Consider a standard principalagent model. The set of possible outputs is Y {y1,y2, . . ., yn} . The probability of output yi is 7:,- (a) where a is the agent's eff: \\ The agent has the following utility r? '1 LOJ \"(M0(a), where u is strictly increasing and strictly concave while '0 is strictly increasing and strictly convex. The agent's outside option is normalized to 0. The risk-neutral prin- cipal wants to design a compensation scheme that maximizes profit. There are two possible schemes. One option is for the principal to dene a fixed mapping from output to wage, so the set of possible wages is W = {301, 1302,. . . , wn} and the agent is paid wi when output 3/; occurs. In this case, the principal chooses compensation scheme to maximize :17? (a) (3i wt) subject to the participation and incentive constraints. The other option is for the principal to define a mapping from output to a lotteryrandomized wages. In essence, if output y is observed, the wage is being drawn from a lottery with pay- outs {011,319sz . .,wim} with probability distribution 1 > ]P (way) = pi; > 0 and 231:1 pi} = 1. In this case, the principal chooses compensation scheme to maximize i; 7Ti (:3) (3/1- E Paws) 1:1 j=1 subject to the participation and incentive constraints. Show that it is never optimal to use randomized wages