New model of understanding income distribution through graduation of normalized Gini Mean Difference

Abstract

This work covers such a topical problem as the study of income and wealth inequality. It introduces the notion of “graduation”, i.e. rate of wage rate scale customary at time wage system. Graduation means introduction of the index m as a degree of the polynomial based on which the wage rate scale is distributed. In other words, using m allows to graduate Gini mean difference (0<G<1) by assigning integral number or fraction m, 0<m<∞ to every value of Gini index. Similarly, for each m we can calculate and estimate corresponding normalized Gini mean difference (the analog of Gini index used for simplicity of calculations).
Note that in this case we are not talking about distribution in real society, but in the simplest model of this society – a metaphoric community with only one person at each income level. This way we get the most distinct impression of the mechanism of income distribution that gives us the chance to assess scale of inequality. To some extent it clarifies the wide-spread Gini coefficient and “the nature of populations’ wealth”.