This lecture discusses the economic implications of pollution abatement, focusing on a company's emissions and the associated costs and damages. The instructor presents a scenario where a company emits 100 units of pollution, leading to a damage function that is directly proportional to emissions. The lecture explores the reasons behind this proportionality, particularly in the context of small emitters whose contributions do not significantly impact overall damage. The optimal level of abatement is calculated, revealing that reducing emissions by 25 units results in residual emissions of 75 units. The instructor then evaluates whether the company should be mandated to undertake this abatement effort by comparing the net benefits to society against the costs incurred by the company. The analysis concludes that despite the calculated optimal abatement level, the overall net gain is negative, suggesting that requiring the company to reduce emissions may not be desirable. This highlights the complexities involved in environmental economics and the need for careful consideration of both costs and benefits.