Use the following information to answer the questions below:…
Use the following information to answer the questions below: Rick is planning to retire from his career operating an extremely successful business called Creative Cooking. The company provides businesses with a personal chef to cater dinner parties at their office locations. Rick knows that the business is extremely profitable, so he is planning to retain ownership of the business; however, he has decided to let a manager deal with the day-to-day operations, which involves contracting chefs, and coordinating with clients to book dinner parties. Rick wants to hire a manager to run his business, while he spends the first year of his retirement learning to sail in the Caribbean. Rick knows if he works hard, the business is successful. He knows in the past that if he has not worked hard (shirked), he will not earn as much. Rick, being a man of reasonable intelligence, has devised the following payoff table: PAYOFF TABLE Net Income Before Management Remuneration Probability (a1 – work hard) Probability (a2 – shirk) $3,600 80% 40% $625 20% 60% Kathleen is a potential manager that Rick interviews. Kathleen, a retired NAIT Culinary Instructor, who also has over 20 years of experience in the culinary and hospitality industry in addition to teaching. Kathleen is an ideal candidate for the position. Kathleen and Rick need to come to an agreement on compensation though. Kathleen is both risk-averse and effort-averse with a utility for money equal to the square root of the dollar compensation she receives. Kathleen requires a reservation utility of 15 in order to accept the position. Her disutility of effort when she works hard is 5.2, and when she shirks, it is 0.5. Rick offers Kathleen a salary of $80, plus 10% of net income before manager compensation. Kathleen accepts this offer. Her utility 13.97 if she works hard and 15.05 if she shirks. Kathleen accepts the position and shirks her responsibilities for the next year. Rick realizes that Kathleen is shirking and although he is not pleased about it, finding another manager would be difficult due to demand in the current labour market. Therefore, to be competitive, Rick proposes a new compensation contract of a bonus equal to 25% of net income before remuneration, with no fixed salary. Kathleen now realizes her skills are in demand and revises her reservation utility to 20. Her disutility of effort remains the same. The following pay-off table applies: Below some calculations have already been completed for you, in particular the square root of the bonus at 25% at the net income level: PAYOFF TABLE Net Income Before Management Remuneration Square Root of 25% Bonus & Probability(a1) Square Root of 25% Bonus & Probability(a2) 25% Bonus a1 =0.8√(3,600 x 0.25) + 0.20√(625 x 0.25) – 5.20 = 21.30 a2 =0.40√(3,600 x 0.25) + 0.60√(625 x 0.25) – 0.50 = 19.00 Required: What is Kathleen’s revised utility if she shirks?
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