Dependence of Distribution and Velocity of Money on Required Reserve Ratio

Abstract

The impacts of money creation on the statistical mechanics of money circulation were investigated by focusing on the dependence of monetary wealth distribution and the velocity of money on the required reserve ratio in this paper. In reality, money creation is important to economic system. The process of money creation can be represented by the multiplier model of money in traditional economics. From this model, it can be known that the required reserve ratio set by the central bank is one of the main determinants of the monetary aggregate and under some assumptions the monetary aggregate can be expressed as the product of the monetary base and the required reserve ratio in steady state. Taking the role that the required reserve ratio plays in the monetary system into account, we developed a random transfer model by introducing a fractional reserve banking system and carried out some simulations to observe how the monetary aggregate evolves over time, how monetary wealth is distributed among agents, as well as how fast money is transferred in the transferring process. Monetary wealth is found to follow asymmetric Laplace distribution, and the fact that latency time of money follows exponential distribution indicates that the transferring process is Poisson type. The theoretical formulas of monetary wealth distribution and the velocity of money in terms of the required reserve ratio are given respectively which are in a good agreement with the simulation results.