An axiomatic characterization of a generalized index of concentration

✍ Scribed by Satya R. Chakravarty; Wolfgang Eichhorn

• Publisher: Springer
• Year: 1991
• Tongue: English
• Weight: 492 KB
• Volume: 2
• Category: Article
• ISSN: 0895-562X
• DOI: 10.1007/bf00156341

✦ Synopsis

The Hannah-Kay [1977] generalized concentration index contains the well-known Herfindahl [1950]-Hirschman [1945] and the entropy indices as particular cases. In this papaer we show that the Hannah-Kay class can be regarded as a particular member of a generalized family of indices, which we refer to as self-weighted quasilinear means. We then show that among all self-weighted quasilinear means the Hannah-Kay family is the only class of concentration indices which satisfies the replication principle, a requirement which states that an m-fold replication of the industry, firm by firm, will multiply the concentration index by the factor 1/m.