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?