Consider a standard principal-agent model. The set of possible outputs is Y = {y1,y2,. . .,y,,} . The probability of output y,- is 7I, (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 '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 prot. There are two possible schemes. One option is for the principal to define a fixed mapping from output to wage, so the set of possible wages is W = {w1, :02, . . . , wn} and the agent is paid to,- when output y, occurs. In this case, the principal chooses compensation scheme to maximize :7\" (a) (y.- w.) 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 3/,- is observed, the wage is being drawn from a lottery with pay- OUtS {10:1, wig, . . . ,wim} Wlth probabllity distribution 1 > ll3 (wij) = P1} > 0 and 1 pi),- = 1. In this case, the principal chooses compensation scheme to maximize Z\"; 715i (a) (yi f: Pijwij) i=1 j=1 subject to the participation and incentive constraints. Show that it is never optimal to use randomized wages