The paper proves the existence of equilibrium in non-renewable resource markets when extraction costs are non-convex and resource storage is possible. Inventories flatten the consumption path and eliminate price jumps at the end of the extraction period. Market equilibrium becomes then possible. The authors distinguish between two types of solutions, one with immediate and one with delayed build-up of inventories. It is found that optimum resource extraction involves increasing quantities over a period of time. What is generally interpreted as an indicator of increasing resource abundance is thus perfectly compatible with constant resource stocks.