Finding Pareto efficiency with negative externalities
Your statement &quot;Isn’t any level of noise Pareto-Efficient?&quot; would be true only if the only good traded was &quot;levels of noise&quot;. Indeed, given a single good, Pareto-Efficient means that you simply do not waste anything.

I understand that here you have two exchangeable goods, Decibels and Money, and you need to evaluate possible combinations of the two. You'll see that, your task is to find the combinations of decibels and money, which is done by finding the contract curve.


The common method, as I'm sure you have learnt, is the comparison of the two persons' Marginal Rates of Substitution, in your example: $ MRS_F = MRS_S$, as given by the Edgeworth Box:
Notice how all Pareto-Efficient contracts lie in the contract curve? You can use this equation to input values for decibels and get the requested &quot;Pareto-Efficient&quot; level. The hint on the budgets of the two students also works in favor of you finding a proper budget constraint and finding precise levels for the two commodities.
This would be my process.