optimal production plan Ralph, who is risk neutraI, owns a produetion process. Produetion requires input from a manager. This input ean be one of three possible quantities: L < B <

H. Output will be one of two possible quantities: XI < X2' The manager is risk averse and ineurs a personal eost in supplying input. The manager's utility for wealth w is given by U(W) = -exp(-rM, with r = .0001. If the manager suppHes input aE{L,B,H} and subsequently is paid amount I, wealth totals w = I - ca' We assume eL = 0, eB = 4,000 and CH = to,OOO. Also, the manager's outside opportunity guarantees a wealth of M = 40,000. The output probabilities are as follows.

input H input B input L XI o

.1

.9 X2 1

.9

.1 a] Suppose the parties ean eontract on the output and the input supplied.

Determine the best eontraet from Ralph's perspeetive that will insure supply of input

(i) H, (ii) B, and (iii) L.

bJ Suppose the parties ean contraet on the output, but not the input supplied.

Determine the best eontraet from Ralph' s perspeetive that will insure supply of input

(i) H, (ii) B, and (iii) L.

e] Let XI = 0 and x2 = 55,000. Determine Ralph's optimal plan under the contraeting eonditions in [a] and under the contraeting conditions in [b] above.

dj Let xI = 0 and x2 = 59,000. Determine Ralph's optirna! plan under the contraeting conditions in [a] and under the eontraeting eonditions in [b] above.

Carefully explain your condusions.

e] Let Xl = 41,000 and x2 = 46,100. Detennine Ralph's optimal plan under the contraeting conditions in la] and under the contraeting conditions in [b] above.
Carefully explain your conelusions.AppendixLO1