.1... Consider a standcard'principalgent model. The set of possible outputs is Y = {y1,y2,. . .,yn}. The probability of output yi is 71'1' (a) where a: is the agent's effort. The agent has the following utility u(w)v(a), where u is strictly increasing and strictly concave while 7) 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 prot. There are two possible schemes. One option is for the principal to define a xed mapping from output to wage, so the set of possible wages is W = {301, mg, . . . , wn} and the agent is paid wi when output yi occurs. In this case, the principal chooses compensation scheme to maximize rst (a) (yi wi) 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 yi is observed, the wage is being drawn from a lottery with pay- outs {wi1,wi2,...,wim} with probability distribution 1 > IP (ml-j) = pij > 0 and 1 pi}.- = 1. In this case, the principal chooses compensation scheme to maximize i: 7T5 (at) (yi E pijwij) i=1 1:1 subject to the participation and incentive constraints. Show that it is never optimal to use randomized wages