“ Thermal ” and “ superthermal ” two - class structure of the personal income distribution

– We show that income distribution in the USA has a well-defined two-class structure. The majority of population (97–99%) belongs to the lower class characterized by the exponential Boltzmann-Gibbs (“thermal”) distribution. The upper class (1–3% of population) has a Pareto power-law (“superthermal”) distribution, whose parameters change in time with the rise and fall of stock market. We also discuss the concept of equilibrium inequality in a society, based on the principle of maximal entropy, and quantitatively show that it applies to the majority of population. Attempts to apply the methods of exact sciences, such as physics, to describe a society have a long history [1]. At the end of the 19th century, Italian physicist, engineer, economist and sociologist Vilfredo Pareto suggested that income distribution in a society is described by a power law [2]. Modern data indeed confirm that the upper tail of income distribution follows the Pareto law [3–6]. However, the majority of population does not belong there, so characterization and understanding of their income distribution remains an open problem. Drăgulescu and Yakovenko [7] proposed that the equilibrium distribution should follow an exponential law analogous to the Boltzmann-Gibbs distribution of energy in statistical physics. The first factual evidence for the exponential distribution of income was found in Ref. [8]. Coexistence of the exponential and power-law parts of the distribution was recognized in Ref. [9]. However, these papers, as well as Ref. [10], studied the data only for a particular year. Here we analyze income distribution in the USA for the period of 1983–2001. We show that the US society has a well-defined two-class structure. The majority of population (97–99%) belongs to the lower class and has a very stable in time exponential (“thermal”) distribution of income. The upper class (1–3% of population) has a power-law (“superthermal”) distribution, whose parameters significantly change in time with the rise and fall of stock market. We discuss the concept of equilibrium inequality in a society, based on the principle of maximal entropy, and quantitatively show that it applies to the bulk of population. Most of academic and government literature on income distribution and inequality [11–14] does not attempt to fit the data by a simple formula. When fits are performed, usually the log-normal distribution [15] is used for the lower part of the distribution [4, 6]. Only recently the idea of the exponential distribution started to penetrate into income studies [16,17], and agent-based economic models showing formation of two classes started to appear [18].