Breakdown of the mean-field approximation in a wealth distribution model
arXiv:0809.4139 · doi:10.1088/1742-5468/2009/02/P02014
Abstract
One of the key socioeconomic phenomena to explain is the distribution of wealth. Bouchaud and Mézard have proposed an interesting model of economy [Bouchaud and Mézard (2000)] based on trade and investments of agents. In the mean-field approximation, the model produces a stationary wealth distribution with a power-law tail. In this paper we examine characteristic time scales of the model and show that for any finite number of agents, the validity of the mean-field result is time-limited and the model in fact has no stationary wealth distribution. Further analysis suggests that for heterogeneous agents, the limitations are even stronger. We conclude with general implications of the presented results.
11 pages, 3 figures
References in corpus (16)
- Power laws, Pareto distributions and Zipf's law
- Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States
- Statistical mechanics of money
- Wealth Distributions in Models of Capital Exchange
- Multiplicative processes and power laws
- Inelastically scattering particles and wealth distribution in an open economy
- Kinetic Exchange Models for Income and Wealth Distributions
- Power Laws of Wealth, Market Order Volumes and Market Returns
- Evidence for Power-law tail of the Wealth Distribution in India
- Numerical schemes for continuum models of reaction-diffusion systems subject to internal noise
- Effects of network topology on wealth distributions
- Wealth Dynamics on Complex Networks
- Mean-field limit of systems with multiplicative noise
- Finite market size as a source of extreme wealth inequality and market instability
- Critical Behaviour of Non-Equilibrium Phase Transitions to Magnetically Ordered States
- Size limiting in Tsallis statistics
Cited by in corpus (5)
- On growth-optimal tax rates and the issue of wealth inequalities
- Redistribution spurs growth by using a portfolio effect on human capital
- Power-law exponent of the Bouchaud-Mézard model on regular random network
- On absence of steady state in the Bouchaud-Mézard network model
- Anomaly, class division, and decoupling in income dynamics