So it looks like from an e-mail I got our cleaning services people won't clean the microwave in our departmental common area. The question then becomes.
How Many Economists Does It Take to Clean a Microwave?
Answers (in jest):
None, if it was optimal to clean the microwave one would have already done it.
One, once the dirtiness level surpasses the economist with the lowest threshold they will clean it themselves creating a public good.
Two, one to clean it and the other to point out that the other does not have a comparative advantage in cleaning.
Never more than three because there are diminishing returns to labor when cleaning a microwave