Optimal goodwill path to introduce a new product

We consider the problem of determining an optimal goodwill path for the introduction of a new product in a market, while looking for the maximum foreseen profit. The foreseen revenue depends on the product introduction time and on the goodwill level at the same time. We focus on the advertising costs associated with the goodwill evolution and assume that the cost function possesses some rather general features which are shared by the cost functions of the Nerlove-Arrow type models. The dynamic optimization problem is discussed in the calculus of variations framework. A few examples associated with special cost functions are discussed in detail.