# Rosenbluth index

The Rosenbluth Index (also Rosenbluth concentration coefficient ) is an index for the absolute concentration on markets. It is a statistical measure of concentration .

It is used to measure the concentration (or unequal distribution) of n market participants , who each have a market share h i and a rank i (ordered according to decreasing market shares) . The Rosenbluth index is based on a graphic representation of the market shares: the market participants are entered on the X-axis (sorted in decreasing order of size), the market shares for the first, the first two, the first three (etc. .) Market participants. The result is a curve of market shares from zero to 1 (100 percent).

The Rosenbluth Index is defined as:

${\ displaystyle K_ {R} = {\ frac {1} {2A}} = {\ frac {1} {2 \ left (\ sum _ {i = 1} ^ {n} ih_ {i} \ right) - 1}}}$

Here, h i is the frequency of the respective expression; i the rank of the feature bearer; A is the area above the concentration curve; since it is 0.5 for a single market participant (monopoly, 100%) - the curve halves the square from (0 | 0) to (1 | 1) - the area is multiplied by 2; at a maximum concentration (monopoly, complete inequality) the Rosenbluth index is therefore 1. At a minimum concentration (egalitarian distribution) the Rosenbluth index is 1 / n .

## literature

• Rosenbluth, G. (1955): Measures of Concentration . In: GJ Stigler (ed.): Business Concentration and Price Policy by National Bureau of Economic Research . Princeton: Princeton University Press
• Rosenbluth, G. (1957): Concentration in Canadian Manufacturing Industries . Princeton: Princeton University Press