two-sided contrai problem Ralph wants to hire a manager. The manager's output ean be either Xl or xz.

The manager' s input ean be L or H. Ralph is risk neutrai. The probabilities are:

Ralph wants supply of input H in all that follows.
The manager is modeled in the usual way, with utility for wealth w given by U(W) = -exp(-rW) and wealth measured as the net of payment I and personal cost ea. The manager's next best opportunity offers a eertain equivalent of M = 8,000.
Assume eH = 5,000, eL = 0 and r = .0001.
a] Detennine an optimal pay-for-perfonnanee arrangement, assuming the only observable for eontraeting purposes is the manager's output.
b] Now suppose a monitor is available. Independent of the output this monitor will report good news with probability .90 if input H is supplied, and bad news otherwise. Also it will report bad news with probability .90 if input L is supplied, and good news otherwise. Determine an optimal pay-for-performance arrangement.
Explain the ranking of the performance payments.
e] Now suppose Ralph (not the manager) privately sees the monitor report in [b]
above. This observation is made before the output is known. Is it ineentive compatible for Ralph to use the pay-for-performance schedule in [b] and honestly announee to the manager what the monitor has reported?
d] Consider the following payment structure for the story in [e] above: Ilg = 13,059.77, Ilb = 4,505.37, 12g = 13,132.04 and 12b = 15,270.64. (Iii is the manager's payment when Ralph cIaims to have reeeived report j and output i is subsequently observed.) Verify that the best the manager ean do is accept this contraet and supply H; and the best Ralph ean do is honestly convey whatever report is delivered by the monitor. CarefuIly explain howand why this scheme differs from that in [e].AppendixLO1

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input H input L 226 X2 .2 .8 .6 .4