Answer: b. pay you at least $100 but less than $200 to live with the clutter.
Step-by-step explanation:
The options are:
a. stop her messy habits or else move out.
b. pay you at least $100 but less than $200 to live with the clutter.
c. continue to be messy and force you to move out.
d. demand payment of at least $100 but no more than $200 to clean up after herself.
According to the Coase theorem, if a party has the rights to a property, then an efficient output level will be achieved when there is some sort of bargaining between the parties that are involved.
Since the roommate gets a $200 benefit from being messy but imposes a $100 cost on me, an efficient solution would be for my roommate to pay me at least $100 but less than $200 to live with the clutter.