Optimal Goodwill Model with Consumer Recommendations and Market Segmentation

We propose a new dynamic model of product goodwill where a product is sold in many market segments, and where the segments are indicated by the usage experience of consumers. The dynamics of product goodwill is described by a partial differential equation of the Lotka–Sharpe– McKendrick type. The main novelty of this model is that the product goodwill in a segment of new consumers depends not only on advertising effort, but also on consumer recommendations, for which we introduce a mathematical representation. We consider an optimal goodwill model where in each market segment the control variable is the company’s advertising efforts in order to maximize its profits. Using the maximum principle, we numerically find the optimal advertising strategies and corresponding optimal goodwill paths. The sensitivity of these solutions is analysed. We identify two types of optimal advertising campaign: ‘strengthening’ and ‘supportive’. They may assume different shapes and levels depending on the market segment. These experiments highlight the need for both researchers and managers to consider a segmented advertising policy