16. communication in root utility case Ralph’s manager acquires information after acting, but before output is realized. As usual, Ralph, is risk neutral. The manager has preferences for cash income z and labor input a given by √z − V (a). Two labor inputs are possible, H or L. Ralph seeks supply of H. Conflict is present, as V (H) = 20 > V (L) = 0. Also, the manager demands an expected utility of 40 to sign on with Ralph. It turns out that weather plays an important role in the production process. Suppose the weather can be dry, regular, or wet with equal probability. The output possibilities (interpreted as cash before any payments to the manager) are as follows:

dry regular wet input H 11,000 11,000 5,000 input L 11,000 5,000 5,000

(a) Suppose the manager acts in a self-interested manner and that only the output can be contracted on. Determine an optimal pay-for-performance arrangement.

(b) Now suppose a monitor is available. This monitor will report good news if the weather is not wet and bad news if the weather is wet. The monitor’s report will be publicly observed at the end of the game. Determine an optimal pay-for-performance arrangement.

(c) Next, suppose the monitor will be privately observed by the manager, after the manager acts but before the output is observed.
The manager can now tell Ralph what was observed, and the contract can depend on the claimed observation as well as the publicly observed output. Determine an optimal pay-forperformance arrangement.

(d) What roles are played by output in part

(c) above?