In this paper, we solve the problem of the optimal control of product diffusion by quality in a context of monopolistic competition. To do so, we introduce a dynamic demand function leaning on two hypotheses : first, price acts as a signal to quality , second, demand is more sensitive to quality than to price. Using the maximum principle of Pontryagin, we then characterize the optimal dynamic trajectory of quality and its qualitative properties.
EL OUARDIGHI, F. et TAPIERO, C. (1996). Qualité et diffusion des produits. Recherche et Applications en Marketing, pp. 35-51.