A Mathematical Model of Consumers' Buying Behaviour Based on Multiresolution Analysis

Abstract

In this paper we have presented a generalized mathematical model of consumers' buying behaviour. This model provides better insights and perceptions that can be used to take many important managerial decisions for any product to improve the buying behaviour of consumers towards that product. In this paper we have proved that consumers' buying behaviour is a L2(ℝ) function. Such functions can take two values. 1 (if the buying behaviour is satisfied) or 0 (if the buying behaviour is not satisfied). Through multiresolution analysis (MRA), we have proved that all the factors affecting consumers' buying behaviour are the subspaces of L2(ℝ). We have also proved that the satisfaction of consumers' buying behaviour is convex with respect to all the factors that affect it. We have given a relationship among all the factors influencing consumers' buying behaviour.We have provided a way by which the overall inclination of buying behaviour of any consumer or his inclination towards any particular product can be investigated.