Econophysics of income and wealth distributionshBikas K. Chakrabarti ... [et al

The Distribution Of Wealth And Income Is Never Uniform, And Philosophers And Economists Have Tried For Years To Understand The Reasons And Formulate Remedies For Such Inequalities. This Book Introduces The Elegant And Intriguing Kinetic Exchange Models That Physicists Have Developed To Tackle These Issues. This Is The First Monograph In Econophysics Focussed On The Analyses And Modelling Of These Distributions, And Is Ideal For Physicists And Economists. It Is Written In Simple, Lucid Language, With Plenty Of Illustrations And In-depth Analyses, Making It Suitable For Researchers New To This Field As Well As Specialized Readers. It Explores The Origin Of Economic Inequality And Examines The Scientific Steps That Can Be Taken To Reduce This Inequality In The Future-- 1. Introduction -- 2. Income And Wealth Distribution Data For Different Countries -- 3. Major Socio-economic Modellings -- 4. Market Exchanges And Scattering Process -- 5. Analytic Structure Of The Kinetic Exchange Market Models -- 6. Microeconomic Foundation Of The Kinetic Exchange Models -- 7. Dynamics: Generation Of Income, Inequality And Development -- 8. Outlook. Bikas K. Chakrabarti, Anirban Chakraborti, Satya R. Chakravarty, Arnab Chatterjee. Includes Bibliographical References And Index. Cambridge University Press Contents 7 Preface 9 1 Introduction 13 2 Income and wealth distribution data for different countries 19 2.1 What are money, wealth and income? 19 2.2 Analyses using data from earlier periods 20 2.3 Analyses using data from recent periods 22 2.4 Measures of income inequality: Gini coefficient and Lorenz curve 40 3 Major socioeconomic modelling 47 3.1 Models of income distribution 47 3.2 Models of wealth distribution 48 3.2.1 Lotka-Volterra models 48 3.2.2 The Bouchaud-Mezard and related models 49 3.2.3 Models for evolving society 52 3.2.4 Models of wealth distribution with a risk aversion factor 55 3.2.5 Asset exchange models 58 3.3 Statistical equilibrium theory of markets 64 4 Market exchanges and scattering process 67 4.1 Gas-like models 67 4.1.1 Model with uniform savings 69 4.1.2 Model with distributed savings 71 4.1.3 Model with `annealed' savings 76 4.1.4 Further studies 77 4.1.5 Dynamics of agents 82 4.2 Models with commodity 99 4.2.1 Ideal-gas trading market in the presence of a non-consumable commodity 99 4.2.2 Self-organizing model with single commodity 102 4.2.3 Another model with commodity 106 4.3 Models on networks 109 4.3.1 Models on directed networks 109 4.3.2 Preferential transactions and weighted trade network 115 4.4 Models with debt 117 4.5 Models with tax 119 4.6 Other related models 120 4.6.1 Inelastic scattering in an open economy 120 4.6.2 A threshold-induced phase transition in the kinetic exchange models 121 5 Analytic structure of the kinetic exchange market models 126 5.1 Analytic results for the CC model 126 5.1.1 Does the CC model produce gamma distribution? 128 5.1.2 Upper bound form at low wealth range 134 5.1.3 The gas model analogy 136 5.2 Analytic results for the CCM model 139 5.2.1 Distribution of money difference 139 5.2.2 Master equation and its analysis 141 5.2.3 A transition matrix formalism 145 5.2.4 Entropy maximization in a heterogeneous system 147 5.3 Analytic results for other models 151 5.3.1 Autoregressive models and non-conservative form 151 5.3.2 Analytic structure of Slanina's model 155 5.3.3 Another generalized approach to the kinetic exchange models 157 6 Microeconomic foundation of the kinetic exchange models 162 6.1 Derivation of the basic kinetic exchange model 162 6.1.1 Random exchange 166 6.1.2 Exchange with savings 167 6.2 Production of a vector of commodities 168 6.3 A generalized version of the CC model 169 6.4 Inequality reversal 171 6.5 Global market 175 6.6 Steady-state distribution of money and price 176 6.7 Discussion 177 7 Dynamics: generation of income, inequality and development 180 7.1 The economic significance 180 7.2 Analysis of income distributions 181 7.3 Analysis of wealth distributions 194 8 Outlook 205 8.1 Chapters in a nutshell 206 8.2 Beyond income and wealth 207 8.2.1 Probability distribution of energy