Colloquium: Statistical mechanics of money, wealth, and income

Abstract

This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by the exponential ("thermal") distribution, whereas a small fraction of the population in the upper class is characterized by the power-law ("superthermal") distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium.Comment: 24 pages, 13 figures; v.2 - minor stylistic changes and updates of references corresponding to the published versio

Inequality measures in kinetic exchange models of wealth distributions

“…The 'economy' is assumed to be a 'closed' one, in the sense that neither the number of agents change nor does that total amount of wealth in the system, and the economic activity is limited to exchange of wealth according to certain rules. The basic model in the framework is just the random sharing of wealth, motivated by random exchange of energy between gas molecules, as in the framework of kinetic theory of gases [6]. The basic money exchange model [21] imitates the kinetic exchange in an ideal gas, but subsequently developed models incorporate the notion of 'savings'.…”

“…Subsequent studies have revealed that the distributions of income and wealth possess some globally robust features (see, e.g., [7]): the bulk of both the income and wealth distributions seem to reasonably fit both the log-normal and the Gamma distributions. Economists have a preference for the log-normal distribution [15,16], while statisticians [17] and physicists [6,18,19] root for the Gamma distribution for the probability density or Gibbs/exponential distribution for the corresponding cumulative distribution. The high end of the distribution, known as the 'tail', is well described by a power law as observed by Pareto.…”

“…Socio-economic inequality often results in crisis, political unrest and instability, conflict, war, criminal activity and finally affects economic growth [5]. Initially, economic inequalities were studied in the context of income and wealth [6][7][8], but the notions and observations have led to widespread research, see e.g. Ref.…”

Distribution of wealth in a network model of the economy

“…[1] Here, we study a network model of the economy proposed by Bouchaud and Mézard (BM). [2] In the mean field (MF) limit of a completely connected network, where any two agents in the network are linked, the model yields the inverse gamma (IGa) stationary wealth distribution.…”

Invariant features of spatial inequality in consumption: The case of India

“…Subsequent studies revealed that the distributions of income and wealth possess a number of fairly robust features: the bulk of both the income and wealth distributions seem to reasonably fit both the log-normal and the Gamma distributions (see, e.g., [6]). Economists prefer the lognormal distribution [10,11], while statisticians [12] and physicists [13][14][15][16][17] emphasize on the Gamma distribution for the probability density or Gibbs/ exponential distribution for the corresponding cumulative distribution. However, the high end of the distribution (known as the 'tail') fits well to a power law as observed by Pareto, the exponent known as the Pareto exponent, usually ranging between 1 and 3 (see e.g.…”