This paper presents a dynamic model of a competitive R&D and production duopoly subject to knowledge spillovers. Two asymmetric firms operate for a limited period of time and dispose their knowledge capital in the end. Both firms and the social planner prefer the R&Dcooperative strategy over the competitive one regardless of the intensity of knowledge spillovers. Accumulation of knowledge capital results allows the monopolist to have lower marginal cost of production and charge a lower market price than a fully competitive duopoly. Being able to define the degree of knowledge exchange when creating a research joint venture, the firms do not necessary choose the highest degree of cooperation available.