Consider a principal who hires a salesman to approach a client. The reservation utility level of the salesman is 3. A high level of effort gives no sale with probability 0.2, a $100 sale with probability 0.4 and a $400 sale with probability 0.4. For a low level of effort, the three probabilities are 0.4, 0.4, 0.2 respectively. The principal is risk neutral. The agent is risk averse, and if the wage is w and the effort is a, he gets utility u(w,a) = VW-a. (High effort requires a = 3 and low effort requires a = 0.) (a) For starters, assume that the principal could observe the level of effort put by the salesman. Characterize the first-best wage schedule. (b) From now on, assume that contracts can be made contingent on the size of the sale only (effort is unobservable). What is the optimal way to induce the salesman to put in a low level of effort? (c) What is the optimal way to induce the salesman to put in a high level of effort? (d) What is the optimal contract (from the principal's perspective) to offer the salesman? Consider a principal who hires a salesman to approach a client. The reservation utility level of the salesman is 3. A high level of effort gives no sale with probability 0.2, a $100 sale with probability 0.4 and a $400 sale with probability 0.4. For a low level of effort, the three probabilities are 0.4, 0.4, 0.2 respectively. The principal is risk neutral. The agent is risk averse, and if the wage is w and the effort is a, he gets utility u(w,a) = VW-a. (High effort requires a = 3 and low effort requires a = 0.) (a) For starters, assume that the principal could observe the level of effort put by the salesman. Characterize the first-best wage schedule. (b) From now on, assume that contracts can be made contingent on the size of the sale only (effort is unobservable). What is the optimal way to induce the salesman to put in a low level of effort? (c) What is the optimal way to induce the salesman to put in a high level of effort? (d) What is the optimal contract (from the principal's perspective) to offer the salesman