This article presents an endogenous growth model that is designed to be roughly consistent with the experience of high-tech firms like Intel. In the model, industry leaders invest in R&D to improve their products, small firms invest in R&D to become industry leaders, and innovating becomes progressively more difficult over time. Consistent with the empirical evidence, the model implies that economic growth is independent of economy size and R&D intensity is independent of firm size. For plausible parameter values, it is optimal to heavily subsidize R&D activities.