communication in root urility case Ralph' s manager acquires information after acting, but before output is realized.

As usual, Ralph, the principal, is risk neutral. The manager has preferences for cash income z and labor input a given by,rz - V(a). Two labor inputs are possible, a = H and a = L. Ralph seeks supply of H. Conflict is present, as V(H) = 20 > V(L) = O.

Also, the manager demands an expected utility of 40 to sign on with Ralph.

Weather plays an important role in the produetion process. Suppose the weather ean be dry, regular, or wet with equal probability. The output possibilities (interpreted as eash before any payments to the manager) are as follows:
dry regular wet input H input L 11,000 11,000 5,000 11,000 5,000 5,000 Notice the ideal arrangement, where the manager' s behavior is observed (or the manager is eommitted to cooperative behavior), is explained by risk sharing; the manager is paid a wage of 3,600 dollars in exchange for input H.
a] Suppose the manager aets in a self-interested manner and that only the output ean be eontraeted on. Determine an optimal pay-for-performance arrangement.
b] Now suppose a monitor is available. This monitOT will report good news if the weather is not wet and bad news if the weather is wet. (The monitor does not distinguish dry from regular weather.) The monitor's report will be publicIy observed at the end of the game. Determine an optimal pay-for-performanee arrangement.
e] Next, suppose the monitor will be privately observed by the manager, after the manager aets but before the output is observed. The manager ean now tell Ralph what was observed, and the contraet ean depend on the claimed observation as well as the publicly observed output. Determine an optimal pay-for-performance arrangement.
d] Do you think private observation and communication are always equivalent to public observation? Why?
e] What happens in part [e] if the manager communieates after observing the output? What daes this teIl you about how the information eonveyed by the output is used in your elaborate input supply, communication scheme in part [e]? More broadly, what roles are played by output in part [el above?AppendixLO1