William started a business many years ago and wants to retire. He has decided to hire a manager to run the business for him. He will receive all income after paying the manager's compensation. Therefore, minimizing the compensation and maximizing profits are important to him. William enters into a contract with Fran to be the manager. Fran is risk and effort averse. Her utility function is the square root of her income. Her disutility for effort is 4 for high effort and 2 for low effort. Her reservation utility is 11. William has noted that when he makes a high level of effort, profits have been $2,000 90% of the time and $900 10% of the time. However, if William does not work hard, profits are $900 90% of the time and $2,000 10% of the time. William offers Fran a contract paying $100 plus 10% of profits. a. What will Fran choose to do (high or low effort) and how much will income likely be? Show computations for full credit. b. Would William want to change this contract after observing income for two years? Propose some changes that he could make to result in an outcome that is more beneficial to him? use the FSAB code or similar