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Kinetic exchange models of markets

January 07, 2023

Kinetic exchange models are multi-agent dynamic models inspired by the statistical physics of energy distribution, which try to explain the robust and universal features of income/wealth distributions.

Understanding the distributions of income and wealth in an economy has been a classic problem in economics for more than a hundred years. Today it is one of the main branches of econophysics.

Data and basic tools

In 1897, Vilfredo Pareto first found a universal feature in the distribution of wealth. After that, with some notable exceptions, this field had been dormant for many decades, although accurate data had been accumulated over this period. Considerable investigations with the real data during the last fifteen years (1995–2010) revealed[1] that the tail (typically 5 to 10 percent of agents in any country) of the income/wealth distribution indeed follows a power law. However, the majority of the population (i.e., the low-income population) follows a different distribution which is debated to be either Gibbs or log-normal.

Basic tools used in this type of modelling are probabilistic and statistical methods mostly taken from the kinetic theory of statistical physics. Monte Carlo simulations often come handy in solving these models.

Overview of the models

Since the distributions of income/wealth are the results of the interaction among many heterogeneous agents, there is an analogy with statistical mechanics, where many particles interact. This similarity was noted by Meghnad Saha and B. N. Srivastava in 1931[2] and thirty years later by Benoit Mandelbrot.[3] In 1986, an elementary version of the stochastic exchange model was first proposed by J. Angle.[4]

In the context of kinetic theory of gases, such an exchange model was first investigated by A. Dragulescu and V. Yakovenko.[5][6] The main modelling effort has been put to introduce the concepts of savings,[7][8] and taxation[9] in the setting of an ideal gas-like system. Basically, it assumes that in the short-run, an economy remains conserved in terms of income/wealth; therefore law of conservation for income/wealth can be applied. Millions of such conservative transactions lead to a steady state distribution of money (gamma function-like in the Chakraborti-Chakrabarti model with uniform savings,[7] and a gamma-like bulk distribution ending with a Pareto tail[10] in the Chatterjee-Chakrabarti-Manna model with distributed savings[8]) and the distribution converges to it. The distributions derived thus have close resemblance with those found in empirical cases of income/wealth distributions.

Though this theory had been originally derived from the entropy maximization principle of statistical mechanics, it had been shown by A. S. Chakrabarti and B. K. Chakrabarti [11] that the same could be derived from the utility maximization principle as well, following a standard exchange-model with Cobb-Douglas utility function. Recently it has been shown [12] that an extension of the Cobb-Douglas utility function (in the above-mentioned Chakrabarti-Chakrabarti formulation) by adding a production savings factor leads to the desired feature of growth of the economy in conformity with some earlier phenomenologically established growth laws in the economics literature. The exact distributions produced by this class of kinetic models are known only in certain limits and extensive investigations have been made on the mathematical structures of this class of models.[13][14] The general forms have not been derived so far.

Criticisms

This class of models has attracted criticisms from many dimensions.[15] It has been debated for long whether the distributions derived from these models are representing the income distributions or wealth distributions. The law of conservation for income/wealth has also been a subject of criticism.

