Model for a hierarchically organized market functioning perfectly

We propose a model for a market which structure is of the tree form. Each branch of the tree is made of identical firms, its root (the branch of the first level) is formed by firms producing raw materials, and the branches of the last level are the retail outlets. The branching points (tree nodes) are micromarkets for firmsvforming branches connected with a given node. Prices and the production rate are controlled by the balance 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 whose extremal gives the governing equations for the given market. It turns out that this ideal market is degenerated with respect to its structures.