Mechanism of Self-regulation in a Simple Model of Hierarchically Organized Market

Abstract

We propose a model for a market which structure is of the tree form. Each branch of the tree is composed by identical firms, its root (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 ballance in supply and demand, the competition is assumed to be perfect. We show that such a market functions perfectly: the prices are specified by the production expense only, whereas demand determines the production rate. We construct an efficiency functional which extremal 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 market functions ideally: the prices are determined by the costs on production of the goods, and the level of production of the goods of any kind defined only by demand for the goods of this sort.