract

Frequent controversies on the mathematical consistency and the economic significance of measures of concentration suggest an analysis of the principles of concentration measurement. The well‐known division in concentration measures and inequality measures is formalized with a catalogue of desirable properties of these measures. This way, a qualifying concentration measure corresponds to an inequality measure, and vice versa. The discussion of some concentration measures shows the superiority of the entropy measure because of its axiomatic foundation. However, antitrust authorities may prefer simpler measures such as the recently proposed ‘comprehensive concentration index’ and the ‘concentration ratios’ to observe concentrated industries. On the other hand, the entropy measure should be applied for a more detailed analysis of the dynamics of economic concentration. Häufige Kontroversen über mathematische Konsistenz von Konzentrationsmassen und deren ökonomische Bedeutung und Anwendbarkeit werfen Fragen nach den Grundlagen der Konzentrationsmessung suf. Die bekannte Einteilung in « eigentliche » Konzentrationsmasse und Disparitätsmasse wird mit Hilfe eines Kataloges wünschenswerter Eigenschaften dieser Masse formalisiert. Ein in dieser Hinsicht qualifiziertes Konzentrationsmass erlaubt die Herleitung eines entsprechenden Disparitatsmasses und umgekehrt. Die Diskussion einiger Konzentrationsmasse zeigt die Überlegenheit des Entropiemasses auf Grund seiner axiomatischen Fundierung. Eingedenk der ökonomischen Zielsetzung der Konzentrationsmessung sind jedoch einfacherc Masse wie der kürzlich vorgeschlagene «comprehensive concentration index» oder die «concentration ratios» durchaus als nützliche Instrumente fur die Kartellbehörden anzusehen, sofern es sich um Beobachtungen oligopolistischer Marktstrukturen handelt. Für eingehendere Analysen des Konzentrationsprozesses wird sich die Anwendung des Entropiemasses empfehlen. Des controverses fréquentes en ce qui concerne la consistance mathématique et la signification économique des mesures de concentration suggèrent une analyse des principes de ces mêmes mesures. La division bien connue dans le domaine des mesures de concentration et des mesures de disparité prend forme avec le catalogue des propriétés souhaitées de ces mêmes mesures. Ainsi, une mesure qualificative de concentration correspond à une mesure de disparité, et vice versa. La discussion relative à certaines mesures de concentration permet de conclure à la supériorité de la mesure entropique du fait de son fondement axiomatique. Cependant, les autorités anti‐trust préféreraient des unités de mesure plus simples ainsi que les proposent récemment le comprehensive Concentration index et les concentration ratios afin de pouvoir observer les grandes unités industrielles. D'autre part, la mesure entropique devrait être utilisée pour une analyse plus détaillée de la dynamique de concentration économique.

Suggested Citation

  • Christian Marfels, 1971. "Absolute And Relative Measures Of Concentration Reconsidered," Kyklos, Wiley Blackwell, vol. 24(4), pages 753-766, November.
    • Handle: RePEc:bla:kyklos:v:24:y:1971:i:4:p:753-766
    DOI: 10.1111/j.1467-6435.1971.tb00631.x
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    Cited by:

    1. Paul Latreille & James Mackley, 2011. "Using Excel to Illustrate Hannah and Kay's Concentration Axioms," International Review of Economic Education, Economics Network, University of Bristol, vol. 10(1), pages 117-127.
    2. Daniel F. Leach, 1997. "Concentration‐Profits Monopoly Vs. Efficiency Debate: South African Evidence," Contemporary Economic Policy, Western Economic Association International, vol. 15(2), pages 12-23, April.
    3. Oscar Bajo & Rafael Salas, 2002. "Inequality foundations of concentration measures: An application to the Hannah-Kay indices," Spanish Economic Review, Springer;Spanish Economic Association, vol. 4(4), pages 311-316.
    4. Dilip B. Madan & King Wang, 2023. "Measuring Dependence in a Set of Asset Returns," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 30(2), pages 363-385, June.
    5. P. Owen & Michael Ryan & Clayton Weatherston, 2007. "Measuring Competitive Balance in Professional Team Sports Using the Herfindahl-Hirschman Index," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 31(4), pages 289-302, December.
    6. Stark, Oded, 1978. "Economic-Demographic Interactions in Agricultural Development: The Case of Rural-to-Urban Migration," EconStor Books, ZBW - Leibniz Information Centre for Economics, volume 6, number 232285, September.
    7. Jean-Pascal Simonin, 1980. "Indices de concentration, pouvoir de monopole et variations conjecturales : quelques extensions," Revue Économique, Programme National Persée, vol. 31(1), pages 121-135.
    8. Guglielmo D’Amico & Giuseppe Di Biase & Raimondo Manca, 2011. "Immigration Effects On Economic Systems Through Dynamic Inequality Indices," Global Journal of Business Research, The Institute for Business and Finance Research, vol. 5(5), pages 11-25.

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