Economists have widely endorsed pricing CO2 emissions to internalize climate changerelated externalities. Doing so would significantly affect coal, which is the most carbonintensive major energy source. However, U.S. coal markets exhibit an additional distortion, as the railroads that transport coal to power plants can exert market power. This upstream distortion can mute the price signal of a corrective tax, due to changes in markups or incomplete tax pass-through. In this paper, I provide the first empirical estimates of how coal-by-rail markups respond to changes in coal demand. I find that rail carriers reduce coal markups when downstream power plant demand changes, due to a decrease in the price of a natural gas (a competing fuel). I estimate markup changes that vary substantially across coal plants, resulting from a combination of heterogeneous transportation market structure and plant-specific demand shocks. Since low natural gas prices and a CO2 emissions tax similarly disadvantage coal, observed decreases in coal markups imply that pass-through of a federal carbon tax to coal power plants may be heterogeneous and incomplete. This could substantially erode the environmental benefits of a price-based climate policy. My results suggest that decreases in coal markups have increased recent climate damages by $2.4 billion, compared to a counterfactual where markups do not change.