Probabilistic approach to mathematical description of market equilibrium

The article is focused on a probabilistic model of market equilibrium that allows for the change in time of the market price of the goods. The demand and supply are shown to be fully determined using the following random variables: the points in time of goods delivery to the market by producers; the points in time of goods purchase by consumers; the purchasing power of the consumer; the cost price of the producer's goods. In these terms, there has been derived an equation determining the dependence of the equilibrium market price on time. In the case when the laws of distribution of purchasing power and the cost price of goods coincide, the analytical expression describing the dynamics of the equilibrium market price can be found and the conditions under which this dynamics is stable can be determined. Numerical simulation of the found solution for several particular distribution laws of four above-mentioned random variables was carried out. Within the framework of the proposed model, the time dependence is found that approximates the real price dynamics for the Apple iPhone 6S Plus 16Gb smartphone, which was observed during the period from September 2015 to April 2018. The proposed model possesses practical significance in terms of ability to make decisions on practicability of purchasing (producing) goods in different points of the time, i.e. optimize expenses brought by purchasing (producing) of the goods.