Economic sciences / 8. Mathematical methods in economy

Gimanova I.A., Litvin N.V.

The Khakas State University named after  N.F.Katanov, Russia

INTERACTIONS OF ECONOMIC AGENTS IN INTERMEDIARY ACTIVITY

 Annotation. The given research belongs to researches considering the appendix of the theory of counts and the theory of the ordinary differential equations, describing the channels of trade distribution and intermediary network. Such researches will allow the companies of a network to monitor prices dynamics and sales volumes constantly. They will also help to make the decision of the best distribution of available resources and to choose the best direction to increase the competitive stability and to expand the influence of a consumer market.

Various interaction approaches of economic agents in a chain of intermediary activity are considered in this paper. It is offered to apply the theory of counts, methods of research of the ordinary differential equations and stability criteria of linear systems to research trade systems.

Interaction of the buyer and the seller in the market is an interesting and hot topic for research. This question draws attention to that the way of goods from the producer to the end user can be considered using system approach. Within the trade and economic system participants interact, possessing different purposes and preferences. Therefore throughout the development of economic science researchers have been developing models and theories how (descriptive theories) interact or (standard theories) economic agents have to interact.

The goods movement from the producer to the consumer becomes so difficult that there are extensive intermediary networks which are engaged in the goods distribution and the delivery to the end user. The structure of these networks plays a crucial role in definition of what goods will be offered in the market, i.e. goods competitiveness and consumption volumes in various regions. The choice of distribution channels and goods delivery to the end user is actual and strategically important direction in the development of business for all participants of a network. The most responsible role belongs to the producer who considers the risk factor of merchandising, estimates expenses and profits, makes the decision how to choose the structure of a distribution system in the market.

Network formation models between producers, intermediaries and consumers have been considered by various authors who have drawn more attention to different aspects and motives of distribution networks formation. It is possible to analyze trade and intermediary system as commodity distribution, logistic, network, multiagent, exchange one.

K. Begvell and R. Steydzher, S. Goyal and S. Yosha, T. Furusava and H. Konisha and other scientists research the questions of agreements structure formation on duty-free trade (free trade networks) between the countries and the influence of this structure on public welfare.

In K. Kubota's research [1] the influence of network eksternaliya of more general nature on processes of negotiations between economic subjects and on formation of free trade networks have been considered. Some reasons of network distribution formation are called the expenses connected with receiving and processing of information about suppliers and buyers.

In S. Guriev, I. Pospelov and M. Shakhova's article [2] processes of distribution networks self-education in economies with imperfect infrastructure are considered. In R. Krenton and D. Maynkhart [3] article the model of trade agreement formation between suppliers and buyers is considered where economy efficiency with free competition is limited by means of these agreements.

In X. Konisha article [4] and R. Dzhokhari's, and in Sh. Mennor, and J. Tsitsiklis research [5], the main reason of distribution network formation is transportation costs on goods movement from suppliers to consumers.

In article [6] the author consider the model of distribution network formation between geographically distributed agents of the companies who can produce goods, sell it in "the" market or resell to other companies, having transport costs on the basis of the games theory.

Network market models have found broad application in experimental economy. Researches of A. Nagurnya [7] are devoted to network models of economy where the author consider the principles of economy network functioning, gives the characteristic of the market of information services and products, makes the analysis of priority and new types of the information technologies allowing to organize information exchange between network knots, describes the principles of pricing in the new information market.

Economic theories carry out the application of mathematical apparatus of state equilibrium of economic systems and reduce their statements when one speaks about crises and other unstable states in economy [8].

Nowadays the price is one of the least developed categories. It is discussed in various publications devoted to questions of the price theory and practice of pricing testifies. It is known that the prices aren't in balance, and constantly make fluctuations. Last time researches spent a lot of efforts to create the models of the adequate description of exchange prices fluctuation. But the reason of these fluctuations isn't considered. Economists consider it is enough to explain that the prices strive to balance, and prices fluctuation is connected with casual exchange acts. But if these fluctuations don't fade in a balance point, the point isn't steady. At the same time, fluctuations happen not randomly, but round the most unstable equilibrium point, i.e. the movement – is steady [9].

