On statistical modeling of random distribution of funds against various conditions

Introduction. The survey simulates a number of real financial and economic processes in their extreme manifestation of no control (randomness) with some idealization (provided initial capitals are equal, interactions are linear by their multiplicative nature, working coefficients are arbitrary chosen, etc.). Purpose. The research aims at investigating random distribution of funds within a statistical ensemble of participants with subsidized and donor regimes, when the total capital increases or decreases (the regimes are defined by two parameters of the multiplicative change in the capital). Results. Dynamics of relative distribution of capital by five groups of relative wellbeing is calculated. When two participants randomly meet, commercially determined models imply the transfer of a certain part of the capital from a participant with a smaller capital to a participant with a larger capital (provided the participants interact). When conditions are equal, a certain part of the capital is transferred from a participant with a large capital to a participant with a smaller capital. All regimes are found to show an initial short-term growth of the group with large capitals in the system, which is then (except for equal conditions) dominated by the group with the smallest capitals. The results illustrate that 1) if no mixing occurs, one could observe a very smooth transition to the dominance of the poorest group; this transition is slower in the donor regime and faster in the subsidized regime; 2) once the ensemble or its part interact with the environment and mix in commercial conditions in both regimes, one could observe a smooth transition to the dominance of the poorest group; 3) equal conditions give an abrupt transition to the dominance of the group with a middle-sized capital. If the ensemble’s members which have not yet interacted with the environment interact with others within a group, then both commercial and equal (somewhat stronger) conditions give a smooth transition to the dominance of the poorest group. This transition is slower in the donor regime and faster in the subsidized regime. Conclusions. At first guess, the results of this work could be used to interpret some economic elements in the national history.