Coal in Order to Reach Renewables: Carbon Capture, Synthetic Fuels, and the Atmospheric Ceiling

We study the optimal use of energy from carbon emissions in an economy drawing useful energy from coal, a standard renewable, and methanol synthesised by combining captured CO2 with an otherwise inexploitable non-standard renewable, subject to a ceiling on atmospheric carbon. Captured CO2 carries a dual shadow value - atmospheric relief and productive feedstock - and we show that a credible ceiling is necessary and sufficient to activate the non-standard renewable: the ceiling, not any output subsidy, prices the feedstock that makes synthesis competitive. The optimal sequence departs from least-cost-first ordering, with coal and methanol used concurrently, and the pre-ceiling energy price may follow a U-shaped path driven by a rising shadow value rather than falling costs. A uniform Pigouvian carbon tax does not decentralise the optimum; a supplementary storage subsidy is required, and the net capture instrument is a subsidy or tax according to whether emission reduction dominates the coal rebound.