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DESIGUALDAD Y DISTRIBUCIÓN DE LA RIQUEZA José Roberto Iglesias Instituto de Física y Faculdade de Ciências Económicas, U.F.R.G.S., Porto Alegre, Brazil AFA, setiembre 2006, Villa de Merlo

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Porto Alegre, Brasil Geography and Pictures Porto Alegre (30 o S)

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Autores y colaboradores Porto Alegre: Sebastián Gonçalves Vanessa Hoffmann Gaspar Machado Caon Bruno Requião da Silva Tobías Heinfart Sabino Porto (FCE) Grenoble (Francia) Mirta Gordon Viktoriya Semeshenko S.C. de Bariloche Miguel Fuentes Marcelo Kuperman Guillermo Abramson Sebastián Risau Gusman M. Fabiana Laguna Mérida (México) Cristian Moukarzel

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Master of the Mint Warden and Master of the Mint Isaac Newton was appointed to a position in the Mint in 1696 on the recommendation of the Chancellor of the Exchequer Charles Montague. At first sight this may seem a somewhat curious, even backward, step for a man in his early fifties whose life had been spent in the academic surroundings of Trinity College, Cambridge. Public office was something new to him, but it was actually something that he had sought, and so the offer of the position of Warden of the Mint would not have been unwelcome. The Mint was then in the Tower of London and it was to the Tower that Newton came in April 1696 to take up his new duties. It was a time of great activity. The Mint was grappling with the recoinage of old silver coins that dated back to the reign of Elizabeth and even to earlier reigns. Newton was quickly caught up in the pressure of the moment. The operation was completed within three years, leaving Newton more time to devote to his main duty of investigating and bringing to justice those who clipped and counterfeited the coin of the realm. Master of the Mint In 1699 the post of Master of the Mint fell vacant and though technically less senior than that of Warden it was more lucrative since the Master acted as a contractor to the Crown, profiting from the rates at which he put the work out to sub-contractors. The post was offered to Newton and he took up his duties with effect from Christmas Day 1699, his fifty-seventh birthday. He remained as Master until his death in March 1727. To know more visit: http://www.royalmint.com/about/newton.asp Sir Isaac Newton

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Louis Bachelier (1870-1946) The tragic hero of financial economics was the unfortunate Louis Bachelier. In his 1900 dissertation, Theorie de la Spéculation, he anticipated much of now standard financial theory: random walk of financial market prices, Brownian motion and martingales (note: all before both Einstein and Wiener!) His innovativeness was not appreciated by his professors. His dissertation received poor marks from his teachers and, consequently blackballed, he quickly dropped into the shadows of the academic underground. He ended up obscurely teaching in Besançon for much of the rest of his life. His work was largely ignored until the 1960s.

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F. Black & M. Scholes: F. Black & M. Scholes: The pricing of options and corporate liabilities. J. Pol. Econ. 81 (1973) 637 V(S,t) option value S stock price t expiring time volatility r interest rate Black-Scholes equation is a diffusion equation (Brownian motion) studied by Bachelier, Wiener and Einstein. Scholes and Merton got the Nobel Prize in Economy in 1997 Myron Scholes and Fischer Black

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Ved en trono a la noble igualdad…. Todos los hombres nacen iguales…

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Pareto´s law

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Paretos law

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Distribution laws Distribution Power law Exponential Logarithmic Representation Straight line in log-log - is the slope Straigth line in semi-log - is the slope

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Benoit Mandelbrot. The Variation of Certain Speculative Prices. Journal of Business 36: 394 (1963)

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Lévy distributions Shape of the symmetric Lévy distribution with =0.8, 1.2, 1.6 and 2.0 (Gaussian)

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Lévy (truncated) distributions in stock markets

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Wealth distribution in Japan (1998) Log-normal + power law

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The exponential + power law behavior (Dragulescu & Yakovenko, 2001)

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Wage distribution in Brazil

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GNI 2002 Global and per capita

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Other Power laws Earthquakes (Gutenberg – Richter law) Extinctions of species

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Inequality, Gini coefficient

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Gini coefficient Map

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Statistical Mechanics of Money Agents are molecules of an ideal gas, that exchange money as molecules exchange energy. This simple model (D-Y) delivers a Boltzmann – Gibbs (exponential) distribution Ch. et. al. introduced a kind of multiplicative noise: saving propensity and are able to obtain power laws distribution Critics: Economists: Money is not wealth. It is not a fundamental element in economics. Physicists: There is nothing new in obtaining B-G distribution from elastic collisions

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Each agent is characterized by a wealth-parameter (the fitness in the original model). Agents have closer ties with nearest neighbors. Rule to update the wealth: to look for the lowest wealth site, to select in a random way its new wealth, and to deduce (or add) the wealth difference from (to) 2k - nearest neighbors (NN-version) or to random neighbors (R-version). Global wealth is constant (conservative model). Agents may be in red (negative wealth) A Conservative SOC Model

