Annual change of Pareto index dynamically deduced from the law of detailed quasi-balance

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 quasi-balance. The relation is confirmed in the empirical data nicely.