5. When Julia is a risk-neutral owner of a firm that manufactures and sells a single product. She is considering hiring Willie to work at her firm as a sales manager. If Willie is hired and works hard at his job, then expected sales will be relatively high. But, if he is hired and does not work hard at his job, then expected sales will be relatively low. Willie is risk-averse, and his utility function is U(w, e) = \\(w) -e, where w is the compensation that Julia will pay Willie, and e = er = 0 if Willie is completely lazy, and e = en = 1 if Willie works very hard. If Willie is not hired by Julia, then he can start his own business and earn reservation utility of 3.5. Julia's utility function is U(x, w) = x - w, where x = XL = 0 is "low" sales, x = xu = 100 is "high" sales, and w is the compensation Julia will pay Willie. Assume both Julia and Willie try to maximize their respective expected utility functions. In addition, assume Willie will work for Julia if working for Julia generates the same expected utility as working elsewhere. The following table captures how Willie's effort affects sales: Probability Probability X = XI X = XH e = CL 30% 70% e = CH 10% 90% Required: a. Suppose Julia cannot observe Willie's choice of e. What contract will Julia offer if she wants Willie to work for her and choose ey