cost versus profit center and information content Ralph owns a produetion funetion and seeks the services of a manager. The manager' s input ean be L or H; Ralph desires input H. The manager will oversee a process that will incur a eost that is low or high. Denote the scaled eost possibilities as eost = 1 and eost = 2. Associated revenue, in scaled format, will be revenue = 4 or revenue = 5. The eost/revenue probabilities are displayed below:

input H input L eost/revenue eombination 1/4 1/5 2/4 2/5

.49 .41 .01 .09

.15 .15 .35 .35 Ralph is risk neutral. The manager is described in the usual fashion. The manager' s utility for wealth w is given by U(W) = -exp(-rW). If the manager supplies input aE{H,L}, thereby incurring personal eost el' and is paid amount I, wealth will total I - el. We use CH = 5,000 and eL = 1,000, along with a risk aversion parameter of r

= .0001. Also, the manager's opportunity eost is U(M), with M = 4,000. Ralph eannot observe the manager' s input, so eontracting is eonfined to the observable eost and revenue.

al Suppose Ralph treats the manager as a eost center. Determine an optimal payfor-

performance arrangement. Why is the manager paid more when a low eost is observed?

b I Suppose Ralph treats the manager as a revenue center. What difficulty emerges when Ralph attempts to seeure input H by evaluating the manager in terms of the revenue outeome? Is revenue eontrollable by the manager?

e] Suppose Ralph treats the manager as a profit center. Determine an optimal payfor-
performance arrangement that uses the eost and revenue outeomes. Explain the stroeture of the optimal arrangement. Why is revenue a useless eontraeting variable when used alone, but useful when used in eonjunetion with the eost observation?
d] What general principle for ehoosing between a eost center and a profit center evaluation is illustrated here? How does this apply to choice between a profit center and an investment center?AppendixLO1