Wealth condensation in a simple model of economy

By Jean-Philippe Bouchaud, M. M'ezard. 2000

528 citations recorded by the source corpus.

We introduce a simple model of economy, where the time evolution is described by an equation capturing both exchange between individuals and random speculative trading, in such a way that the fundamental symmetry of the economy under an arbitrary change of monetary units is insured. We investigate a mean-field limit of this equation and show that the distribution of wealth is of the Pareto (power-law) type. The Pareto behaviour of the tails of this distribution appears to be robust for finite range models, as shown using both a mapping to the random ‘directed polymer’ problem, as well as numerical simulations. In this context, a phase transition between an economy dominated by a few individuals and a situation where the wealth is more evenly spread out, is found. An interesting outcome is that the distribution of wealth tends to be very broadly distributed when exchanges are limited, either in amplitude or topologically. Favouring exchanges (and, less surprisingly, increasing taxes) seems to be an efficient way to reduce inequalities.

Subfields: Condensed Matter Physics, Economics and Econometrics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b85525b51b7eb5cbedb26a64c68daf9d09f23460

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

In Economics and Econometrics

In Mathematical Physics

Citations in the corpus

Evolution of networks (2001, background): “It was shown [229,230] that the average wealth w(t) approaches a fixed value w at long times, and these equations produce the following stationary distribution”
The statistical physics of cities (2019, background): “In the mean-field limit in which all cities are exchanging individuals with each other (J+8 = J/N, N the number of cities), the stationary distribution ρ of the normalized population w@ = P@/P (P the average population) is [23]”
Growth and fluctuations of personal income (2002, background): “a boundary eﬀect that income should not be less than a value, and derived a power-law distribution [9, 10]. Another approach is to construct a simple but minimal economic model in a network of wealth [13]. Actually there have been proposed many kinds of scenarios [23] which predict a power-law distr”
Fokker–Planck equations in the modeling of socio-economic phenomena (2017, background): “18) has a unique stationary solution of unit mass, given by the Γ-like distribution [18, 36]”
On Steady Distributions of Kinetic Models of Conservative Economies (2008, methodology): “The same Fokker-Planck equation was obtained in [7] as the mean field limit of a stochastic dynamical equation, as well as in [46, 33] in”
Econophysics: Empirical facts and agent-based models (2009, unknown): “Other models describing wealth exchange have been formulated using matrix theory (Gupta (2006)), the master equation (Bouchaud and Mezard (2000); Dragulescu and Yakovenko (2000); Ferrero (2004)), the Boltzmann equation approach (Dragulescu and Yakovenko (2000); Slanina (2004); Repetowicz et al.…”
Kinetic models of conservative economies with wealth redistribution (2009, background): “9) is the Laplace transform of the generalized Γdistribution [4, 11]”
Econophysics review: II. Agent-based models (2011, unknown): “(2007), Bouchaud et al. (2009), Lux and Westerhoff (2009), Yakovenko and Rosser (2009), etc.”