Reference no: EM133007340

Frank is the owner of a small business. When Frank has worked hard (a1) during the year, net income before manager compensation has been $1,600 60% of the time and $400 40% of the time. More recently, Frank has been ill and has had to shirk (a2). Net income has been $1,600 only 30% of the time and $400 70% of the time.Frank realizes that he must hire a manager for one year while he devotes full time to his recovery. Frank is risk neutral, with utility equal to the amount of net income for the year after manager compensation. Frank is negotiating with Michelle for the manager job. He ascertains that Michelle is risk averse, with utility equal to the square root of the dollar compensation received.

• Michelle is willing to work for Frank providing she receives expected utility of at least 6. Michelle advises Frank that she is effort averse, with disutility of effort of 2 if she works hard, and 1 if she does not work hard,

Required:

Problem (A) Frank suggests a salary of $64, Michelle immediately says that she would accept a salary of $64. Which act would she take? Show your work.

Problem (B) However, Frank consults you. You immediately advise against such an offer, suggesting instead a proportion of net income before manager compensation. Why do you advise against?

Problem (C) What proportion of net income do you recommend? Show calculations.

Problem (D) Show calculations to verify that Frank's expected utility is higher if he takes your advice instead of paying Michelle a salary. Why is his utility higher? Show calculations

Problem (E) Assuming that Michelle accepts Frank's new offer, verify that she will in fact work hard. Show
calculations