Traditional resource economics has been criticised for assuming too high elasticities of substitution, not observing material balance principles and relying too much on planner solutions to obtain long-term growth. By analysing a multi-sector R&D-based endogenous growth model with exhaustible natural resources, labour, knowledge, and physical capital as inputs, the present paper addresses this critique. We study transitional dynamics and the long-term growth path and identify conditions under which firms keep spending on research and development. We demonstrate that long-run growth can be sustained under free market conditions even when elasticities of substitution between capital and resources are low and the supply of physical capital is limited, which seems to be crucial for today’s sustainability debate.