Entropy and Other Measures of Concentration

Abstract

In recent years, economists have begun to use the entropy, or redundancy, of a size distribution to measure the extent to which business is concentrated in the control of giant firms. This paper compares these new measures derived from information theory with the classical statistical measures of dispersion and with traditional measures of business concentration derived from the cumulative concentration curve. It shows that when the number of firms is large enough to use statistical distribution theory, the classical statistical measures are superior to the entropy or the redundancy. When the number of firms is small, the entropy is superior to the redundancy, but both are inferior to the traditional measures of concentration derived from the cumulative concentration curve. Consequently, there is little point in using the information theory measures to measure business concentration.