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

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1 Two Neighbors Alice And Bob Live In A Building With Poor Sound Insulation Alice Likes To Play Music Loud And Bob 1 (111.54 KiB) Viewed 25 times

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: TA = $1000 - y - 36 - x)2; Bob: np = $1500 + y - (2 - x)? a) 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 this Pareto optimal? b) What curfew time, x* , maximizes the sum of their utilities, Tea + Tig? What is the sum of their utilities at the optimal curfew? Does this maximization determine the payment y? Explain. c) What is the minimum payment Alice could offer Bob on a take-it-or-leave-it basis to shift the curfew to 1 am (* = 5)? What would their payoffs be if they made this deal? Is this a Pareto- improvement over the board curfew? d) What is the payment that would equalize their utilities, na = 118? What would their payoffs be with this arrangement? e) What payment would equalize their gains from the deal, 1A-1000 = Tb - 1500? What would their utilities be with this arrangement? f) What are the ethical arguments for each of the three payment deals described in parts c), d), and e)?