We build a directed technical change model where one intermediate goods sector uses a fixed quantity of biomass energy (“wood”) and another uses coal at a fixed price, matching stylized facts for the British Industrial Revolution. Unlike previous research, we do not assume the level or growth rate of productivity is inherently higher in the coal-using sector. Analytically, greater initial wood scarcity, initial relative knowledge of coal-using technologies, and/or population growth will boost an industrial revolution, while the converse may prevent one forever. An industrial revolution, with eventual dominance by the coal-using sector, is the model’s main dynamic outcome, but not inevitable if inter-good substitutability is high enough. Empirical calibration for 1560-1900 produces historically plausible results for changes in energy-related variables during British industrialization, and through counterfactual simulations confirms that it was the growing relative scarcity of wood caused by population growth that resulted in innovation to develop coal-using machines.