Optimal advertising with a continuum of goods

In this paper, we present a model of optimal advertising with a continuum of goodsdifferentiated by their vintage. The model is an infinite horizon/infinite dimensional optimalcontrol model and the firm advertises a continuum of goods. We prove that the goodwill ofa good accumulated through advertising does not necessarily reach its maximum when it islaunched onto the market: it can be a single peaked function of the good vintage.