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We study dynamic innovation and pricing decisions in a two-echelon supply chain consisting of a seller and a buyer who then ultimately sells the product to end consumers. We refer to innovation as efforts made on improving product quality or process. We model a Stackelberg differential game in which the seller first announces its wholesale price and innovation efforts over time and the buyer responds by deciding its retail price and its innovation efforts over time. We obtain feedback policies for the players as well as for a centralized channel. We obtain useful managerial insights through analytical and numerical means.