Summary 

Using economic-mathematical methods, the paper investigates an unexplored problem of world economic sciences, such as determining the optimal level of the Gini coefficient reflecting social justice-injustice, under which conditions the sum of joint costs of social distribution of income will be minimal, and the sum of positive effects will be maximal. For this purpose, all possible costs, positive effects of equal and unequal income distribution and their dependence on the Gini coefficient were identified. We were given the opportunity to solve the problem by the fact that under conditions of growth of the Gini coefficient, the costs and positive effects of both equal and unequal distribution change in the opposite direction. In these conditions, the sum of each takes an extreme level for the determined critical value of the Gini coefficient. Based on the goals of the research, regularities between the analyzed events were determined, their corresponding algebraic functions were obtained, and their correspondence with real socio-economic processes was proved by mathematical analysis. The developed economic-mathematical method of optimal social distribution of incomes is presented in such a way that its practical application does not represent a great difficulty.

Key words: equal and unequal distribution of income, social justice and injustice, symmetry of positive and negative consequences of equal and unequal distribution of income, optimal combination of social justice and equality, optimal value of the Gini coefficient, economically feasible socially just equality.