Patents are necessary to appropriate the returns to the firm’s own R&D, but patents also create potential claims against the rents of rival firms. Analysis of the model reveals a general necessary condition for the existence of a positive correlation between the firm’s R&D intensity and the number of patents it obtains. When that condition is violated, changes in exogenous parameters that induce an increase in firms’ patenting can also induce a decline in R&D intensity. Such a negative relationship is more likely when (1) there is sufficient overlap in firms’ technologies so that each firm’s inventions are likely to infringe the patents of another firm, (2) firms are sufficiently R&D intensive, and (3) patents are cheap relative to both the cost of R&D and the value of final output.