A Study of Demand Functions of Mutually Substitutable Products and Pricing Models

A good model of the relationship between the market demand and prices plays a very important role in economic decision-making. In this work we shall state four basic requirements which should be satisfied by any realistic demand function. The fourth of these is apparently new: essentially it requires that the total demand for substitutable products in a closed system should not increase for any increase in prices. We shall justify the importance of this requirement and design a realistic model of demand functions for a system of mutually substitutable products. Such a model is needed to assist all sellers/companies involved in the market to set different prices for these products. In this paper, we formulate the demand functions facing all sellers using a Linear Complementarity Problem (LCP). We will consider a competitive market, where all sellers are playing a non-cooperative game, and this model of demand functions will be incorporated into the best response problem of each seller involved. This leads to a complementarity constrained pricing problem facing each seller. It will be shown that the complementarity constraints in this pricing model can be eliminated in some instances, while in other instances, elimination of such constraints will lead to an inferior pricing model.