Power-law Distributions in Circulating Money: Effect of Preferential Behavior

Empirical studies on many social issues show that numerous statistical distributions follow power laws, such as stock-price fluctuations, the probability distribution of the population of cities, the degree distributions in many networks and distribution of income or wealth. In particular, the wealth distribution which is an old topic has recently been renewed by a small band of econophysicists. They proposed multi-agent interaction models to explore the mechanism of wealth distribution, in which wealth is simply represented by money. However, to our knowledge, the simulation results of these works show that the steady states of money have Gibbs or Gamma distributions, leaving the power-law phenomena of wealth distribution unexplained. It has been shown that preferential behavior assumption plays an essential role in generating power-law distributions in some cases, such as in networks and in money dynamics. The soul of preferential assumption is to break the equality among agents, some of which are entitled to more power in getting corresponding entity. In this paper, we investigate how the individual preferential behavior generates power law phenomena in money circulation process. The statistical distributions involved in monetary circulation are composed of two aspects. One is over the time interval the money stays in agents’ hands which is named as holding time, the other is over the amount of money held by agents.