Inequality in the Distribution of Wealth and Income as a Natural Consequence of the Equal Opportunity of All Members in the Economic System Represented by a Scale-Free Network
Authors: Ingersoll John G. 
Published: August 2024

The purpose of this work is to examine the nature of the historically observed and empirically described by the Pareto law inequality in the distribution of wealth and income in an economic system. This inequality is presumed to be the result of unequal opportunity by its members. An analytical model of the economic system consisting of a large number of actors, all having equal access to its total wealth (or income) has been developed that is formally represented by a scale-free network comprised of nodes (actors) and links (states of wealth or income). The dynamic evolution of the complex network can be mapped in turn, as is known, into a system of quantum particles (links) distributed among various energy levels (nodes) in thermodynamic equilibrium. The distribution of quantum particles (photons) at different energy levels in the physical system is then derived based on statistical thermodynamics with the attainment of maximal entropy for the system to be in a dynamic equilibrium. The resulting Planck-type distribution of the physical system mapped into a scale-free network leads naturally into the Pareto law distribution of the economic system. The conclusions of the scale-free complex network model leading to the analytical derivation of the empirical Pareto law are multifold. First, any complex economic system behaves akin to a scale-free complex network. Second, equal access or opportunity leads to unequal outcomes. Third, the optimal value for the Pareto index is obtained that ensures the optimal, albeit unequal, outcome of wealth and income distribution. Fourth, the optimal value for the Gini coefficient can then be calculated and be compared to the empirical values of that coefficient for wealth and income to ascertain how close an economic system is to its optimal distribution of income and wealth among its members. Fifth, in an economic system with equal opportunity for all its members there should be no difference between the resulting income and wealth distributions. Examination of the wealth and income distributions described by the Gini coefficient of national economies suggests that income and particularly wealth are far off from their optimal value. We conclude that the equality of opportunity should be the fundamental guiding principle of any economic system for the optimal distribution of wealth and income. The practical application of this conclusion is that societies ought to shift focus from policies such as taxation and payment transfers purporting to produce equal outcomes for all, a goal which is unattainable and wasteful, to policies advancing among others education, health care, and affordable housing for all as well as the re-evaluation of rules and institutions such that all members in the economic system have equal opportunity for the optimal utilization of resources and the distribution of wealth and income. Future research efforts should develop the scale-free complex network model of the economy as a complement to the current standard models.