The equivalent share of a dominant firm: an approach based on distances

ABSTRACT

The concept of concentration has been widely used in social sciences and applied to different areas, particularly industrial economics, business, sports economics or political science. We construct a new family of concentration indices, based on the mathematical concept of distance. By construction, its value is the monopoly ratio. It complies with the set of properties traditionally required at concentration indices. The index can be interpreted like the equivalent share of the dominant firm in a distribution with many elements in which all the others firms are of an equal size. Our index solves the problems linked to the limited cardinality of the majority of the existing indices. Cardinality property may be relevant in modelling and political economic decisions.

KEYWORDS:

• Concentration
• Euclidean distance
• distance to competitive balance index
• equivalent share of a dominant firm

JEL Classification:

• L11
• L41

Acknowledgments

We are grateful to Rosario Gómez and José M. Ordoñez from the University of Málaga for their useful comments on previous versions of the article.

Disclosure statement

Authors declare that we have no conflict of interest.

Additional information

Funding

This work was supported by the Secretaría de Estado de Investigación, Desarrollo e Innovación (Spain) [ECO2017-86245-P].