2 Bearcat University hires Mr LeBron to coach its basketball

Last updated: 4/12/2023

2 Bearcat University hires Mr LeBron to coach its basketball team LeBron s utility function is u w 6e where w denotes his wage and e his effort He can choose either low effort eL 1 or high effort ey 2 If Bearcat wins its division the university s profit will be 600 Otherwise the university s profit will be 200 LeBron s reservation utility is 4 The university cannot observe LeBron s effort The probabilities of outcomes given LeBron s effort are e 1 2 Bearcat does not win its division 71 200 0 8 0 2 Bearcat wins its division T 600 0 2 0 8 a Let w and we be the wage paid to LeBron if profit is and respectively What are the individual rationality condition and the incentive compatibility condition needed to induce ex b Assuming e is the more desirable of the two effort levels find the optimal wage contract What is the university s expected net profit c If the university wanted to induce LeBron to choose e what wage contract should it use What would be the university s expected net profit