This lecture discusses the comparison between different environmental instruments, specifically focusing on caps and taxes for emissions reduction. The instructor outlines the challenges faced by an environmental authority in determining the optimal level of emissions reduction when the abatement cost function is unknown. The authority must decide whether to impose a cap on emissions or a tax based on its assumptions about the marginal abatement cost. The lecture includes graphical representations of marginal gains and costs, illustrating how the choice of instrument affects the net surplus. The instructor explains that if the authority underestimates the abatement costs, the cap may allow too much emissions, while a tax could lead to excessive abatement. The discussion emphasizes the importance of understanding the actual marginal abatement costs and how they influence the effectiveness of the chosen instrument. The lecture concludes by highlighting scenarios where either caps or taxes may be more effective, depending on the slope of the marginal gain curve and the nature of the emissions being regulated.