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