Following the work by Pareto (1897), much attention was focused on the power-law upper tail of income distribution and less on the lower part. In contrast to more complicated functions discussed in the economic literature (Atkinson and Bourguignon, 2000; Champernowne and Cowell, 1998; Kakwani, 1980),
Dr˘agulescu and Yakovenko (2001a) demonstrated that
the lower part of income distribution can be well fitted with the simple exponential function P(r) = c exp(−r/Tr), which is characterized by just one parameter, the “income temperature” Tr. Then Dr˘agulescu and Yakovenko (2001b, 2003) showed that the whole income distribution can be fitted by an exponential function in the lower part and a power-law function in the upper part.
Dr˘agulescu and Yakovenko (2001a) demonstrated that
the lower part of income distribution can be well fitted with the simple exponential function P(r) = c exp(−r/Tr), which is characterized by just one parameter, the “income temperature” Tr. Then Dr˘agulescu and Yakovenko (2001b, 2003) showed that the whole income distribution can be fitted by an exponential function in the lower part and a power-law function in the upper part.
The straight line on the log-linear scale in the inset of Fig. 6 demonstrates the exponential Boltzmann-Gibbs law, and the straight line on the log-log scale in the main panel illustrates the Pareto power law. The fact that income distribution consists of two distinct parts reveals the two-class structure of the American society (Silva and Yakovenko, 2005; Yakovenko and Silva, 2005). Coexistence of the exponential and power-law distributions is also known in plasma physics and astrophysics, where they are called the “thermal” and “superthermal” parts (Collier, 2004; Desai et al., 2003; Hasegawa et al., 1985).