1. Best Rest Hotels is a franchiser of mid-range hotels. Each of its hotels is independently managed. Hotel managers can
Posted: Wed Apr 27, 2022 10:57 am
1. Best Rest Hotels is a franchiser of mid-range hotels. Each of
its hotels is independently managed. Hotel managers can choose low
or high effort. With high effort, there is a .50 probability that
the hotel will earn $20,000 per month and .50 that it will earn
$12,000 per month. With low effort, there is a .50 probability that
the hotel will earn $12,000 and a .50 probability that it will earn
$10,000. Exerting effort costs the manager $3,000. However, Best
Rest cannot observe whether managers are exerting high effort – it
only sees the resulting earnings. Best Rest can choose from the
following contracts. I – Each manager pays a royalty of X dollars
per month and gets to keep all the profit. II – Managers get a
portion of the profit of ɵ, and Best Rest keeps the rest, (1 – ɵ).
III – Each manager is paid a fixed salary of $6,000 per month plus
a bonus of B if and only if the hotel receives $20,000 in revenue.
a) What is the expected value for Best Rest and hotel managers
under each contact? Show your work using the symbols X, ɵ, and B.
b) Can we induce the hotel manager to exert high effort under each
contract? How large do X, ɵ, and B have to be to get the manager to
exert high effort? c) If you owned Best Rest¬, which contact would
you choose, and how would you design it. Explain why.
its hotels is independently managed. Hotel managers can choose low
or high effort. With high effort, there is a .50 probability that
the hotel will earn $20,000 per month and .50 that it will earn
$12,000 per month. With low effort, there is a .50 probability that
the hotel will earn $12,000 and a .50 probability that it will earn
$10,000. Exerting effort costs the manager $3,000. However, Best
Rest cannot observe whether managers are exerting high effort – it
only sees the resulting earnings. Best Rest can choose from the
following contracts. I – Each manager pays a royalty of X dollars
per month and gets to keep all the profit. II – Managers get a
portion of the profit of ɵ, and Best Rest keeps the rest, (1 – ɵ).
III – Each manager is paid a fixed salary of $6,000 per month plus
a bonus of B if and only if the hotel receives $20,000 in revenue.
a) What is the expected value for Best Rest and hotel managers
under each contact? Show your work using the symbols X, ɵ, and B.
b) Can we induce the hotel manager to exert high effort under each
contract? How large do X, ɵ, and B have to be to get the manager to
exert high effort? c) If you owned Best Rest¬, which contact would
you choose, and how would you design it. Explain why.