6. Consider two college roommates, one who smokes and one who does not. The smoker wishes to smoke in the room, and the nonsmoker dislikes smoking in the room. Suppose the smoker would be willing to pay $500 to be allowed to smoke in the room during the semester, and the nonsmoker would be willing to pay $600 to keep the room smoke-free.

a. What would be the socially optimal outcome?

Why is it optimal?

b. How might this outcome be achieved by an agreement between the two roommates? What theorem does this illustrate?

c. Suppose that the most the nonsmoker would be willing to pay was $200. Would this change the socially optimal outcome? Why or why not?