MATHEMATICAL MODEL OF THE OPTIMAL MARKET OF ONE GOODS
Abstract
The market process consists of many acts of exchange of goods and services. Each such act involves a seller, on whose side there is a supply of goods, and a buyer, represented by a demand for goods. Of course, supply and demand are closely related and continuously interacting categories and serve as a link between production and consumption. The result of the interaction of supply and demand is the equilibrium price. It characterizes the state of the market in which the volume of demand is equal to the supply. To determine the point of market equilibrium and study the dynamics of commodity prices in the process of market transition from some non-equilibrium to equilibrium is considered, in addition to demand lines, the criterion of optimal behavior of the seller in the market. In a competitive market in which there are a large number of buyers and sellers, we determine the equilibrium price, excluding prices at which a surplus or shortage of a product is formed. So, at a high price, manufacturers want to produce a large amount of a product, but buyers are ready to purchase only a small amount of a product, and overproduction occurs. At a low price, buyers are ready to purchase a large amount of a product, but manufacturers are ready to produce a small amount of goods, and there is a shortage of goods and services. At a certain average price, an equilibrium price, producers are ready to produce exactly as much as consumers wish and are able to purchase. There is no surplus in the market, in which the market would push the price of a product down, nor does a shortage of a product arise, in which the market does not cause an increase in the price of a product. At such an equilibrium price, the amount of supply and demand is balanced. The article analyzes the mathematical model of the optimal market in the case of one product. To achieve this goal, the paper analyzes the theory and problems of market modeling. The supply-demand model is built in accordance with a system of recommendations for economic behavior in the market, and is represented by a nonlinear problem of mathematical programming. By combining mathematical models of supply and demand, the mathematical model of the market solves the issue of purposefulness of market participants in the aggregate. Its solution is based on the normalization of criteria and the principle of a guaranteed result. The methodology for modeling the market, taking into account the functions of supply and demand, includes setting a problem, building a model and directly forecasting.
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