Over the past decades, private R&D spending in the United States and other developed countries has been growing faster than gross domestic product. At the same time, the growth rates of per-capita and aggregate output have been rather stable, possibly declining slightly. This article proposes a growth model that can account for the observed phenomenon by explicitly describing competition among technological leaders and followers in individual markets in a way that is consistent with existing studies on firms' motivation to invest in R&D. The model shows the possibility that the unsustainable trend of rising R&D intensity persists for a very long time. (JEL O3, O4, L1)