Mathematical modeling of probability distribution of money by means of potential formation

The work is devoted to the development of a mathematical model for studying the probability distribution of money of an agent. The model is based on the Fokker–Planck equation. To calculate the diffusion term, we used the quadratic dependence of the money balance of an agent in the Yakovenko model. To calculate the drift term, we propose to use a function (potential) that takes into account the income (i.e. the influx of money) and expenditures (i.e. the outflow of money) for an agent. For an analytical description of the income of an agent, a linear dependence on money balance was used. Expenditures were characterized by the demand for essential goods, long-term and luxury goods. Tornquist functions were used to describe the demand functions. The construction of the potential made it possible to identify atypical conditions for the formation of the probability distribution of money.