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 , and Best Rest keeps the rest, (1 ).

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.

1. What is the expected value for Best Rest and hotel managers under each contact? Show your work using the symbols X, , and B.
2. Can we induce the hotel manager to exert high effort under each contract? How large do X, , and B have to be to get the manager to exert high effort?
3. If you owned Best Rest, which contact would you choose, and how would you design it. Explain why.