Consider the following principal-agent problem. The agent may take one of two actions e {0, 1}. His Bernoulli utility over wages, w, and actions, e, is given by u(w, a) = w e, and his reservation utility level is u = 1. There are four possible (verifiable) profit levels for the risk-neutral principal {0, 10, 20, 30}. The distributions over the profit levels conditional on the agent's actions are: P r(0|0) = P r(10|0) = 1 2 ; P r(20|0) = P r(30|0) = 0, P r(0|1) = P r(10|1) = P r(20|1) = P r(30|1) = 1 4 . Assume that the principal is interested in implementing e = 1. (a) If the agent's actions were verifiable, what wage w 1 , would the principal offer? (b) What are the individual rationality and incentive compatibility constraints when the actions are not verifiable? (c) What are the four possible values for the likelihood ratio, L() = P r(|0) P r(|1) ? (d) Based on your answer to part c), what can you say about the optimal compensation function, w (), when actions are not verifiable? (e) Find the optimal compensation function w () when actions are not verifiable. (f) What is the expected payment to the agent E[w (|e = 1)]? Briefly explain why it differs from w 1 .