Statistical mechanics of money: how saving propensity affects its distribution

Abstract

We consider a simple model of a closed economic system where the total money is conserved and the number of economic agents is fixed. Analogous to statistical systems in equilibrium, money and the average money per economic agent are equivalent to energy and temperature, respectively. We investigate the effect of the saving propensity of the agents on the stationary or equilibrium probability distribution of money. When the agents do not save, the equilibrium money distribution becomes the usual Gibb's distribution, characteristic of non-interacting agents. However with saving, even for individual self-interest, the dynamics becomes cooperative and the resulting asymmetric Gaussian-like stationary distribution acquires global ordering properties. Intriguing singularities are observed in the stationary money distribution in the market, as functions of the marginal saving propensity of the agents.

Inelastically scattering particles and wealth distribution in an open economy

“…This finding was interpreted as a result of a conservation law for total wealth, leading to the robust Boltzmann-like exponential distribution, whatever the random wealth exchange be, in full analogy with the energy distribution in a gas of elastically scattering molecules. This, together with older studies within the same spirit [43], lead to the view of economic activity as a scattering process of agents, analogous to inelastically scattering particles [29,30,31,44,45,46,47]. Indeed, the inelasticity is indispensable to explain the power-law tail and it is also reasonable to suppose that the total wealth increases on average.…”

“…Both of these schemes are formalized by a kinetic equation describing the exchange of wealth between agents and global redistribution of wealth which plays the role of repelling from zero. Related approaches were subsequently pursued by a number of studies and simulations [24,25,26,27,28,29,30,31,32,33,34,35, * Electronic address: slanina@fzu.cz 36,37,38,39,40].…”

Pareto and Boltzmann–Gibbs behaviors in a deterministic multi-agent system

“…Analysis of real economic data from U.K. and U.S.A. [6] has shown that one phase possesses an exponential or Boltzmann-Gibbs probability distribution that involves about 95% of individuals, mainly those with low and medium wealths, and that the other phase, consisting of the the 5% of individuals with highest wealths, shows a power law distribution or Pareto behavior. Several economic models based on diverse probabilistic mechanisms for interaction between agents have been proposed in order to reproduce these types of statistical behavior [7,8,9,10,11]. However, in most cases, both classes of distributions do not appear in a simple model; changes in the interaction rules between agents are required in order to obtain either type of behavior.…”

Recent Advances in Opinion Modeling: Control and Social Influence

“…Resembling the model for wealth exchange in a multi-agent society introduced in [38], this new model has an additional parameter to quantify the personal conviction, representing a measure of the influencing ability of individuals [31]. Individuals with high conviction are resistant to change opinion, and have a prominent role in attracting other individuals towards their opinions.…”