Dynamic Process of Money Transfer Models

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. Dragulescu 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 to another
in the trading process.

• n A group of individual agents
• A pile of money
• A specific trading rule.

5
Basic Model and Its Applications
Trading Rule
6
Distribution
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Distribution of Money
A. Dragulescu 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 Fishers Exchange Equation
The relationship between velocity and average
holding time
Average holding time
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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
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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)

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Model I Same Saving Factor
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Model II Diverse Saving Factors
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Model III Preferential Dispensing

• Random spending
• Preferential dispensing

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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)
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Distribution of Money (Model III)
N. Ding, Y. Wang, J. Xu and N. Xi,
Int.J.Mod.Phys. B18, 17-19, 2725 (2004)
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Comparison of These Three Cases
Model I
Model II
Model III
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Holding Time Distribution (Model I)
N.Ding, N. Xi, Y. Wang, Eur.Phys. J. B, 36, 149
(2003)
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Holding Time Distribution (Model II)
N.Ding, N. Xi, Y. Wang, Eur.Phys. J. B, 36, 149
(2003)
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The Velocity versus Saving Rate
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Mobility of Ranking (Model I s0.5)
l0.58129
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Mobility of Ranking (Model II)
l0.19671
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Mobility of Ranking (Model III)
l0.14828
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The Mobility versus Saving Rate
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Dependence of Mobility on Sampling Time Interval
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Time Evolution of Rank for Some Rich Individuals
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Time Evolution of Rank for Some Medium Individuals
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Time Evolution of Rank for Some Poor Individuals
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Time Evolution of Rank for Some Very Poor
Individuals
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Scatter-Plot of All Agents
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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. B 36 (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).

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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).