Mathematical Marketing

Abstract

The subject of this chapter is a type of model known as a Random Utility Model, or RUM. RUMs are very widely applied marketing models, especially to the sales of frequently purchased consumer packaged goods; in other words; the kind of stuff you see in a supermarket. All of the models in this chapter logically follow from Thurstone's Law of Comparative Judgment that we covered in Chapter 12. However, in this chapter we will consider the situation in which consumers pick one brand from a set of more than two brands, and we will also contemplate distributions other than the normal. We can summarize the assumptions of Thurstone's Law, and of the models in this chapter, as follows: Assumption one is that choice is a discrete event. What this means is that choice is all-or-nothing. The consumer, as a rule, cannot leave the supermarket with .3432 cans of Coke and .6568 cans of Pepsi. They will tend to leave with 1 can of their chosen brand, and 0 cans of their not chosen brand. Thus choice is not a continuous dependent variable. Assumption two is that the attraction or utility towards a brand varies across individuals as a random variable. In Thurstone's Law, we called this the discriminal dispersion and we assumed it was normal. By using the term utility, we are being consistent with economic theory. We also fequently use the term attraction, we are being consistent with the retailing literature. In any case, assumption two is all about the word " random " in the label random utility model.