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 efforte 1 or high effort e = 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 universitycannot observe LeBron's effort. The probabilities of outcomes given LeBron's effort are:e = 1еH = 2(Bearcat does not winits division)π = 2000.80.2(Bearcat wins itsdivision)π₂ = 6000.20.8a. Let w₁ and w₂ be the wage paid to LeBron if profit is ₁ and ₂, respectively. What arethe individual rationality condition and the incentive compatibility condition needed toinduce еx?b. Assuming e, is the more desirable of the two effort levels, find the optimal wagecontract. What is the university's expected net profit?c. If the university wanted to induce LeBron to choose e, what wage contract should ituse? What would be the university's expected net profit?

A utility function is a mathematical representation of an individual's preferences over different…

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 e 1 or high effort eH=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 еH=2 (Bearcat does not win its division) TL1 200 0.8 0.2 (Bearcat wins its division) T₂=600 0.2 0.8 a. Let w, and we be the wage paid to LeBron if profit is ₁ and ₂, 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?

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 e 1 or high effort eH=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 еH=2 (Bearcat does not win its division) TL1 200 0.8 0.2 (Bearcat wins its division) T₂=600 0.2 0.8 a. Let w, and we be the wage paid to LeBron if profit is ₁ and ₂, 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?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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