taxes and incentives Consider a setting where the manager' s input ean be L or H and the output ean be Xl = 10,000 or x2 = 50,000. The manager' s preferenees are described in the usual fashion, with utility for wealth w given by U(W) = -exp(-rW), where w is the net of payment I and personal eost ea' Let r = .0001. Also, the manager's opportunity eost of working for this organization is U(M), with M = O. The owner is risk neutraI.

The output probabilities are:

Assume eH = eL = 5,000. Input H is desired throughout the exereise.
a] Detennine and interpret an optimal contraet.
b] Suppose the owner is subjeet to a 20% income tax (Le., a tax equal to 20% of the net of Xi - I;), while the manager faees a zero marginai tax rate. Detennine and interpret an optimal contraet.
e] Repeat [b] above for the ease where the owner is subjeet to a 20% income tax on income in excess of 20,000.
d] Repeat [e] above for the ease eL = 4,000.
e] Repeat [e] above for the ease eL = O.AppendixLO1

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input H input L 818 .1 .8 .9 792