Two neighbors, Alice and Bob, live in a building with poor sound insulation.

economics

Description

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?


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