The influence of consumer recommendations on advertising strategies in a non-linear optimal goodwill model with market segmentation

We propose a new dynamical model of product goodwill. It is assumed that the product is sold in many market segments. The segments here are distinct according to the age of the consumers. We take into account the fact that the product goodwill in a segment of new consumers strongly depends on: the level of product goodwill in existing consumer segments, on consumer recommendations, and on advertising efforts which are diverse for different market segments and times. In our optimal control model, the control variables are the company’s advertising efforts in order to maximize its profits. The optimal solution of this model is obtained by the use of the maximum principle. Additionally, the sensitivity of this solution to different analytical forms of consumer recommendation functions is briefly analysed