The authors propose a new method for estimating the power-law exponents of firm size variables. Their focus is on how to empirically identify a range in which a firm size variable follows a power-law distribution. On the one hand, as is well known a firm size variable follows a power-law...

We start from Gibrat’s law and quasi-inversion symmetry for three firm size variables (i.e., tangible fixed assets K, number of employees L, and sales Y) and derive a partial differential equation to be satisfied by the joint probability density function of K and L.We then transform K and L,...

The authors propose a new method for estimating the power-law exponents of firm size variables. Their focus is on how to empirically identify a range in which a firm size variable follows a power-law distribution. On the one hand, as is well known a firm size variable follows a power-law...

We propose a new method for estimating the power-law exponent of a firm size variable, such as annual sales. Our focus is on how to empirically identify a range in which a firm size variable follows a power-law distribution. As is well known, a firm size variable follows a power-law distribution...

We discuss a mechanism through which inversion symmetry (i.e., invariance of a joint probability density function under the exchange of variables) and Gibrat’s law generate power-law distributions with different tail exponents. Using a dataset of firm size variables, that is, tangible fixed...

Employing data on the assessed value of land in 1983–2005 Japan, we investigate the dynamical behavior in the high scale region of non-equilibrium systems. From the detailed quasi-balance and Gibrat's law, we derive a relation between the change of Pareto index and a symmetry in the detailed...

In order to understand the characteristics common to distributions which have both fractal and non-fractal scale regions in a unified framework, we introduce the concept of a typical scale. We employ a model of 2d gravity modified by the R2 term as a tool to understand such distributions through...

We discuss a mechanism through which inversion symmetry (i.e., invariance of a joint probability density function under the exchange of variables) and Gibrat’s law generate power-law distributions with different tail exponents. Using a dataset of firm size variables, that is, tangible fixed...

In order to study the phenomenon in detail that income distribution follows Pareto law, we analyze the database of high income companies in Japan. We find a quantitative relation between the average capital of the companies and the Pareto index. The larger the average capital becomes, the...

Employing profits data of Japanese companies in 2002 and 2003, we confirm that Pareto's law and the Pareto index are derived from the law of detailed balance and Gibrat's law. The last two laws are observed beyond the region where Pareto's law holds. By classifying companies into job categories,...