In this note we reconsider the paper of Brod and Shivakumar (1999), published in the Journal of Industrial Economics, who analyze a twostage model in which the firms compete in two dimensions and examine the effect of semi-collusion when the non-production activity is R&D. They shed light on the fact that in the presence of spillovers, firms and consumers could be both better off, peradventure both worse off, by a semi-collusive production cartel. We are motivated to study their setup by this fascinating outcome. Trying to approach the in-depth analysis and to understand the driving forces of this result, we find however that the findings of Brod and Shivakumar (1999) are disputable. By focusing upon their calculative errors, we show how the correct solution can be obtained, furthermore, we explain why the main propositions in their paper don't hold.