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DESIGUALDAD Y DISTRIBUCIÓN DE DESIGUALDAD Y DISTRIBUCIÓN DE LA RIQUEZA LA RIQUEZA
José Roberto IglesiasJosé Roberto IglesiasInstituto de Física y Faculdade de Ciências Instituto de Física y Faculdade de Ciências
Económicas, Económicas, U.F.R.G.S., Porto Alegre, BrazilU.F.R.G.S., Porto Alegre, Brazil
AFA, setiembre 2006, Villa de Merlo
Porto Alegre, Brasil
Geography Geography and Picturesand Pictures
Porto Alegre (30o S)
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
Master of the MintMaster of the MintWarden 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 MintIn 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
Louis BachelierLouis Bachelier (1870-(1870-1946)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.
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 valueS stock pricet expiring time volatilityr 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 Scholesand Fischer Black
Ved en trono a la noble igualdad….
Todos los hombres nacen iguales…
Pareto´s lawPareto´s law
Pareto’s lawPareto’s law
α)(
x
Ax N
Distribution lawsDistribution laws
xAx loglog)(log N
DistributionPower law
Exponential)exp()( αxAx N
Logarithmic Representation Straight line in log-log - is the slope
Straigth line in semi-
log - is the slope
αx
Ax )(N
Benoit Mandelbrot. Benoit Mandelbrot. The Variation of Certain Speculative Prices. Journal of Business 36: 394 (1963)
Lévy distributionsLévy distributions
Shape of the symmetric Lévy distribution with =0.8, 1.2, 1.6 and 2.0 (Gaussian)
Lévy (truncated) distributions in Lévy (truncated) distributions in stock marketsstock markets
Wealth distribution in Japan Wealth distribution in Japan (1998)(1998)
Log-normal + power law
The exponential + power law behavior(Dragulescu & Yakovenko, 2001)
Wage distribution in BrazilWage distribution in Brazil
GNGNII 200 2002 Global and per 2 Global and per capitacapita
Other Power lawsOther Power laws
Earthquakes (Gutenberg – Richter law)
Extinctions of species
Inequality, Gini coefficient
Gini coefficient MapGini coefficient Map
Rank CountryGiniindex
Richest 10%
to poorest 10%
Richest 20%
to poorest 20%
Survey
year1 Denmark
24.7
8.1 4.3 1997
2 Japan24.9
4.5 3.4 1993
3 Sweden 25 6.2 4 2000
4 Belgium 25 7.8 4.5 1996
5 Czech Republic25.4
5.2 3.5 1996
6 Norway25.8
6.1 3.9 2000
7 Slovakia25.8
6.7 4 1996
8Bosnia and Herzegovina
26.2
5.4 3.8 2001
9 Uzbekistan26.8
6.1 4 2000
10 Finland26.9
5.6 3.8 2000
11 Hungary26.9
5.5 3.8 2002
12Republic of Macedonia
28.2
6.8 4.4 1998
13 Albania28.2
5.9 4.1 2002
14 Germany28.3
6.9 4.3 2000
15 Slovenia28.4
5.9 3.9 1998
16 Rwanda28.9
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
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
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
Statistical Mechanics of Statistical Mechanics of “Money”“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) distributionCh. 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
wtwttw
wtwttw
jj
ii
)()(
)()(
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 A Conservative SOC ModelModel
Exponential Exponential distribution with a distribution with a
poverty linepoverty line
Threshold 0.42 is the “Poverty line”
Comparing the real Comparing the real world withworld with
the simulations the simulations
A model with Risk A model with Risk AversionAversion
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
])1(;)1min[( 2211 wwdw
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
12
12
2
1
ww
wwfp
What happens? Condensation (or a frozen society, where just one agent concentrates all the wealth)
Effect of Risk aversion Effect of Risk aversion and pand pexchexch
Critical line for condensation(Moukarzel et al, 2006)
Rule of minimumRule of minimum
])1(;)1min[( 2211 wwdw
12
12
2
1
ww
wwfp
MoralejaMoraleja
• Los pobres son pobres porque ganan Los pobres son pobres porque ganan poco…poco…
• Versión Susanita:Versión Susanita:• Los pobres: ¿Cómo no van a ser Los pobres: ¿Cómo no van a ser pobres si compran nada más que pobres si compran nada más que porqueríasporquerías
Rule the winner takes allRule the winner takes all
Rule WTA Rule minimum
And if correlations are included between risk-aversion and
expected profits (winning probabilities)?
To appear in Physica A (2006)
“Rational” agents
We assume agents have previous knowledge of their winning probability and they adjust in order to minimize their harms.
of “Rational” agents
Wealth distribution of rational agents
The poorer agent changes strategyN=100.000 agentsinitial wealth uniformly distributed {0,1000}
Gini, red points
“Irrational” agents
Wealth distribution of irrational agents
The richer agent changes strategyPower law exponent –1.125
Gini: green points,(blue points, poorer agentChange strategy)
Wealth Wealth depending depending interactionsinteractions
Agents only interact when their wealth is within a threshold u |wi-wk| < u
Gini coefficientsGini coefficients
Cooperation and competitionVanessa de Quadros, J.R. Iglesias
1. Agents are organized in economic groups (societies, enterprises, countries)
2. We consider a matrix of 20x20 groups3. 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.
AA AA BB AA BB AA
AA BB BB BB AA BB
AA BB AA AA AA BB
BB AA BB AA BB BB
AA AA BB AA AA BB
AA BB BB AA BB AA
Interaction Matrix
Interacting groups (70% type A, 30% type
B)AA or BB cooperate, AB compete
GNGNII 200 2002 Global and per 2 Global and per capitacapita
Continuará…
Model on a network
Game theory: theory of conflict. Conflict and cooperation
Taxes and other regulatory mechanisms
Correlation between inequalities and economic growth
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…
Some ReferencesSome References1. 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