Kate and Ali can live together in a two-bedroom apartment for $600 per month, or they can each rent a one-bedroom apartment for $400 per month. Apart from the rent, they are indifferent between living together and living apart, except for one problem: Kate hates Ali's taste in music. Kate would be willing to pay up to $100 a month to avoid hearing Ali's music. Ali would give up listening to her music for no less than $300 per month. Which, if any, of the following ways of splitting the total monthly rent would induce them to live together?
A)Kate pays $150 per month and Ali pays $450 per month
B)Kate pays $250 per month and Ali pays $350 per month
C)Kate pays $375 per month and Ali pays $125 per month
D)There is no way to split the rent to induce them to live together

Question

Quizplus · Accepted Answer

Since the benefit to Ali of listening to her music ($300)is greater than the cost to Kate of hearing Ali's music ($100), Ali will play her music if they live together. Kate's surplus from living together will be the rent she saves by not living alone ($400)minus her share of the rent when living together minus the $100 cost of listening to Ali's music. Ali's surplus from living together will be the rent she saves by not living alone ($400)minus her share of the rent when living together. So, if Kate pays $250 per month and Ali pays $350 per month, then Kate's net surplus from living together will be $400 - $250 - $100 = $50, and Ali's net surplus from living together will be $400 - $350 = $50. That is, under this arrangement they will each be $50 better off than when they live alone.

Kate and Ali Can Live Together in a Two-Bedroom Apartment