A STUDY OF THE MARKET OF THREE INTERCHANGEABLE GOODS FOR SUSTAINABILITY

Abstract

This paper presents a study of the market dynamics of three interchangeable goods based on a mathematical model that takes into account the interaction between sellers, buyers and the state. The stability of the equilibrium state of the system for different values of the model parameters is analyzed. Analytical expressions for conditions of equilibrium stability were obtained. The impact of demand elasticity and taxation on market stability is studied. It is shown that, under certain conditions, even a small change in model parameters can lead to a loss of equilibrium. The dynamic model of the competitive market of three interchangeable goods is presented as a system of nonlinear ordinary differential equations with respect to the price vector. The model is built on the basis of accounting for the economic forces of sellers, buyers, the state and the economic forces of competition. The functional expressions of such forces are used, taking into account the economic laws of the commodity market. In the model, it is assumed that the volume of sales is a function of the price, which depends on the elasticity parameters, and the economic system is in equilibrium. The problem of equilibrium stability in the main and in the critical case of one zero root is studied. The conditions of asymptotic stability of the equilibrium are defined for the general case and for individual cases with different assumptions about the parameters of the model. The conditions of sustainable market development for symmetric and overlapping characteristics of competing goods are obtained. The results of the study showed that the stability of the market depends significantly on such factors as the elasticity of demand, the level of taxation and the intensity of competition. The figure shows regions of stability and instability of equilibrium depending on the values of the main parameters of the model. The obtained results can be used to develop recommendations for regulating the market and forecasting its behavior in various economic conditions.