DESIGUALDAD Y DISTRIBUCIÓN DE LA RIQUEZA

1. 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

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

3. 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

4. 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

5. 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.

6. F. Black & M. Scholes:The pricing of options and corporate liabilities.J. Pol. Econ. 81(1973) 637 Myron Scholes and Fischer Black 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

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

8. Pareto´s law

9. Pareto’s law

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

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

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

13. Lévy (truncated) distributions in stock markets

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

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

16. Wage distribution in Brazil

17. GNI 2002 Global and per capita

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

19. Inequality, Gini coefficient

21. Gini coefficient Map

22. Rank Country Giniindex Richest 10%to poorest 10% Richest 20%to poorest 20% Surveyyear 1 Denmark 24.7 8.1 4.3 1997 2 Japan 24.9 4.5 3.4 1993 3 Sweden 25 6.2 4 2000 4 Belgium 25 7.8 4.5 1996 5 Czech Republic 25.4 5.2 3.5 1996 6 Norway 25.8 6.1 3.9 2000 7 Slovakia 25.8 6.7 4 1996 8 Bosnia and Herzegovina 26.2 5.4 3.8 2001 9 Uzbekistan 26.8 6.1 4 2000 10 Finland 26.9 5.6 3.8 2000 11 Hungary 26.9 5.5 3.8 2002 12 Republic of Macedonia 28.2 6.8 4.4 1998 13 Albania 28.2 5.9 4.1 2002 14 Germany 28.3 6.9 4.3 2000 15 Slovenia 28.4 5.9 3.9 1998 16 Rwanda 28.9 5.8 4 1983 17 Croatia 29 7.3 4.8 2001 18 Ukraine 29 6.4 4.3 1999 19 Austria 30 7.6 4.7 1997 20 Ethiopia 30 6.6 4.3 1999

23. 85 Ecuador 43.7 44.9 17.3 1998 86 Uruguay 44.6 18.9 10.4 2000 87 Cameroon 44.6 15.7 9.1 2001 88 Côte d’Ivoire 44.6 16.6 9.7 2002 89 People's Republic of China 44.7 18.4 10.7 2001 90 Bolivia 44.7 24.6 12.3 1999 91 Philippines 46.1 16.5 9.7 2000 92 Costa Rica 46.5 25.1 12.3 2000 93 Guinea-Bissau 47 19 10.3 1993 94 Dominican Republic 47.4 17.7 10.5 1998 95 Madagascar 47.5 19.2 11 2001 96 The Gambia 47.5 20.2 11.2 1998 97 Burkina Faso 48.2 26.2 13.6 1998 98 Venezuela 49.1 62.9 17.9 1998 99 Malaysia 49.2 22.1 12.4 1997 100 Peru 49.8 49.9 18.4 2000 101 Malawi 50.3 22.7 11.6 1997 102 Mali 50.5 23.1 12.2 1994 103 Niger 50.5 46 20.7 1995 104 Nigeria 50.6 24.9 12.8 1996 105 Papua New Guinea 50.9 23.8 12.6 1996 106 Argentina 52.2 39.1 18.1 2001

24. 107 Zambia 52.6 41.8 17.2 1998 108 El Salvador 53.2 47.4 19.8 2000 109 Mexico 54.6 45 19.3 2000 110 Honduras 55 49.1 21.5 1999 111 Panama 56.4 62.3 24.7 2000 112 Zimbabwe 56.8 22 12 1995 113 Chile 57.1 40.6 18.7 2000 114 Colombia 57.6 57.8 22.9 1999 115 Paraguay 57.8 73.4 27.8 2002 116 South Africa 57.8 33.1 17.9 2000 117 Brazil 59.3 68 26.4 2001 118 Guatemala 59.9 55.1 24.4 2000 119 Swaziland 60.9 49.7 23.8 1994 120 Central African Republic 61.3 69.2 32.7 1993 121 Sierra Leone 62.9 87.2 57.6 1989 122 Botswana 63 77.6 31.5 1993 123 Lesotho 63.2 105 44.2 1995 124 Namibia 70.7 128.8 56.1 1993

25. 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

26. A Conservative SOC Model • Each agent is characterized by awealth-parameter(the“fitness”in the original model). Agents have closer ties with nearest neighbors. • Rule to update the wealth: to look for thelowest wealthsite, 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 inred (negative wealth)

27. Exponential distribution with a poverty line Threshold  0.42 is the “Poverty line”

28. Comparing the real world with the simulations

29. A model with Risk Aversion What happens? Condensation (or a frozen society, where just one agent concentrates all the wealth) • A random (or not) fraction, , of the agent´s wealth is saved (A. Chatterjee et. al.) • The site with the minimum wealth (w1) exchanges with a random site (w2) 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 agentp, 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

30. Effect of Risk aversion and pexch Critical line forcondensation (Moukarzel et al, 2006)

31. Rule of minimum

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

33. Rule the winner takes all Rule minimum Rule WTA

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

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

37.  of “Rational” agents

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

39. “Irrational” agents

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

41. Wealth depending interactions Agents only interact when their wealth is within a threshold u |wi-wk| < u

42. Gini coefficients

43. Cooperation and competition Vanessa de Quadros, J.R. Iglesias • Agents are organized in economic groups (societies, enterprises, countries) • We consider a matrix of 20x20 groups • Neighboring groups cancooperateorcompetebetween them. • Each time step each group has areturngiven by a Gaussian distribution. • The next time step the mean value of the gaussianis shiftedproportional to the previous return,plusthe average return of thecooperative neighborsminusthe average return ofcompetitive neighbors.

44. Interaction Matrix

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

46. GNI 2002 Global and per capita

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

48. And finally… 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

49. Some References • Pareto V (1897), Cours d'Economie Politique, Vol. 2, F. Pichou, Lausanne • Dragulescu A and Yakovenko VM (2000) Statistical Mechanics of Money, The European J. of Physics B 17:723 • Pianegonda S, Iglesias JR, Abramson G and Vega JL (2003) Wealth redistribution with conservative exchanges Physica A: Statistical and Theoretical Physics 322:667 • Pianegonda S and Iglesias JR (2004) Inequalities of wealth distribution in a conservative economy , Physica A: Statistical and Theoretical Physics 342:193 • 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 • Chakraborti A and Charkrabarti BK (2000) Statistical mechanics of money: how saving propensity affects its distribution, The European J. of Physics B 17:167 • 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 • 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 • 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 • 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