If your worker works hard there is a 3/5 possibility that revenues will be $150 and a 2/5 probability that revenues will be $50. If she works at a lower level of effort, there is a 50% chance of each revenue outcome. Working hard costs her $6. Working moderately costs $3. Her outside utility is zero. She is risk-neutral, with utility equal to W - C , where W is the wage and C is the Cost of Effort (3 or 6 depending on whether she works with low or high effort, resp.) If you could contract for effort, would it be profitable to induce high effort? Explain why. What would your profits be? If you cannot contract for effort, find an incentive-compatible pay scheme that will induce high effort. Set up the incentive and participation

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
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Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.3P
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If your worker works hard there is a 3/5 possibility that revenues will be $150 and a 2/5 probability that revenues will be $50. If she works at a lower level of effort, there is a 50% chance of each revenue outcome. Working hard costs her $6. Working moderately costs $3. Her outside utility is zero. She is risk-neutral, with utility equal to W - C , where W is the wage and C is the Cost of Effort (3 or 6 depending on whether she works with low or high effort, resp.) If you could contract for effort, would it be profitable to induce high effort? Explain why. What would your profits be? If you cannot contract for effort, find an incentive-compatible pay scheme that will induce high effort. Set up the incentive and participation constraints and find the z (payment when revenue is 150) and y (payment when revenue is 50) where both are exactly satisfied. Would it be profitable to use this scheme? Why? Now suppose that y can never be negative. What incentive compatible scheme will give you the highest profits, given this constraint. Will you use this scheme or settle for a flat wage and low effort? Explain.
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