Final answer:
To maximize welfare in the presence of pollution, the government should tax a polluting good not at the marginal cost of production but at the marginal external cost of pollution. This aligns private costs with social costs, addressing the market failure and leading to an efficient level of production that considers the full societal costs.
Step-by-step explanation:
To address the student's question: to maximize welfare in a competitive market with a negative externality, such as pollution during production, the government should not tax the good at the marginal cost of producing the good, but rather at the marginal external cost of the pollution created.
When there is a market failure due to a negative externality, private markets fail to achieve efficient output levels because they do not factor in all social costs. In the specific context of pollution, social costs exceed the private costs reflected in the market price, resulting in overproduction of the polluting good.