See also

References

  1. ^ Chatterjee, A.; Yarlagadda, S.; Chakrabarti, B.K. (2005). Econophysics of Wealth Distributions. Springer-Verlag (Milan).
  2. ^ Saha, M.; Srivastava, B.N. (1931). A Treatise on Heat. Indian Press (Allahabad). p. 105. (the page is reproduced in Fig. 6 in Sitabhra Sinha, Bikas K Chakrabarti, Towards a physics of economics, Physics News 39(2) 33-46, April 2009)
  3. ^ Mandelbrot, B.B. (1960). "The Pareto-Levy law and the distribution of income". International Economic Review. 1 (2): 79–106. doi:10.2307/2525289. JSTOR 2525289.
  4. ^ Angle, J. (1986). "The surplus theory of social stratification and the size distribution of personal wealth". Social Forces. 65 (2): 293–326. doi:10.2307/2578675. JSTOR 2578675.
  5. ^ Dragulescu, A.; Yakovenko, V. (2000). "The statistical mechanics of money". European Physical Journal B. 17 (4): 723–729. arXiv:cond-mat/0001432. Bibcode:2000EPJB...17..723D. doi:10.1007/s100510070114. S2CID 16158313.
  6. ^ Garibaldi, U.; Scalas, E.; Viarenga, P. (2007). "Statistical equilibrium in exchange games". European Physical Journal B. 60 (2): 241–246. Bibcode:2007EPJB...60..241G. doi:10.1140/epjb/e2007-00338-5. S2CID 119517302.
  7. ^ a b Chakraborti, A.; Chakrabarti, B.K. (2000). "Statistical mechanics of money: how savings propensity affects its distribution". European Physical Journal B. 17 (1): 167–170. arXiv:cond-mat/0004256. Bibcode:2000EPJB...17..167C. doi:10.1007/s100510070173. S2CID 5138071.
  8. ^ a b Chatterjee, A.; Chakrabarti, B.K.; Manna, K.S.S. (2004). "Pareto law in a kinetic model of market with random saving propensity". Physica A. 335 (1–2): 155–163. arXiv:cond-mat/0301289. Bibcode:2004PhyA..335..155C. doi:10.1016/j.physa.2003.11.014. S2CID 120904131.
  9. ^ Guala, S. (2009). "Taxes in a simple wealth distribution model by inelastically scattering particles". Interdisciplinary Description of Complex Systems. 7 (1): 1–7. arXiv:0807.4484. Bibcode:2008arXiv0807.4484G.
  10. ^ Chakraborti, A.; Patriarca, M. (2009). "Variational Principle for the Pareto Power Law". Physical Review Letters. 103 (22): 228701. arXiv:cond-mat/0605325. Bibcode:2009PhRvL.103v8701C. doi:10.1103/PhysRevLett.103.228701. PMID 20366128. S2CID 909820.
  11. ^ A. S. Chakrabarti; B. K. Chakrabarti (2009). "Microeconomics of the ideal gas like market models". Physica A. 388 (19): 4151–4158. arXiv:0905.3972. Bibcode:2009PhyA..388.4151C. doi:10.1016/j.physa.2009.06.038. S2CID 14908064.
  12. ^ D. S. Quevedo; C. J. Quimbay (2020). "Non-conservative kinetic model of wealth exchange with saving of production". European Physical Journal B. 93 (10): 186. Bibcode:2020EPJB...93..186Q. doi:10.1140/epjb/e2020-10193-3. S2CID 224849350.
  13. ^ During, B.; Matthes, D.; Toscani, G. (2008). "Kinetic equations modelling wealth distributions: a comparison of approaches" (PDF). Physical Review E. 78 (5): 056103. Bibcode:2008PhRvE..78e6103D. doi:10.1103/physreve.78.056103. PMID 19113186.
  14. ^ Cordier, S.; Pareschi, L.; Toscani, G. (2005). "On a kinetic model for a simple market economy". Journal of Statistical Physics. 120 (1–2): 253–277. arXiv:math/0412429. Bibcode:2005JSP...120..253C. doi:10.1007/s10955-005-5456-0. S2CID 10218909.
  15. ^ Mauro Gallegati, Steve Keen, Thomas Lux and Paul Ormerod (2006). "Worrying Trends in Econophysics". Physica A. 371 (1): 1–6. Bibcode:2006PhyA..370....1G. doi:10.1016/j.physa.2006.04.029.{{cite journal}}: CS1 maint: multiple names: authors list (link)

Further reading

  • Brian Hayes, Follow the money, American Scientist, 90:400-405 (Sept.-Oct.,2002)
  • Jenny Hogan, There's only one rule for rich, New Scientist, 6-7 (12 March 2005)
  • Peter Markowich, Applied Partial Differential Equations, Springer-Verlag (Berlin, 2007)
  • Arnab Chatterjee, Bikas K Chakrabarti, Kinetic exchange models for income and wealth distribution, European Physical Journal B, 60:135-149(2007)
  • Victor Yakovenko, J. B. Rosser, Colloquium: statistical mechanics of money, wealth and income, Reviews of Modern Physics 81:1703-1725 (2009)
  • Thomas Lux, F. Westerhoff, Economics crisis, Nature Physics, 5:2 (2009)
  • Sitabhra Sinha, Bikas K Chakrabarti, Towards a physics of economics, Physics News 39(2) 33-46 (April 2009)
  • Stephen Battersby, The physics of our finances, New Scientist, p. 41 (28 July 2012)
  • Bikas K Chakrabarti, Anirban Chakraborti, Satya R Chakravarty, Arnab Chatterjee, Econophysics of Income & Wealth Distributions, Cambridge University Press (Cambridge 2013).
  • Lorenzo Pareschi and Giuseppe Toscani, Interacting Multiagent Systems: Kinetic equations and Monte Carlo methods Oxford University Press (Oxford 2013)
  • Kishore Chandra Dash, "Story of Econophysics" Cambridge Scholars Press (UK, 2019)
  • Marcelo Byrro Ribeiro, Income Distribution Dynamics of Economic Systems: An Econophysical Approach, Cambridge University Press (Cambridge, UK, 2020)
  • Giuseppe Toscani, Parongama Sen and Soumyajyoti Biswas (Eds), "Kinetic exchange models of societies and economies" Philosophical Transactions of the Royal Society A 380: 20210170 (Special Issue, May 2022)

