Wealth Distribution in Villages. Transition From Socialism to Capitalism in View of Exhaustive Wealth Data and a Master Equation Approach

Abstract

Socio-economic inequalities derived from an exhaustive wealth distribution is studied in a closed geographical region from Transylvania (Romania). Exhaustive wealth data is computed from the agricultural records of the Sancraiu commune for three different economic periods. The data is spanning two different periods from the communist economy and gives a glance to the present situation after 31 years of free market economy in Romania. The local growth and reset model based on an analytically solvable master equation is used to describe the observed data. The model with realistically chosen growth and reset rates is successful in describing both the experimentally observed distributions and the inequality indexes (Lorenz curve, Gini coefficient, and Pareto point) derived from this data. The observed changes in the inequality measures are discussed in the context of the relevant socio-economic conditions.

Comments on Mathematical Aspects of the Biró–Néda Model

“…To conclude the present section, let us remark that, regardless of the differential equation for P 0 , the (nontrivial) stationary solution to be defined by (7) is not necessarily normalizable for arbitrary sequences {γ n }, {µ n }. In fact, taking γ n = µ n = e −n leads to Q n ∝ (e/2) n , which is clearly not summable.…”

“…Thus, S 0 = 1 is indeed satisfied for the simplest cases considered in Refs. [1,2,[5][6][7]15], and in particular for constant sequences {γ n }, with {µ n } being also constant or linearly growing with n, but it fails even for constant {γ n } sequences if {µ n } grows like n 1+ǫ .…”

“…In recent years, Biró, Néda, and collaborators have successfully applied a simple dynamical model to address the behavior of complex systems of a varied nature, including high energy physics systems, ecology, population distribution, scientific citations, and social media popularity [1][2][3][4]. In addition, particularly promising are more recent applications to income and wealth distributions [5][6][7]. These latter applications contribute to an ongoing effort to model social and economic phenomena by means of simple mathematical models, often inspired in statistical physics and stochastic processes (see e.g., [8][9][10]).…”

Tree size distribution as the stationary limit of an evolutionary master equation

“…This second scenario considering a state-dependent smart reset rate offers much more flexibility and it is more appropriate for modeling the tree growth dynamics in the ecosystems where our data was collected from. Such an attempt was considered recently for modeling the distribution of wealth and income in human societies 33,34 .…”

“…Based on the form of the µ(x) growth-and γ (x) reset rates, the LGGR model is able to reproduce stationary probability distributions, ρ s (x) , that are frequently encountered in complex systems 24,25,32,33 . The LGGR's mathematical apparatus has been comprehensively studied in recent years 24,25,31,39,40 , encompassing aspects of convergence and applicability to various fields of science 24,[32][33][34][35]41 .…”