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Transfer potentials shape and equilibrate monetary systems

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  • Fischer, Robert
  • Braun, Dieter

Abstract

We analyze a monetary system of random money transfer on the basis of double entry bookkeeping. Without boundary conditions, we do not reach a price equilibrium and violate text-book formulas of economist's quantity theory (MV=PQ). To match the resulting quantity of money with the model assumption of a constant price, we have to impose boundary conditions. They either restrict specific transfers globally or impose transfers locally. Both connect through a general framework of transfer potentials. We show that either restricted or imposed transfers can shape Gaussian, tent-shape exponential, Boltzmann-exponential, pareto or periodic equilibrium distributions. We derive the master equation and find its general time-dependent approximate solution. An equivalent of quantity theory for random money transfer under the boundary conditions of transfer potentials is given.

Suggested Citation

  • Fischer, Robert & Braun, Dieter, 2003. "Transfer potentials shape and equilibrate monetary systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(3), pages 605-618.
    • Handle: RePEc:eee:phsmap:v:321:y:2003:i:3:p:605-618
    DOI: 10.1016/S0378-4371(02)01746-6
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    Citations

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    Cited by:

    1. Aktaev, Nurken E. & Bannova, K.A., 2022. "Mathematical modeling of probability distribution of money by means of potential formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    2. Fischer, Robert & Braun, Dieter, 2003. "Nontrivial bookkeeping: a mechanical perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 266-271.
    3. Braun, Dieter, 2006. "Nonequilibrium thermodynamics of wealth condensation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 714-722.
    4. Victor M. Yakovenko, 2007. "Econophysics, Statistical Mechanics Approach to," Papers 0709.3662, arXiv.org, revised Aug 2008.
    5. Yougui Wang & Ning Ding & Ning Xi, 2005. "Prospects for Money Transfer Models," Papers physics/0507161, arXiv.org.
    6. Stein, Julian Alexander Cornelius & Braun, Dieter, 2019. "Stability of a time-homogeneous system of money and antimoney in an agent-based random economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 232-249.

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