Growth and fluctuations of personal income

Paretoʹs law states that the distribution of personal income obeys a power-law in the high income range. Its dynamical nature has been little studied hitherto, mostly due to the lack of empirical work. Using an exhaustive list of taxpayers in Japan for two consecutive years, when the economy was relatively stable, we report here that the law is a consequence from universal distribution of the growth rate of income and approximate time-reversal symmetry of incomes in the successive years. We also find a relation between positive and negative growth rates that shows good agreement with the data