Pareto index induced from the scale of companies

Employing profits data of Japanese companies in 2002 and 2003, we confirm that Paretoʹs law and the Pareto index are derived from the law of detailed balance and Gibratʹs law. The last two laws are observed beyond the region where Paretoʹs law holds. By classifying companies into job categories, we find that companies in a small-scale job category have more possibilities of growing than those in a large-scale job category. This kinematically explains that the Pareto index for the companies in the small-scale job class is larger than that for the companies in the large-scale job class.