Imagine a signaling model where there are two types of workers, low-productivity workers with a productivity of 10, and high-productivity workers with a productivity of 30. The proportion of low-productivity workers is .5. Firms are competitive and obtain profit equal to the productivity of the worker they hire. Workers can obtain one of three levels of education: e1, e2, and e3. Workers get utility equal to their wage minus the cost of education. Wages must be between 10 and 30. The cost of getting an education for low-productivity workers is e1 = 0, e2 = 9, e3 = 18. The cost of getting an education for high-productivity workers is e1 = 0, e2 =4, e3 = 8. Are there any separating equilibria in this model? If so, find them, if not show why they do not exist.

Imagine a signaling model where there are two types of workers, low-productivity workers with a productivity of 10, and high-productivity workers with a productivity of 30. The proportion of low-productivity workers is .5. Firms are competitive and obtain profit equal to the productivity of the worker they hire. Workers can obtain one of three levels of education: e1, e2, and e3. Workers get utility equal to their wage minus the cost of education. Wages must be between 10 and 30. The cost of getting an education for low-productivity workers is e1 = 0, e2 = 9, e3 = 18. The cost of getting an education for high-productivity workers is e1 = 0, e2 =4, e3 = 8. Are there any separating equilibria in this model? If so, find them, if not show why they do not exist.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.10P

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Imagine a signaling model where there are two types of workers, low-productivity workers with a productivity of 10, and high-productivity workers with a productivity of 30. The proportion of low-productivity workers is .5. Firms are competitive and obtain profit equal to the productivity of the worker they hire. Workers can obtain one of three levels of education: e1, e2, and e3. Workers get utility equal to their wage minus the cost of education. Wages must be between 10 and 30. The cost of getting an education for low-productivity workers is e1 = 0, e2 = 9, e3 = 18. The cost of getting an education for high-productivity workers is e1 = 0, e2 =4, e3 = 8. A) Are there any pooling equilibria in this model? If so find all of them, if not, show why they do not exist.
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