Laplace transform analysis of a multiplicative asset transfer model

Andrey Sokolov, Andrew Melatos and Tien Kieu

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 14, 2782-2792

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∈(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.

Keywords: Wealth distribution; Master equation; Laplace transform; Boltzmann entropy (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:14:p:2782-2792

DOI: 10.1016/j.physa.2010.02.045

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