multiple tasks Ralph owns a produetion function. Output can be either Xl or ~, with Xl

The manager' s input ean be one of two quantities, L or H. Ralph is risk neutral. The probabilities are:

Ralph wants supply of input H in all that follows.
The manager is risk averse imd incurs an unobservable, personal eost in supplying the labor input. We model this in the usual way. The manager's utility for wealth w is given by U(W) = -exP{-rW> and wealth is the net of payment I and personal eost ea' Set eH = 5,000, eL = 0, and r = .0001. Also, the manager's opportunity eost of working for this organization is U(M), with M = 10,000. The only observable for eontracting purposes is the manager's output.
a] What is the best way to motivate supply of input H by the manager? What is the eost (i.e., the expected payment from Ralph to the manager)? How mueh would Ralph pay to be able to observe the manager's input?
b] eall the above task one. A seeond task, task two, requires the same personal eost, and so on. The only differenee is the probability stmeture:

Suppose only this task is present. What is the best way to motivate supply of input H? What is the eost (i.e., the expeeted payment from Ralph to the manager)? How much would Ralph pay to be able to observe the manager's input?
e] Now suppose both tasks are present, and Ralph wants supp ly of input H to both.
To keep things dosely aligned to the above two stories, ehange the manager's outside opportunity to M = 20,000. The output of eaeh task is separately observed.
Also, the manager does not see the outeome of the first task before providing input to the second; so the input supply options are H to both, L to both, L and H or Hand L. Will the above two ineentive schemes motivate supply of input H to both tasks?
Verify your daim, and give the intuition.
d] What is the best way to motivate supply of input H to both tasks?
e] How mueh wouId Ralph pay to observe the input supplied to task one? Why does this differ from your originaI answer when task one is the only task?AppendixLO1

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input H input L X18 .1 X2 .9 .8 .2