Individual level and exhaustive income data for Romania (Cluj county) is analysed for several consecutive years. The income distributions collapse on a master-curve when a properly normalised income is considered. The Beta Prime distribution is appropriate to fit the collapsed data. A dynamical model based on a master equation with growth and reset terms is successful in explaining the observed distribution in a self-consistent manner, i.e. the growth and reset rates are evaluated from the same individual level data. Income distribution derived for other countries are following similar trends. The collapse on the master-curve is not perfect however, suggesting that for a more realistic modelling specific socio-economic characteristics have to be taken also into account. Significance StatementAlthough income inequalities are in the constant focus of many studies in ecnomics, sociology, mathematical modelling and econo-physics, presently we do not have a satisfactory description for the entire income distribution function. Here we provide an analytically treatable model that describes in a unified manner income distribution for all income categories. It is found that the properly renormalized income distributions collapse on a master-curve, which is a described by a Beta Prime distribution. As a consequence, the much-debated Pareto-exponent and its universality for the tail of the distribution function should be reconsidered.

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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.

Universalities and intriguing analogies in the statistics of avalanches are revealed for three physical systems defined on largely different length and energy scales. Earthquakes induced by tectonic scale dynamics, micro-scale level quakes observed from slipping crystallographic planes in metals and a one-dimensional, room-scale spring-block type Burridge-Knopoff model is studied from similar statistical viewpoints. The validity of the Gutenberg-Richter law for the probability density of the energies dissipated in the avalanches is proven for all three systems. By analysing data for three different seismic zones and performing acoustic detection for different Zn samples under deformation, universality for the involved scaling exponent is revealed. With proper parameter choices the 1D Burridge-Knopoff model is able to reproduce the same scaling law. The recurrence times of earthquakes and micro-quakes with magnitudes above a given threshold present again similar distributions and striking quantitative similarities. However, the 1D Burridge-Knopoff model cannot account for the correlations observed in such statistics.

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 situations. The gathered data is spanning two different periods from the communist economy and 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 these inequality measures are discussed in the context of the relevant socio-economic conditions. Keywords socio-economic inequalities • wealth distribution • master equation • Gini index • Lorenz curve • Pareto point