Wealth Distribution in a Network with Correlations Between Links and Success

Abstract

A study of the distribution of the income of workers, companies and countries was presented, a little more than a century ago, by Italian economist Vilfredo Pareto. He investigated data of personal income for different European countries and found a power law distribution that seems not to be dependent on the different economic conditions of the countries. In his book Cours d’Economie Politique [1] he asserted that in all countries and times the distribution of income and wealth follows a power law behaviour where the cumulative probability P(w) of people whose income is at least w is given by P(w) ∝ w −α, where the exponent α is named today Pareto index, while the power law is known as Pareto law. The exponent α for several countries was 1.2 ≤ α ≤ 1.9. However, recent data indicates that, even though Pareto’s distribution provides a good fit to the distribution of high range of income, it does not agree with observed data over the middle and low range of income. For instance, data from Japan [2, 3], Italy [4], India [5], Brazil [6], the United States of America and the United Kingdom [7, 8, 9] are fitted by a lognormal or Gibbs distribution with a maximum in middle range plus a power law for high income one.