We consider a theoretical model where firms can reduce their initial unit costs by spending on R&D. We show that the degree of product market collusion (captured by the coefficient of cooperation) might reduce firms' profits if innovation is made non-cooperatively. The intuition is that non-cooperative R&D introduces a negative externality where firms invest over and above the amount required to minimize costs so as to extract profits from their rival firm. Therefore, when product market competition drops below a certain level, a relatively large amount is spent on R&D with just a small output, making further collusion unprofitable. On the contrary, a Research Joint Venture (RJV) helps to internalize the externality and further product market collusion always increases firms' profits. As a consequence, total welfare may be lower if R&D is made cooperatively.