This paper presents a Cournot oligopoly model with R&D spillovers both within and across industries. The aim is to provide an appropriate theoretical foundation for three different hypotheses regarding the impact of the local production structure on innovation and output, as well as addressing mixed empirical results in this area. Both the effective R&D and total industry output are shown to increase with the variety of industries, which is aligned with Jacobs externalities. With respect to the concentration, the outcome is more ambiguous, where it depends on the variety, both spillover rates, and the R&D efficiency. If the variety is limited, then partial support is given to both Marshall-Arrow-Romer externalities in the case of effective R&D, and to Porter externalities in the case of the total industry output. The use of a relative rather than an absolute measure of variety is also shown to be important.