Unstable states describe the nonlinear differential equations truely. In economic science the similar mathematical apparatus is practically not applied, generally it is the games theory and optimization. Knowledge of various methods and models of pricing will allow the intermediary of a distribution network to react in the best way to the changing market conditions and to make optimum decisions during the change of purchases volumes and sales prices.

According to researches [10-12], it is possible to present a single trade system of sales of the same goods as networks where elements are producers, intermediaries and consumers. Distribution of commodity streams is carried out from the producer, through intermediaries, to end users under the influence of supply and demand. Subjects of a distribution network can be presented  as sources and consumers of commodity streams: producers (sellers) – sources; intermediaries – both sources, and consumers; end users – only consumers. End users combine various groups and can be attached to some of the micromarkets. The goods distribution system connects the subjects of the market together. "Joint" the intermediary consumer or the intermediary producer is the micromarket where which each of participants receives information about the price, volumes of purchase and sale, number of participants, etc.

Empirical researches of trade statistics according to the method offered by A.A.Shananin [13] have shown that the behavior of all consumers of the country for decades can be described as rational behavior of one consumer with a certain function of consumption usefulness [14]. Having the network of commodity streams distribution as set of the micromarkets connected between them through the subjects of the market it is possible to make structural model.

The looked-through stream processes can be considered in statics and dynamics. To model a dynamic model, it is chosen such a tool as the ordinary differential equations which allow to estimate the prices in knots of a distribution network and volumes of the goods streaming along the branches, to research the stability of interrelation between the buyer and seller.

Using the graph model of a network, considering sequence and parallelism of connections of elements it is possible to construct the integro-differential equations [11], that allows to receive qualitative characteristics, to calculate the course of real process interaction between the buyer and seller, to predict further behavior of system and research its stability.

Literature:

1.     Kubota K. Trade negotiation in the presence of network externalities. Papers of World Bank Country Economics Department, 1999.

2.     Guriev S., Pospelov I., Shakhova M. Self-organization of Trade Networks in an Economy with Imperfect Infrastructure. Series "Computing in Economics and Finance" of Society of Computational Economics, 1996.

3.     Kranton R., Minehart D. A theory of Buyer-Seller Networks. Unpublished manuscript. 2000.

4.     Konishi H. Uniqueness of User Equilibrium in TransportationNetworks with Heterogeneous Commuters. Unpublished manuscript, 2002.

5.     Johari R., Mannor S., Tsitsiklis J. A Contract-Based Model for Directed Network Formation. Unpublished manuscript, 2003.

6.     Губко М.В. Рыночное равновесие в задаче формирования торговой сети. / Управление большими системами. Выпуск 7.  - М.: ИПУ РАН, 2004. -  С.17-32.

7.     Nagurney А. Network Economics: А Variational Inequality Approach, second revised  edition Dordrecht. - Netherlands: Kluwer Academic Publishers, 1999.

8.     Чеканский А.Н. Фролова Н.Л. Теория спроса, предложения и рыночных структур. - М.: Экономический факультет МГУ, ТЭИС, 1999. - 421 с.

9.     Куснер Ю.С., Царёв И.Г. Принципы движения экономической системы. - М.: ФИЗМАТЛИТ, 2008. - 200 с.

10. Дулесов А.С. Линейные пассивные цепи торговой системы. // ПИР-2005. Материалы 9-ой Всероссийской научно-практической конференции. Т.2.  Красноярск, 2005.

11. Дулесов А.С., Курынова И.А. Упрощённая математическая модель регионального потребительского рынка одного товара // Современные проблемы науки и образования. – 2012. – № 4; URL: www.science-education.ru/104-6595 (дата обращения: 08.10.2015).

12. Гиманова И.А. Моделирование процессов обмена в торговых системах // Вестник Московского университета им. С.Ю. Витте. Образовательные ресурсы и технологии. - 2016. - №2(14). - С. 300-303

13. Петров А.А., Поспелов И.Г., Шананин А.А. Опыт математического моделирования экономики. - М.: Энергоатомиздат,1996. -  544 с.

14. Поспелов И.Г. Модели экономической динамики, основанные на равновесии прогнозов экономических агентов.  М.: ВЦ РАН, 2003. -  204 с.