We consider a theoretical model where firms can reduce their initial unit costs by spending on RΔ 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.