consumption 207 8.2.2 Kinetic models of opinion formation 210 8.3 Open problems and challenges 211 References 213 Index 225 9781107013445 Contents......Page 7 Preface......Page 9 1 Introduction......Page 13 2.1 What are money, wealth and income?......Page 19 2.2 Analyses using data from earlier periods......Page 20 2.3 Analyses using data from recent periods......Page 22 2.4 Measures of income inequality: Gini coefficient and Lorenz curve......Page 40 3.1 Models of income distribution......Page 47 3.2.1 Lotka-Volterra models......Page 48 3.2.2 The Bouchaud-Mezard and related models......Page 49 3.2.3 Models for evolving society......Page 52 3.2.4 Models of wealth distribution with a risk aversion factor......Page 55 3.2.5 Asset exchange models......Page 58 3.3 Statistical equilibrium theory of markets......Page 64 4.1 Gas-like models......Page 67 4.1.1 Model with uniform savings......Page 69 4.1.2 Model with distributed savings......Page 71 4.1.3 Model with `annealed' savings......Page 76 4.1.4 Further studies......Page 77 4.1.5 Dynamics of agents......Page 82 4.2.1 Ideal-gas trading market in the presence of a non-consumable commodity......Page 99 4.2.2 Self-organizing model with single commodity......Page 102 4.2.3 Another model with commodity......Page 106 4.3.1 Models on directed networks......Page 109 4.3.2 Preferential transactions and weighted trade network......Page 115 4.4 Models with debt......Page 117 4.5 Models with tax......Page 119 4.6.1 Inelastic scattering in an open economy......Page 120 4.6.2 A threshold-induced phase transition in the kinetic exchange models......Page 121 5.1 Analytic results for the CC model......Page 126 5.1.1 Does the CC model produce gamma distribution?......Page 128 5.1.2 Upper bound form at low wealth range......Page 134 5.1.3 The gas model analogy......Page 136 5.2.1 Distribution of money difference......Page 139 5.2.2 Master equation and its analysis......Page 141 5.2.3 A transition matrix formalism......Page 145 5.2.4 Entropy maximization in a heterogeneous system......Page 147 5.3.1 Autoregressive models and non-conservative form......Page 151 5.3.2 Analytic structure of Slanina's model......Page 155 5.3.3 Another generalized approach to the kinetic exchange models......Page 157 6.1 Derivation of the basic kinetic exchange model......Page 162 6.1.1 Random exchange......Page 166 6.1.2 Exchange with savings......Page 167 6.2 Production of a vector of commodities......Page 168 6.3 A generalized version of the CC model......Page 169 6.4 Inequality reversal......Page 171 6.5 Global market......Page 175 6.6 Steady-state distribution of money and price......Page 176 6.7 Discussion......Page 177 7.1 The economic significance......Page 180 7.2 Analysis of income distributions......Page 181 7.3 Analysis of wealth distributions......Page 194 8 Outlook......Page 205 8.1 Chapters in a nutshell......Page 206 8.2.1 Probability distribution of energy consumption......Page 207 8.2.2 Kinetic models of opinion formation......Page 210 8.3 Open problems and challenges......Page 211 References......Page 213 Index......Page 225 "The distribution of wealth and income is never uniform, and philosophers and economists have tried for years to understand the reasons and formulate remedies for such inequalities. This book introduces the elegant and intriguing kinetic exchange models that physicists have developed to tackle these issues. This is the first monograph in econophysics focussed on the analyses and modelling of these distributions, and is ideal for physicists and economists. It is written in simple, lucid language, with plenty of illustrations and in-depth analyses, making it suitable for researchers new to this field as well as specialized readers. It explores the origin of economic inequality and examines the scientific steps that can be taken to reduce this inequality in the future"-- Provided by publisher Introducing the elegant and intriguing kinetic exchange models that physicists have developed to tackle the distribution of wealth and income, this book is ideal for physicists and economists. It is written in simple, lucid language, making it suitable for researchers new to this field as well as specialized readers.