Econophysics of Income and Wealth Distributions

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