Advertising in a segmented market: comparison of media choices

Abstract

Segmentation is a core strategy in modern marketing but, to the best of our knowledge, it is not considered in most dynamic advertising models. In this paper we aim at filling such a gap and we present a dynamic advertising model which includes market segmentation. First, we model the goodwill evolution in a segmented market under the assumption that the decision maker may choose independently the advertising intensity directed to each different segment. Then, we assume that the decision maker has to use a single medium, which reaches several segments with different effectiveness. We obtain the explicit solutions of the relevant optimal control problems. These results permit us to compare the two different contexts and to obtain a preference index for advertising media.

Advertising and production of a seasonal good for a heterogeneous market

“…Although the infinite horizon formulation is the natural setting for the analysis of some dynamic optimization problems in advertising, as for instance in the recent papers (Jørgensen et al, 2001), (Weber, 2005), (Grosset and Viscolani, 2008), there are special situations for which a finite horizon formulation is obviously needed. Examples of this case are advertising for an event, as in (Jørgensen et al, 2006), introducing a new product, as in (Buratto et al, 2006a), and advertising for a seasonal product, as in (Favaretto and Viscolani, 2004).…”

“…Nevertheless, market segmentation is not well represented in mathematical models in advertising, and in particular in the literature on optimal control models (Feichtinger et al, 1994;Jørgensen and Zaccour, 2004). Buratto, Grosset and Viscolani have brought some market segmentation concepts into models concerning the advertising process while introducing a new product in a market (Buratto et al, 2006a,b), and the advertising process for sales over an infinite horizon (Grosset and Viscolani, 2008). Here we want to do the same in the context of an advertising and production problem for a seasonal product with Nerlove-Arrow's linear goodwill dynamics (Nerlove and Arrow, 1962), which has been discussed widely under the usual assumption of a homogeneous market (Favaretto et al, 1996;Favaretto and Viscolani, 1997, 1999.…”

When does a royalty clause with a guarantee lead to a no‐equilibrium situation in a licensing contract?

“…Nevertheless, it is quite a common hypothesis in the literature dealing with the goodwill stock models for marketing strategies (see, e.g., [12]). Furthermore, in more sophisticated models, as for example, in the age-sensitive model in [13] and in the advertising plan for a segmented market in [14], this type of assumption permits analytical tractability, and this will be also the case of our model.…”

“…After plugging the optimal advertising strategies (13) and (14) in the motion (3) and solving it with the initial condition (5), we obtain…”

“…N p 2 , N q 2 / D .1, 0/. If R 6 min¹rS .1,0/ .T /, rS .1 r, r/ .T /º, then there exists a unique Stackelberg equilibrium with optimal advertising strategies a l .t /, a L .t / described in (13) and (14) with . N p 2 , N q 2 / D .1 r, r/.…”