Laplace transform analysis of a multiplicative asset transfer model
AbstractWe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1004.5169.
Date of creation: Apr 2010
Date of revision:
Publication status: Published in Physica A 389 (2010) 2782-2792
Contact details of provider:
Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-05-08 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- A. Chatterjee & B. K. Chakrabarti, 2007. "Kinetic exchange models for income and wealth distributions," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, Springer, vol. 60(2), pages 135-149, November.
- S. Ispolatov & P.L. Krapivsky & S. Redner, 1998. "Wealth distributions in asset exchange models," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, Springer, vol. 2(2), pages 267-276, March.
- Anirban Chakraborti & Bikas K. Chakrabarti, 2000. "Statistical mechanics of money: How saving propensity affects its distribution," Papers cond-mat/0004256, arXiv.org, revised Jun 2000.
- Marco Patriarca & Anirban Chakraborti & Els Heinsalu & Guido Germano, 2006. "Relaxation in statistical many-agent economy models," Papers physics/0608174, arXiv.org, revised Aug 2008.
- Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
- A. Chakraborti & B.K. Chakrabarti, 2000. "Statistical mechanics of money: how saving propensity affects its distribution," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, Springer, vol. 17(1), pages 167-170, September.
- Angle, John, 2006. "The Inequality Process as a wealth maximizing process," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 367(C), pages 388-414.
- Ali Saif, M. & Gade, Prashant M., 2007. "Emergence of power-law in a market with mixed models," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 384(2), pages 448-456.
- Arnab Chatterjee & Bikas K. Chakrabarti, 2007. "Kinetic Exchange Models for Income and Wealth Distributions," Papers 0709.1543, arXiv.org, revised Nov 2007.
- M. Patriarca & A. Chakraborti & E. Heinsalu & G. Germano, 2007. "Relaxation in statistical many-agent economy models," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, Springer, vol. 57(2), pages 219-224, 05.
- Arnab Chatterjee & Bikas K. Chakrabarti & Robin B. Stinchcombe, 2005. "Master equation for a kinetic model of trading market and its analytic solution," Papers cond-mat/0501413, arXiv.org, revised Aug 2005.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.