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The new merger guidelines, issued on June 14, 1982, by the Department of Justice, shift from using the familiar four-firm concentration ratio to the unfamiliar Herfindahl-Hirschman Index (HHI) as a measure or index of market structure. This article explains and interprets HHI, to improve its understanding by members of the antitrust bar. Successive sections: 1. define HHI as the summed, squared market shares of individual firms in the market in percentage form, with an explicit link to the dispersion or variability in the individual market shares and to the number of firms in the market, and with hypothetical examples; 2. interpret HHI as (a) a weighted average of the individual market shares, (b) the numbers equivalent, and (c) one member of a family of related structural indices; 3. give an example of the HHI calculation based on the sales stipulation in the 1975 Gypsum case; 4. discuss the theoretical and empirical bases for HHI, in comparison with other structural measures; and 5. compare CR4 (and its changes) in the 1968 Guidelines with HHI (and its changes) in the 1982 Guidelines for horizontal mergers.

The paper analyses the phenomenon of market concentration in the context of
the most popular industrial organization approaches: the structure-
conduct-performance (SCP) approach and the efficiency hypothesis (EH). The
theory of market concentration evaluation is briefly presented, followed by
an analysis of the main concentration indicators and their application in
recent empirical research. The main problem in the practical application of
the Herfindahl-Hirschman index (HHI) - the necessity to incorporate the
market shares of all the enterprises in the market - is further addressed
and the issue of calculating the minimum value of the HHI is analysed from
the theoretical point of view and by modelling hypothetical markets.

Herfindahl–Hirschman has been one of the renowned techniques for the measurement of market concentration. This article proposes an assessment of concentration with the aid of a matrix termed as a multi-dimensional Herfindahl–Hirschman index for a set of outputs which are possibly categorised under line items. The extant research is aimed to achieve the sole objective of investigating and obtaining a direction vector for augmenting the market share of a firm in a specified manner to strengthen the competitive position. The first eigenvector computed from the normalised non-centred covariance matrix of output set is found to be carrying high degree of explanation of the market concentration. Directional distance additive model (DDAM) is applied to detect the peer firm while replacing the input–output vector of a firm with its vector of market share due to these inputs and outputs. The first eigenvector of the above stated covariance matrix is proved to be a legitimate direction vector which is inherited by the DDAM itself. Benefits of this model is illustrated finally with the aid of an example.