January 07, 2023
kinetic, exchange, models, markets, this, article, technical, most, readers, understand, please, help, improve, make, understandable, experts, without, removing, technical, details, december, 2018, learn, when, remove, this, template, message, kinetic, exchang. This article may be too technical for most readers to understand Please help improve it to make it understandable to non experts without removing the technical details December 2018 Learn how and when to remove this template message Kinetic exchange models are multi agent dynamic models inspired by the statistical physics of energy distribution which try to explain the robust and universal features of income wealth distributions Understanding the distributions of income and wealth in an economy has been a classic problem in economics for more than a hundred years Today it is one of the main branches of econophysics Contents 1 Data and basic tools 2 Overview of the models 3 Criticisms 4 See also 5 References 6 Further readingData and basic tools EditIn 1897 Vilfredo Pareto first found a universal feature in the distribution of wealth After that with some notable exceptions this field had been dormant for many decades although accurate data had been accumulated over this period Considerable investigations with the real data during the last fifteen years 1995 2010 revealed 1 that the tail typically 5 to 10 percent of agents in any country of the income wealth distribution indeed follows a power law However the majority of the population i e the low income population follows a different distribution which is debated to be either Gibbs or log normal Basic tools used in this type of modelling are probabilistic and statistical methods mostly taken from the kinetic theory of statistical physics Monte Carlo simulations often come handy in solving these models Overview of the models EditSince the distributions of income wealth are the results of the interaction among many heterogeneous agents there is an analogy with statistical mechanics where many particles interact This similarity was noted by Meghnad Saha and B N Srivastava in 1931 2 and thirty years later by Benoit Mandelbrot 3 In 1986 an elementary version of the stochastic exchange model was first proposed by J Angle 4 In the context of kinetic theory of gases such an exchange model was first investigated by A Dragulescu and V Yakovenko 5 6 The main modelling effort has been put to introduce the concepts of savings 7 8 and taxation 9 in the setting of an ideal gas like system Basically it assumes that in the short run an economy remains conserved in terms of income wealth therefore law of conservation for income wealth can be applied Millions of such conservative transactions lead to a steady state distribution of money gamma function like in the Chakraborti Chakrabarti model with uniform savings 7 and a gamma like bulk distribution ending with a Pareto tail 10 in the Chatterjee Chakrabarti Manna model with distributed savings 8 and the distribution converges to it The distributions derived thus have close resemblance with those found in empirical cases of income wealth distributions Though this theory had been originally derived from the entropy maximization principle of statistical mechanics it had been shown by A S Chakrabarti and B K Chakrabarti 11 that the same could be derived from the utility maximization principle as well following a standard exchange model with Cobb Douglas utility function Recently it has been shown 12 that an extension of the Cobb Douglas utility function in the above mentioned Chakrabarti Chakrabarti formulation by adding a production savings factor leads to the desired feature of growth of the economy in conformity with some earlier phenomenologically established growth laws in the economics literature The exact distributions produced by this class of kinetic models are known only in certain limits and extensive investigations have been made on the mathematical structures of this class of models 13 14 The general forms have not been derived so far Criticisms EditThis class of models has attracted criticisms from many dimensions 15 It has been debated for long whether the distributions derived from these models are representing the income distributions or wealth distributions The law of conservation for income wealth has also been a subject of criticism See also EditEconomic inequality Econophysics Thermoeconomics Wealth condensationReferences Edit Chatterjee A Yarlagadda S Chakrabarti B K 2005 Econophysics of Wealth Distributions Springer Verlag Milan Saha M Srivastava B N 1931 A Treatise