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Laplace transform analysis of a multiplicative asset transfer model

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  • Andrey Sokolov
  • Andrew Melatos
  • Tien Kieu

Abstract

We analyze a simple asset transfer model in which the transfer amount is a fixed fraction $f$ of the giver's wealth. The model is analyzed in a new way by Laplace transforming the master equation, solving it analytically and numerically for the steady-state distribution, and exploring the solutions for various values of $f\in(0,1)$. The Laplace transform analysis is superior to agent-based simulations as it does not depend on the number of agents, enabling us to study entropy and inequality in regimes that are costly to address with simulations. We demonstrate that Boltzmann entropy is not a suitable (e.g. non-monotonic) measure of disorder in a multiplicative asset transfer system and suggest an asymmetric stochastic process that is equivalent to the asset transfer model.

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  • Andrey Sokolov & Andrew Melatos & Tien Kieu, 2010. "Laplace transform analysis of a multiplicative asset transfer model," Papers 1004.5169, arXiv.org.
    • Handle: RePEc:arx:papers:1004.5169
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    References listed on IDEAS

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    Cited by:

    1. Diniz, M. & Mendes, F.M., 2012. "Effects of taxation on money distribution," International Review of Financial Analysis, Elsevier, vol. 23(C), pages 81-85.

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