Optimal goodwill path to introduce a new product
This article considers the best goodwill path to introduce a new product, which is modelled as an optimal control problem. The advertising expenditure rate is assumed to be the control variable and it affects the goodwill evolution. The problem is set out in a calculus of variations framework. In the second section after the introduction, the paper introduces the definitions of goodwill, cost and their relationship with the advertising expenditure intensity (rate). In the next section the (foreseen) profit maximisation problem is presented, followed by the optimality conditions. Several types of cost rate functions are considered, for example linear-quadratic, Nerlove-Arrow, power and exponential. The article concludes with suggestions for future expansions of the approach, for example in the case of multi-dimensional goodwill framework.
scientific article; zbMATH DE number 2153861