A Framework for Studying Demand in Hierarchical Networks (Preliminary draft∗)

The aim of this preliminary draft paper is to identify a framework for studying demand in hierarchical networks. A specific choice of technical conditions are given for precisely formulating four equivalent well-known ways to specify the demand of a buyer: by a demand function, an inverse demand function, a valuation function, or a demand set. Unimodality (or quasi-concavity) of profit is a basic property insuring the ability of a seller to find a profit maximizing operating point. Conditions on the demand of a buyer are identified which insure that the profit of a seller with fixed production cost is a unimodality function, of either the price set or quantity sold. Five methods are identified for aggregating the demand of a buyer, and three methods are indentified for combining competing sellers.