Lagrange Principle of Wealth Distribution

Mimkes, Jürgen; Willis, Geoff

doi:10.1007/88-470-0389-x_7

Cited by 13 publications

(11 citation statements)

References 6 publications

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“…It was proposed to call these models the Bennati-Drȃgulescu-Yakovenko game (Garibaldi et al, 2007;Scalas et al, 2006). The Boltzmann distribution was independently applied to social sciences by the physicist Jürgen Mimkes (2000); Mimkes and Willis (2005) using the Lagrange principle of maximization with constraints. The exponential distribution of money was also found by the economist Martin Shubik (1999) using a Markov chain approach to strategic market games.…”

Section: The Boltzmann-gibbs Distribution Of Moneymentioning

confidence: 99%

Colloquium: Statistical mechanics of money, wealth, and income

2009

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This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by the exponential ("thermal") distribution, whereas a small fraction of the population in the upper class is characterized by the power-law ("superthermal") distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium.Comment: 24 pages, 13 figures; v.2 - minor stylistic changes and updates of references corresponding to the published versio

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Section: The Boltzmann-gibbs Distribution Of Moneymentioning

confidence: 99%

Colloquium: Statistical mechanics of money, wealth, and income

2009

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“…Since these two dynamics are time-reversible, they, under the boundary condition of

and

, lead to an equilibrium state characterized by the Boltzmann–Gibbs distribution [ 29 ],

where the effective temperature

of the system is the average wealth; herein the homogeneous saving propensity

, see Figure 1 where a perfect fitting with the theoretical curve is clearly observed. In fact, this exponential equilibrium distribution is theoretic-derived by maximizing the entropy of wealth distribution

under the constraint of wealth conservation, using the method of Lagrange multipliers [ 30 , 31 ]. Although the above models seem to be too simple to describe the reality, there is a possibility that economic interactions among economic agents can be modeled in terms of simple statistical mechanics leading to universal statistical laws.…”

Section: Kinetic Exchange Modelsmentioning

confidence: 99%

Analysis of Solidarity Effect for Entropy, Pareto, and Gini Indices on Two-Class Society Using Kinetic Wealth Exchange Model

Lim

Min

2020

Entropy

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It is well known that two different underlying dynamics lead to different patterns of income/wealth distribution such as the Boltzmann–Gibbs form for the lower end and the Pareto-like power-law form for the higher-end. The Boltzmann–Gibbs distribution is naturally derived from maximizing the entropy of random interactions among agents, whereas the Pareto distribution requires a rational approach of economics dependent on the wealth level. More interestingly, the Pareto regime is very dynamic, whereas the Boltzmann–Gibbs regime is stable over time. Also, there are some cases in which the distributions of income/wealth are bimodal or polymodal. In order to incorporate the dynamic aspects of the Pareto regime and the polymodal forms of income/wealth distribution into one stochastic model, we present a modified agent-based model based on classical kinetic wealth exchange models. First, we adopt a simple two-class society consisting of the rich and the poor where the agents in the same class engage in random exchanges while the agents in the different classes perform a wealth-dependent winner-takes-all trading. This modification leads the system to an extreme polarized society with preserving the Pareto exponent. Second, we incorporate a solidarity formation among agents belonging to the lower class in our model, in order to confront a super-rich agent. This modification leads the system to a drastic bimodal distribution of wealth with a varying Pareto exponent over varying the solidarity parameter, that is, the Pareto-regime becomes narrower and the Pareto exponent gets larger as the solidarity parameter increases. We argue that the solidarity formation is the key ingredient in the varying Pareto exponent and the polymodal distribution. Lastly, we take two approaches to evaluate the level of inequality of wealth such as Gini coefficients and the entropy measure. According to the numerical results, the increasing solidarity parameter leads to a decreasing Gini coefficient not linearly but nonlinearly, whereas the entropy measure is robust over varying solidarity parameters, implying that there is a trade-off between the intermediate party and the high end.

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“…They proposed calling these models the Bennati-Dragulescu-Yakovenko (BDY) game [41]. The Boltzmann distribution was independently applied to social sciences by Jürgen Mimkes using the Lagrange principle of maximization with constraints [42,43]. The exponential distribution of money was also found in Ref.…”

Section: The Boltzmann-gibbs Distribution Of Moneymentioning

confidence: 99%

Econophysics, Statistical Mechanics Approach to

Yakovenko¹

2009

Complex Systems in Finance and Econometrics

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This is a review article for Encyclopedia of Complexity and System Science, to be published by Springer http://refworks.springer.com/complexity/. The terms highlighted in bold in Sec. I refer to other articles in this Encyclopedia. This paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since late 1990s."Money, it's a gas." Pink Floyd Contents Glossary 1 I. Definition of the subject 1 II. Historical Introduction 2 III. Statistical Mechanics of Money Distribution 3 A. The Boltzmann-Gibbs distribution of energy 3 B. Conservation of money 4 C. The Boltzmann-Gibbs distribution of money 5 D. Models with debt 6 E. Proportional money transfers and saving propensity 7 F. Additive versus multiplicative models 8 IV. Statistical Mechanics of Wealth Distribution 9 A. Models with a conserved commodity 9 B. Models with stochastic growth of wealth 10 C. Empirical data on money and wealth distributions 11 V. Data and Models for Income Distribution 12 A. Empirical data on income distribution 12 B. Theoretical models of income distribution 15 VI. Other Applications of Statistical Physics 16 A. Economic temperatures in different countries 16 B. Society as a binary alloy 17 VII. Future Directions, Criticism, and Conclusions 17 A. Future directions 17 B. Criticism from economists 18 C. Conclusions 20 VIII. Bibliography 20 Books and Reviews 24

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Lagrange Principle of Wealth Distribution

Cited by 13 publications

References 6 publications

Colloquium: Statistical mechanics of money, wealth, and income

Colloquium: Statistical mechanics of money, wealth, and income

Analysis of Solidarity Effect for Entropy, Pareto, and Gini Indices on Two-Class Society Using Kinetic Wealth Exchange Model

Econophysics, Statistical Mechanics Approach to

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