This study investigates the role of the production supply chain in the choice of climate policies. We construct an environmental dynamic stochastic general equilibrium (E-DSGE) model that features multiple stages of production and different types of productivity shocks. Existing E-DSGE models for climate policy evaluation assume a single production stage. We find that the optimal carbon tax rates in all production stages are procyclical to aggregate supply shocks and countercyclical to aggregate demand shocks; however, if the shock arises from a particular production stage, the implied optimal carbon tax rates vary across stages and depend on the nature of the shocks. • We construct an E-DSGE model with a supply chain. • The effects of industry-specific carbon taxation in a supply chain are asymmetric. • Optimal carbon tax rates are procyclical to aggregate supply shocks. • Optimal carbon tax rates are countercyclical to aggregate demand shocks. • The optimal carbon tax rate’s cyclicality to industry-specific shocks is ambiguous.