The Herfindahl-Hirschman Index
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The Herfindahl-Hirschman Index (‘HHI’) (also know as
the Herfindahl Index) is a commonly accepted measure of market
concentration. It is calculated as follows, where 
is the market share
of the i’th firm competing in the market (and there are 
such
firms):
The HHI can in principle range from close to zero (very
close to perfect competition, with no one firm having a material market share)
to unity (perfect monopoly). Often the are expressed in
percentage terms, in which case the HHI can range from close to zero to 10,000.
N.B. According to dictionary.reference.com (as at 11 January
2011) the US Department of Justice considers a market with an HHI (using
percentage market shares) of less than 1,000 to be a competitive market place,
one with 1,000 to 1,800 to be a moderately concentrated marketplace and one
resulting in greater than 1,800 a corresponding to a highly concentrated
marketplace.
See also the MnHerfindahlHirschmanIndex
web function.