9. qualitative shape of optimal incentives Consider a costly input setting in which output (xi) can take one of four possible values. Input can be either L or H, with H desired by the risk neutral organizer. The input supplier is risk averse, and incurs an unobservable personal cost associated with input supply. We use the usual constant risk aversion specification of his preferences, with

ρ = .0001, cH = 5, 000 and cL = 0. Let the supplier’s next best opportunity offer a wealth of M = 0. The output probabilities are given below.

x1 x2 x3 x4

π(x|H) .1 .2 .3 .4

π(x|L) .4 .3 .2 .1 Let Ii denote the payment to the input supplier when output xi is observed. Without solving for an optimal arrangement, rank the four payments from lowest to highest. Carefully explain your answer.