Consider a large public university in which a chemistry lecture is usually attended by 300 students or so but with large amounts of available seats on any given day

Is this a pure public good? If not, why not? Is this good likely to be provided in an efficient manner if the professor is vigilant in making sure that only registered students attend? Explain.

This is not a pure public good. For that to be true there would have to be both non-excludability and non-rivalry in consumption. The latter holds true in that one additional student in attendance is not likely to interfere with anyone else's enjoyment of the lecture. However, since the professor is able to exclude students who are not registered the former does not hold true. The fact that he actively practices this policy is likely to result in an inefficient outcome. Why? Additional students could enjoy the lecture without any cost imposed on anyone else. That is, the marginal cost of an additional student in attendance is likely to be zero but the benefits that he or she is likely to enjoy are positive.