Pareto law and Pareto index in income distribution of Japanese companies

In order to study phenomenon in detail that income distribution follows Pareto law, we analyze database of high income companies in Japan. We find a quantitative relation between average capital of the companies and the Pareto index, that the average capital becomes larger the Pareto index becomes smaller. From this relation, we point out a possibility we can explain that Pareto index of company income distribution changes hardly, while Pareto index of personal income distribution changes sharply, from a viewpoint of capital (or means). We also find a quantitative relation between lower bound of capital and the typical scale at which Pareto law breaks, that the lower bound of capital becomes larger the typical scale becomes larger. From this result, the reason there is (no) typical scale at which Pareto law breaks in the income distribution can be understood through (no) constraint, such as the lower bound of capital of companies or means, in the financial system.