Kinetic exchange models for income and wealth distributions

Abstract

Abstract. Increasingly, a huge amount of statistics have been gathered which clearly indicates that income and wealth distributions in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas in equilibrium. However, it also deviates in the low income and more significantly for the high income ranges. Application of physics models provides illuminating ideas and understanding, complementing the observations.

Inequality measures in kinetic exchange models of wealth distributions

“…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.…”

“…The crossover point m c is extracted from the numerical fittings. One of the key class of models uses the kinetic theory of gases [21], where the gas molecules colliding and exchanging energy was mapped to agents meeting to exchange wealth, following certain rules [19]. In these models, a pair of agents agree to trade, each save a fraction λ of their instantaneous money/wealth and exchanges a random fraction of the rest at each trading step.…”

“…To obtain the power law distribution of wealth for the richest, one needs simply to consider each agent as different in terms of the fraction of wealth he/she saves in each trading [24], which is very natural to assume, because it is quite likely that agents in a market think differently from one another. With this very little modification, one can explain the whole range of wealth distribution [19]. When λ is distributed uniformly in [0, 1) and quenched, (CCM model hereafter), i.e., for heterogeneous agents, one obtains a Pareto law for the probability density of wealth P (m) ∼ m −ν with exponent ν = 2 [19,24].…”

“…With this very little modification, one can explain the whole range of wealth distribution [19]. When λ is distributed uniformly in [0, 1) and quenched, (CCM model hereafter), i.e., for heterogeneous agents, one obtains a Pareto law for the probability density of wealth P (m) ∼ m −ν with exponent ν = 2 [19,24]. Several variants of these models, find possible applications in a variety of trading processes [7,25].…”

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.…”