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Analyzing money distributions in `ideal gas' models of markets

Arnab Chatterjee·Bikas K. Chakrabarti·Robin B. Stinchcombe
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Abstract

We analyze an ideal gas like models of a trading market. We propose a new fit for the money distribution in the fixed or uniform saving market. For the marketwith quenched random saving factors for its agents we show that the steady state income ($m$) distribution $P(m)$ in the model has a power law tail with Pareto index $ν$ exactly equal to unity, confirming the earlier numerical studies on this model. We analyze the distribution of mutual money difference and also develop a master equation for the time development of $P(m)$. Precise solutions are then obtained in some special cases.

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Arnab Chatterjee, Bikas K. Chakrabarti, Robin B. Stinchcombe. 2005-05-06. Analyzing money distributions in `ideal gas' models of markets. https://arxiv.org/abs/physics/0505047

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