Self-regulation in a Simple Model of Hierarchically Organized Markets
V. V. Gafiychuk
Institute of Applied Problems of Mathematics and Mechanics,
National Academy of Science of Ukraine,
3b. Naukova St. L'viv, 290601, Ukraine
I. A. Lubashevsky
Yu. L. Klimontovich
Moscow State University,
Department of Physics, Vorobievy Gory,
Moscow, 119899, Russia
Abstract
We study a model for a market which has a tree form structure. Each branch of the tree is composed of identical firms. The branch of the first level is formed by the firms producing raw material, and the branches of the last level are the retail outlets. The branching points (tree nodes) are micromarkets for firms forming branches connected with a given node. The prices and the production rate are controlled by the balance in supply and demand. Due to the material conservation law the network nodes in such a market function perfectly: the prices are specified by the production expense only, whereas demand determines the production rate. We construct an efficiency functional with an extremal that gives the governing equations for the market. It turns out that this ideal market is degenerated with respect to its structure. It is shown that such a market functions ideally: the prices are determined by the costs of producing the goods, and the level of production of goods of any kind is defined only by demand. We propose a simple model of trade interaction among firms which are able to join together in order to decrease total cost. It is shown that self-organization, due to optimization of each firm's profit, leads to hierarchical organization of the trade network.
