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Dynamic Process of Money Transfer Models

Dynamic Process of Money Transfer Models. Yougui Wang. Department of Systems Science School of Management Beijing Normal University Beijing 100875, P.R. of China. Money Transfer Models. S. Ispolatov, P. L. Krapivsky and S. Redner, Eur. Phys. J. B 2, 267(1998).

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Dynamic Process of Money Transfer Models

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  1. Dynamic Process of Money Transfer Models Yougui Wang Department of Systems Science School of Management Beijing Normal University Beijing 100875, P.R. of China

  2. Money Transfer Models • S. Ispolatov, P. L. Krapivsky and S. Redner, Eur. Phys. J. B 2, 267(1998). • A. Drăgulescu and V. M. Yakovenko, Eur. Phys.J. B, 17, 723 (2000). • A. Chakraborti and B. K. Chakrabarti, Eur.Phys. J. B, 17, 167 (2000). • …… • B. Hayes, Am. Scientist 90, 400(2002).

  3. Analogies in Money Transfer Models • Economic System Ideal gas • Agents Molecules • Money Energy • Transactions Collision

  4. The Common Characteristics Money is always transferred from one toanother in the trading process. • nA group of individual agents; • A pile of money; • A specific trading rule.

  5. Basic Model and Its Applications Trading Rule:

  6. Distribution

  7. Distribution of Money A. Drăgulescu and V. M. Yakovenko, Eur. Phys. J. B, 17, 723 (2000)

  8. Transfer Rate Time holding time of money

  9. The circulation of money is a process of Poisson type. Y. Wang, N. Ding and Li Zhang, Physica A 324 (2003) 665

  10. The Velocity of Money The Fisher’s Exchange Equation: The relationship between velocity and average holding time: Average holding time

  11. In the Life-Cycle Model • The optimal problem for a representative individual • Subject to Y. Wang, and Hanqing Qiu, Physica A (2005) in press

  12. Mobility Time

  13. Time Evolution of Rank for Some Individuals

  14. Economic Index of Mobility • Per Capita Aggregate Change in Log-income (or Log-wealth) • In this model, we get

  15. Applications on Some Other Money Transfer Models • Model I: A. Chakraborti and B. K. Chakrabarti, Eur.Phys. J. B, 17, 167 (2000) • Model II: A. Chatterjee, B. K. Chakrabarti and S. S.Manna, Physica A, 335, 155 (2004) • Model III: N. Ding, Y. Wang, J. Xu and N. Xi, Int.J.Mod.Phys. B18, 17-19, 2725 (2004)

  16. Model I: Same Saving Factor

  17. Model II: Diverse Saving Factors

  18. Model III: Preferential Dispensing • Random spending • Preferential dispensing

  19. Distribution of Money (Model I) A. Chakraborti and B. K. Chakrabarti, Eur.Phys. J. B, 17, 167 (2000)

  20. Distribution of Money (Model II) A. Chatterjee, B. K. Chakrabarti and S. S.Manna, Physica A, 335, 155 (2004)

  21. Distribution of Money (Model III) N. Ding, Y. Wang, J. Xu and N. Xi, Int.J.Mod.Phys. B18, 17-19, 2725 (2004)

  22. Comparison of These Three Cases Model I Model III Model II

  23. Holding Time Distribution (Model I) N.Ding, N. Xi, Y. Wang, Eur.Phys. J. B, 36, 149 (2003)

  24. Holding Time Distribution (Model II) N.Ding, N. Xi, Y. Wang, Eur.Phys. J. B, 36, 149 (2003)

  25. The Velocity versus Saving Rate

  26. Mobility of Ranking (Model I: s=0.5) l=0.58129

  27. Mobility of Ranking (Model II) l=0.19671

  28. Mobility of Ranking (Model III) l=0.14828

  29. The Mobility versus Saving Rate

  30. Dependence of Mobility on Sampling Time Interval

  31. Time Evolution of Rank for Some Rich Individuals

  32. Time Evolution of Rank for Some Medium Individuals

  33. Time Evolution of Rank for Some Poor Individuals

  34. Time Evolution of Rank for Some Very Poor Individuals

  35. Scatter-Plot of All Agents

  36. Our Extensions of Money Transfer Models • Money Transfer Rate and Holding Time • Y. Wang, N. Ding and L.Zhang, “The Circulation of Money and Holding Time Distribution,”Physica A 324 (2003) 665. • N. Ding, N. Xi, Y. Wang, “Effects of Sving and Spending Patterns on Holding Time Distribution,”Eur.Phys. J. B36 (2003)149. • Y. Wang, Hanqing Qiu,“The Velocity of Money In a Life-Cycle Model”. Physica A, (2005) in press.

  37. Our Extensions of Money Transfer Models • Distribution of Money • N. Ding, Y. Wang, J. Xu and N. Xi, “Power Law Distribution in Circulating Money: Effect of Preferential Behavior,”Int.J.Mod.Phys. B18, 17-19, (2004)2725. • Impacts of Money Creation • Ning Xi, N. Ding and Y. Wang, “How Required Reserve Ratio Affects Distribution and Velocity of Money,” submitted to Physica A (2005).

  38. Our Extensions of Money Transfer Models • Economic Mobility • N. Ding, N. Xi, Y. Wang, “The Economic Mobility in Money Transfer Models ,” to be submitted to Physica A (2005). • N. Ding, Ning Xi, and Y. Wang, “The Dynamic Character of the Transfer Model with Saving,” to be submitted to Eur.Phys. J. B(2005).

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