Question

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4. 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 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. a. If Kate and Ali decide to live together, is it socially optimal for Ali to play her music in the apartment? b. Which of the following, if any, ways of splitting the total monthly rent induce them to live together? i. Kate pays $150, Ali pays $450 ii. Kate pays $250, Ali pays $350 iii. Kate pays $375, Ali pays $125 iv. There is no way to split the rent that would make them live together

Answer 1

a. The benefit that Ali gets from listening to music is $300 which is higher than the cost to kate from listening that music ie $100. Hence it is socially optimal for Ali to play her music in the apartment.

b. Now they can both rent a one-bedroom apartment for $400 per month or they can live together in a two-bedroom apartment for $600per month. Now option i is not feasible because it requires Ali to pay $450 which is greater than the rent she would pay if she lives separately i.e $400, Hence Ali will not pay $450. Now option iii is not feasible because it requires kate to pay $375 which is marginally lower than the amount she would pay if she lives separately. Hence the optimal split will be;

ii. Kate pays $250 and Ali pays $350

because with this split both will receive benefit from living together in a two bedroom apartment.