Modelos de Distribuio de Riqueza Desigualdade e Criminalidade
Modelos de Distribuição de Riqueza: Desigualdade e Criminalidade José Roberto Iglesias I. F. e F. C. E. - U. F. R. G. S. , Porto Alegre, Brazil Rio de Janeiro, 9 de novembro 2007 APFA 6
Porto Alegre (30 o S) Econofis 2007 Rio de Janeiro 09/11/2007 2
Colaboradores Porto Alegre (Brasil): • Gaspar Machado Caon • Sebastián Gonçalves • Tiago Bonacina • Vanessa Hoffmann • Viktoriya Semeshenko França: • Mirta Gordon • J. -Pierre Nadal Econofis 2007 Rio de Janeiro 09/11/2007 S. C. de Bariloche (Argentina) • Miguel Fuentes • Marcelo Kuperman • Guillermo Abramson • Sebastián Risau-Gusman • M. Fabiana Laguna Mérida (México) • Cristian Moukarzel 3
Motivation. . . Econofis 2007 Rio de Janeiro 09/11/2007 4
Pareto´s law Econofis 2007 Rio de Janeiro 09/11/2007 5
Pareto’s law Econofis 2007 Rio de Janeiro 09/11/2007 6
The exponential + power law behavior (Dragulescu & Yakovenko, 2001) Econofis 2007 Rio de Janeiro 09/11/2007 7
Brazilian income distribution Econofis 2007 Rio de Janeiro 09/11/2007 8
Inequality (Gini coefficient) Econofis 2007 Rio de Janeiro 09/11/2007 9
Econofis 2007 Rio de Janeiro 09/11/2007 11
Gini coefficient Map Econofis 2007 Rio de Janeiro 09/11/2007 12
Models of Wealth Distribution Econofis 2007 Rio de Janeiro 09/11/2007 13
Non-interacting agents Econofis 2007 Rio de Janeiro 09/11/2007 14
A model with fluctuations and interactions Other non-conservative model: Richmond – Solomon (Lotka. Volterra) Econofis 2007 Rio de Janeiro 09/11/2007 15
Interacting conservative models Ø Agents are molecules of an ideal gas, that exchange money as molecules exchange energy. Ø The simplest version (D-Y 2000) delivers a Boltzmann – Gibbs (exponential) distribution Ø Many authors (Iglesias et. al. ; A. Chatterjee et. al. ) introduced a kind of multiplicative noise: “saving propensity” and are able to obtain power laws distribution Ø Effect of size of market and taxes (Ausloss, Pekalski, 2006) Econofis 2007 Rio de Janeiro 09/11/2007 16
A model with Risk Aversion A random (or not) fraction, , of the agent´s wealth is saved An agent site with wealth w 1 exchanges with another of wealth w 2 a quantity (fair rule): Or: The winner takes all, (winner rule) he receives dw from his partner. What happens? Condensation (or a frozen society, where just one agent concentrates all the wealth) §This transaction occurs with a given probability of favoring the poorer agent p, being either p fixed for all the agents or p given by: § being f : 0 f 0. 5 Econofis 2007 Rio de Janeiro 09/11/2007 17
Effect of Risk aversion and pexch Econofis 2007 Rio de Janeiro 09/11/2007 18
About wealth condensation The European Physical Journal – Special Topics, 143, 75 -79 (2007) Critical line for condensation (Moukarzel et al, 2007) Before arriving to condensation the system exhibits power law With growing Pareto exponent, leading to a “thermal death of trade”. But the final state is one of equilibrium but with no equipartition Econofis 2007 Rio de Janeiro 09/11/2007 19
About exchange models: “Man is an animal that makes bargains: no other animal does this - no dog exchanges bones with another” Adam Smith Econofis 2007 Rio de Janeiro 09/11/2007 20
Comparing exchange rules “Fair” Rule (equal opportunities) A Econofis 2007 Rio de Janeiro 09/11/2007 B Rule the winner takes all A B 21
Econofis 2007 Rio de Janeiro 09/11/2007 22
Hierarchy evolution Econofis 2007 Rio de Janeiro 09/11/2007 23
Interactions within the same “economic” class Econofis 2007 Rio de Janeiro 09/11/2007 24
Wealth depending interactions Agents only interact when their wealth is within a threshold u |wi-wk| < u Econofis 2007 Rio de Janeiro 09/11/2007 25
Wealth distribution vs. time Econofis 2007 Rio de Janeiro 09/11/2007 26
And if correlations are included between risk-aversion and expected profits? Econofis 2007 Rio de Janeiro 09/11/2007 27
Wealth distribution of “rational” agents The poorer agent changes strategy N=100. 000 agents Econofis 2007 initial wealth uniformly distributed {0, 1000} Rio de Janeiro 09/11/2007 Gini, red points 28
Wealth distribution of “irrational” agents The richer agent changes strategy Econofislaw 2007 exponent – 1. 125 Power Rio de Janeiro 09/11/2007 Gini: green points, (blue points, poorer agent Change strategy) 29
Economic effects of criminality M. B. Gordon, J. R. I. , J. P. Nadal, V. Semeshenko (to appear) Agents are characerized by its wealth wi and a honesty coefficient Hi (changing) Each “month” agents perceive a wage Number of crime attemps each month depends on <H> p 0 is probability of punishment of small felonies and p 1 of big ones. It varies as a function of booty Punishment consist in prison + fines Econofis 2007 Rio de Janeiro 09/11/2007 30
Criminality Econofis 2007 Rio de Janeiro 09/11/2007 31
Economic indicators Econofis 2007 Rio de Janeiro 09/11/2007 32
Time evolution Econofis 2007 Rio de Janeiro 09/11/2007 33
Wealth distribution Econofis 2007 Rio de Janeiro 09/11/2007 34
Honesty distribution Econofis 2007 Rio de Janeiro 09/11/2007 35
Conclusions Ø Probability of punishment of light and heavy felonies are correlated. Ø Inequality increases and Economic growth decreases with high criminality Ø Time evolution is in avalanches Ø Future: what treatment to relapses Econofis 2007 Rio de Janeiro 09/11/2007 36
It is only by not paying one's bills that one can hope to live in the memory of the commercial classes. Oscar Wilde Quino Econofis 2007 Rio de Janeiro 09/11/2007 37
Publicações: www. if. ufrgs. br/~iglesias MUITO OBRIGADO! Econofis 2007 Rio de Janeiro 09/11/2007 38
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