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Exponential distribution with a poverty line Threshold 0.42 is the Poverty line

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Comparing the real world with the simulations

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A model with Risk Aversion A random (or not) fraction,, of the agent´s wealth is saved (A. Chatterjee et. al.) The site with the minimum wealth (w 1 ) exchanges with a random site (w 2 ) a quantity: Variation of the model: The winner takes all, he gets all the quantity dw This transaction occurs with probability of favor the poorer agent p, being either p fixed for all the agents or p given by: being f : 0 f 0.5 Ref: N. Scafetta, S. Picozzi and B. West, cond-mat/0209373v1 What happens? Condensation (or a frozen society, where just one agent concentrates all the wealth)

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Effect of Risk aversion and p exch Critical line for condensation (Moukarzel et al, 2006)

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Rule of minimum

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Moraleja Los pobres son pobres porque ganan poco… Los pobres son pobres porque ganan poco… Versión Susanita: Versión Susanita: Los pobres: ¿Cómo no van a ser pobres si compran nada más que porquerías Los pobres: ¿Cómo no van a ser pobres si compran nada más que porquerías

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Rule the winner takes all Rule WTA Rule minimum

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And if correlations are included between risk-aversion and expected profits (winning probabilities)? To appear in Physica A (2006)

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Rational agents We assume agents have previous knowledge of their winning probability and they adjust in order to minimize their harms.

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of Rational agents

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Wealth distribution of rational agents The poorer agent changes strategy N=100.000 agents initial wealth uniformly distributed {0,1000} Gini, red points

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Irrational agents

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Wealth distribution of irrational agents The richer agent changes strategy Power law exponent –1.125 Gini: green points, (blue points, poorer agent Change strategy)

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Complexity 9, 31 (2004)

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two

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Wealth depending interactions Agents only interact when their wealth is within a threshold u |w i -w k | < u

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Correlations between Wealth and Risk-aversion

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Gini coefficients

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Cooperation and competition Vanessa de Quadros, J.R. Iglesias 1.Agents are organized in economic groups (societies, enterprises, countries) 2.We consider a matrix of 20x20 groups 3.Neighboring groups can cooperate or compete between them. 4.Each time step each group has a return given by a Gaussian distribution. 5.The next time step the mean value of the gaussian is shifted proportional to the previous return, plus the average return of the cooperative neighbors minus the average return of competitive neighbors.

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AABABA ABBBAB ABAAAB BABABB AABAAB ABBABA Interaction Matrix

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Interacting groups (70% type A, 30% type B) AA or BB cooperate, AB compete

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GNI 2002 Global and per capita

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Continuará… Model on a network Game theory: theory of conflict. Conflict and cooperation Taxes and other regulatory mechanisms Correlation between inequalities and economic growth

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About exchange models: Man is an animal that makes bargains: no other animal does this - no dog exchanges bones with another Adam Smith About the realism of the model: El original es infiel a la traducción Jorge Luis Borges And finally…

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Some References 1.Pareto V (1897), Cours d'Economie Politique, Vol. 2, F. Pichou, Lausanne 2.Dragulescu A and Yakovenko VM (2000) Statistical Mechanics of Money, The European J. of Physics B 17:723 3.Pianegonda S, Iglesias JR, Abramson G and Vega JL (2003) Wealth redistribution with conservative exchanges Physica A: Statistical and Theoretical Physics 322:667 4.Pianegonda S and Iglesias JR (2004) Inequalities of wealth distribution in a conservative economy, Physica A: Statistical and Theoretical Physics 342:193 5.Chatterjee A, Chakrabarti BK and Manna SS (2004), Pareto Law in a Kinetic Model of Market with Random Saving Propensity, Physica A: Statistical and Theoretical Physics 335:155 6.Chakraborti A and Charkrabarti BK (2000) Statistical mechanics of money: how saving propensity affects its distribution, The European J. of Physics B 17:167 7.Iglesias JR, Gonçalves S, Pianegonda S, Vega JL and Abramson G (2003) Wealth redistribution in our small world, Physica A: Statistical and Theoretical Physics 327:12 8.Iglesias JR, Gonçalves S, Abramson G and Vega JL (2004) Correlation between risk aversion and wealth distribution, Physica A: Statistical and Theoretical Physics 342:186 9.Laguna MF, Risau Gusman S and Iglesias JR (2005) Economic exchanges is a stratified society: End of the middle class?, Physica A: Statistical and Theoretical Physics 356:107 10.Fuentes MA, Kuperman M and Iglesias JR (2006), Living in an Irrational Society: Wealth Distribution with Correlations between Risk and Expected Profits, to appear in Physica A

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