 Derivation of the Pareto Index in the Economic System as a Scale-Free Network and Introduction of New Parameters to Monitor Optimal Wealth and Income DistributionsJohn G. Ingersoll ()
Economies, 2025, vol. 13, issue 11, 1-27 Abstract: The purpose of this work is twofold: first, it aims to derive an exact analytical form of the Pareto index based on the already developed model of the economy as a scale-free network comprising a given amount of either wealth or income (total number of links, each link representing a non-zero amount or quantum of income or wealth) distributed among its variable number of actors (nodes), all of whom have equal access to the system), and second, it aims to employ the derived analytical form of the Pareto index to determine the degree to which the observed inequality in wealth and in income as measured by the respective empirical values of the Pareto index is inherent in the economic system rather than the result of externally imposed factors invariably reflecting a lack of equal access. The derived analytical form of the Pareto index for wealth or for income is described by an exponential function whose exponent is the inverse of the average number of wealth or of income per actor (one-half of the average number of links per node) in the economic model. This exponent features prominently in the scale-free model of the economy and has a numerical value of 0.69 when the Pareto index attains a numerical value of 2, which signifies the optimal, albeit still unequal, distribution of wealth or of income in the economy under the condition of equal access. Because of the correspondence of the scale-free model of the economy to a physical system comprising quantum particles such as photons in thermodynamic equilibrium or state of maximum entropy in accordance with the laws of statistical mechanics, the inverse of the exponent is proportional to the temperature of the economic system, and a new parameter introduced to describe in a comprehensible manner the deviation in the economic system from its optimal distribution of wealth or income. A comparison of the empirical wealth and income Pareto indexes based on economic data for the four largest economies in the word, i.e., USA, China, Germany, and Japan, which account for over 50% of the global GDP, versus the corresponding optimal values per the scale-free model of the economy reveals interesting trends that can be explained away by the prevailing degrees of equal access, as manifested by inadequate education, health care, and housing, as well as the existence of rules and institutions favoring certain actors over others, particularly with regard to the accumulation of wealth. It has also been determined that the newly introduced parameters in the scale-free model of the economy of temperature as well as the quanta of wealth and of income should be expressed in power purchase exchange rates for meaningful comparisons among national economies over time. Keywords: inequality; income; wealth; scale-free network; Pareto index; equal opportunity; entropy; temperature; quantum; Boltzmann distribution (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:gam:jecomi:v:13:y:2025:i:11:p:310-:d:1783703 Access Statistics for this article Economies is currently edited by Ms. Hongyan Zhang More articles in Economies from MDPI |
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