Statistical mechanics of money: how saving propensity affects its distribution
Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Calcutta 700 064, India
Published online: 15 September 2000
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.
PACS: 87.23.Ge – Dynamics of social systems / 05.90.+m – Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems / 89.90.+n – Other topics of general interest to physicists
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000