Motivated by the observation that firms invest in carbon emissions reduction to decrease the cost of carbon tax as governments in numerous countries increasingly implement carbon tax to improve the environment,and broad researcher and practitioner agreement that carbon tax implementation always benefits the environment.However,we find that a carbon tax may actually hurt the environment based on a stylized game model with a better-informed retailer (one who controls the demand information sharing with the manufacturer) and a manufacturer.In particular,we find that the carbon emissions reduction may harm the environment if the carbon tax is moderate or both the carbon tax and the demand fluctuation are high.We further reveal free-riding behavior by the retailer,who may enjoy more profit sharing from the supply chain in the presence of carbon emissions reduction.Based on these observations,we argue that a carbon tax does not always benefit the environment when a manufacturer who receives demand information from the retailer responds better to market uncertainty.