We add an extractive sector to an endogenous growth model of expanding varieties and directed technological change. Firms increase their economically extractable stocks of non-renewable resources through R&D investment in extraction technology and reduce their stocks through extraction. We show how the geological distribution of the non-renewable resource interacts with technological change. Our model accommodates long-term trends in non-renewable resource markets - namely stable prices and exponentially increasing extraction - for which we present data going back to 1792. The model suggests that over the long term, development of new extraction technologies neutralizes the increasing demand for non-renewable resources in industrializing countries such as China.