on Heat Indian Press Allahabad p 105 the page is reproduced in Fig 6 in Sitabhra Sinha Bikas K Chakrabarti Towards a physics of economics Physics News 39 2 33 46 April 2009 Mandelbrot B B 1960 The Pareto Levy law and the distribution of income International Economic Review 1 2 79 106 doi 10 2307 2525289 JSTOR 2525289 Angle J 1986 The surplus theory of social stratification and the size distribution of personal wealth Social Forces 65 2 293 326 doi 10 2307 2578675 JSTOR 2578675 Dragulescu A Yakovenko V 2000 The statistical mechanics of money European Physical Journal B 17 4 723 729 arXiv cond mat 0001432 Bibcode 2000EPJB 17 723D doi 10 1007 s100510070114 S2CID 16158313 Garibaldi U Scalas E Viarenga P 2007 Statistical equilibrium in exchange games European Physical Journal B 60 2 241 246 Bibcode 2007EPJB 60 241G doi 10 1140 epjb e2007 00338 5 S2CID 119517302 a b Chakraborti A Chakrabarti B K 2000 Statistical mechanics of money how savings propensity affects its distribution European Physical Journal B 17 1 167 170 arXiv cond mat 0004256 Bibcode 2000EPJB 17 167C doi 10 1007 s100510070173 S2CID 5138071 a b Chatterjee A Chakrabarti B K Manna K S S 2004 Pareto law in a kinetic model of market with random saving propensity Physica A 335 1 2 155 163 arXiv cond mat 0301289 Bibcode 2004PhyA 335 155C doi 10 1016 j physa 2003 11 014 S2CID 120904131 Guala S 2009 Taxes in a simple wealth distribution model by inelastically scattering particles Interdisciplinary Description of Complex Systems 7 1 1 7 arXiv 0807 4484 Bibcode 2008arXiv0807 4484G Chakraborti A Patriarca M 2009 Variational Principle for the Pareto Power Law Physical Review Letters 103 22 228701 arXiv cond mat 0605325 Bibcode 2009PhRvL 103v8701C doi 10 1103 PhysRevLett 103 228701 PMID 20366128 S2CID 909820 A S Chakrabarti B K Chakrabarti 2009 Microeconomics of the ideal gas like market models Physica A 388 19 4151 4158 arXiv 0905 3972 Bibcode 2009PhyA 388 4151C doi 10 1016 j physa 2009 06 038 S2CID 14908064 D S Quevedo C J Quimbay 2020 Non conservative kinetic model of wealth exchange with saving of production European Physical Journal B 93 10 186 Bibcode 2020EPJB 93 186Q doi 10 1140 epjb e2020 10193 3 S2CID 224849350 During B Matthes D Toscani G 2008 Kinetic equations modelling wealth distributions a comparison of approaches PDF Physical Review E 78 5 056103 Bibcode 2008PhRvE 78e6103D doi 10 1103 physreve 78 056103 PMID 19113186 Cordier S Pareschi L Toscani G 2005 On a kinetic model for a simple market economy Journal of Statistical Physics 120 1 2 253 277 arXiv math 0412429 Bibcode 2005JSP 120 253C doi 10 1007 s10955 005 5456 0 S2CID 10218909 Mauro Gallegati Steve Keen Thomas Lux and Paul Ormerod 2006 Worrying Trends in Econophysics Physica A 371 1 1 6 Bibcode 2006PhyA 370 1G doi 10 1016 j physa 2006 04 029 a href Template Cite journal html title Template Cite journal cite journal a CS1 maint multiple names authors list link Further reading EditBrian Hayes Follow the money American Scientist 90 400 405 Sept Oct 2002 Jenny Hogan There s only one rule for rich New Scientist 6 7 12 March 2005 Peter Markowich Applied Partial Differential Equations Springer Verlag Berlin 2007 Arnab Chatterjee Bikas K Chakrabarti Kinetic exchange models for income and wealth distribution European Physical Journal B 60 135 149 2007 Victor Yakovenko J B Rosser Colloquium statistical mechanics of money wealth and income Reviews of Modern Physics 81 1703 1725 2009 Thomas Lux F Westerhoff Economics crisis Nature Physics 5 2 2009 Sitabhra Sinha Bikas K Chakrabarti Towards a physics of economics Physics News 39 2 33 46 April 2009 Stephen Battersby The physics of our finances New Scientist p 41 28 July 2012 Bikas K Chakrabarti Anirban Chakraborti Satya R Chakravarty Arnab Chatterjee Econophysics of Income amp Wealth Distributions Cambridge University Press Cambridge 2013 Lorenzo Pareschi and Giuseppe Toscani Interacting Multiagent Systems Kinetic equations and Monte Carlo methods Oxford University Press Oxford 2013 Kishore Chandra Dash Story of Econophysics Cambridge Scholars Press UK 2019 Marcelo Byrro Ribeiro Income Distribution Dynamics of Economic Systems An Econophysical Approach Cambridge University Press Cambridge UK 2020 Giuseppe Toscani Parongama Sen and Soumyajyoti Biswas Eds Kinetic exchange models of societies and economies Philosophical Transactions of the Royal Society A 380 20210170 Special Issue May 2022 Retrieved from https en wikipedia org w index php title Kinetic exchange models of markets amp oldid 1123346754, wikipedia, wiki, book, books, library,

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