## Two neighbors, Alice and Bob, live in a building with poor sound insulation. Alice likes to play music loud, and Bob likes silence.

### economics

##### Description

Econ 490 (economics of coordination), spring 2020

Quiz 6: 95 points

Due by 11:59 pm Wednesday April 29

1- Two neighbors, Alice and Bob, live in a building with poor sound insulation. Alice likes to play music loud, and Bob likes silence. The building coop board will enforce a curfew forbidding loud music playing after a certain time, x, measured as hours after 8 pm. Thus if x = 3 the curfew will be 11 pm. There is also the possibility that Alice can pay Bob a certain amount per week, y, to extend the curfew hours. If y < 0 the payment would go from Bob to Alice. Their utility functions are:

Alice: ;

Bob:

A. [10points] What are Alice and Bob's own preferred curfew times, ignoring the presence of the other? If the coop board sets x = 3, and there is no payment between them, what would their utilities be? Is setting x =3 lead to a Pareto optimal outcome?

B.  [6 points] What curfew time,  , maximizes the sum of their utilities, ? What is the sum of their utilities at   ? Does this maximization determine the payment y? Explain.

C. [8 points] What is the minimum payment Alice could offer Bob on a take-it-or-leave-it basis to shift the curfew to 1 am (x = 5)? What would their payoffs be if they made this deal? Is this a Pareto-improvement over the board curfew?

D. [6 points] What is the payment that would equalize their utilities, ? What would their payoffs be with this arrangement?

E. [5 points] What payment would equalize their gains from the deal, −1000 =  − 1500? What would their utilities be with this arrangement?

F.  [5 points] Consider the three payment deals described in parts (c), (d), and {e). Which ones rae efficient and which is more fair?