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Suppose that education does not affect worker's productivity, but it is more costly for low-ability workers to obtain the education. If firms cannot distinguish between different workers they must pay them all the wage equal to the expected productivity. If they can distinguish between workers with different abilities, they pay each worker their marginal product of labour and make zero profits. 70% of workers in the population have low ability. The productivity of low-ability workers is Y₁ = 20000, and the productivity of high-ability workers is Y = 50000. The cost of education to high-ability workers is CH (S) =, and the cost of education to low-ability workers is CL = S. 1. Suppose firms cannot observe worker's education. What wage will they offer to a high- ability worker? What is the optimal level of schooling for the high-ability worker? Why? 2. Suppose that firms can observe worker's educational attainment and believe that workers with the level of schooling above some benchmark S* are high-ability workers. For what values of S* high-and low-ability workers choose different levels of educational attainment (separating equilibrium)? 3. What will be the optimal level of schooling for high- and low-ability workers in a separating equilibrium?

Suppose that education does not affect worker's productivity, but it is more costly for low-ability workers to obtain the education. If firms cannot distinguish between different workers they must pay them all the wage equal to the expected productivity. If they can distinguish between workers with different abilities, they pay each worker their marginal product of labour and make zero profits. 70% of workers in the population have low ability. The productivity of low-ability workers is Y₁ = 20000, and the productivity of high-ability workers is Y = 50000. The cost of education to high-ability workers is CH (S) =, and the cost of education to low-ability workers is CL = S. 1. Suppose firms cannot observe worker's education. What wage will they offer to a high- ability worker? What is the optimal level of schooling for the high-ability worker? Why? 2. Suppose that firms can observe worker's educational attainment and believe that workers with the level of schooling above some benchmark S* are high-ability workers. For what values of S* high-and low-ability workers choose different levels of educational attainment (separating equilibrium)? 3. What will be the optimal level of schooling for high- and low-ability workers in a separating equilibrium?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Suppose that education does not affect worker's productivity, but it is more costly for low-ability workers to obtain the education. If firms cannot distinguish between different workers they must pay them all the wage equal to the expected productivity. If they can distinguish between workers with different abilities, they pay each worker their marginal product of labour and make zero profits. 70% of workers in the population have low ability. The productivity of low-ability workers is Y, = 20000, and the productivity of high-ability workers is Yµ = 50000. The cost of education to high-ability workers is CH(S) = . and the cost of education to low-ability workers is CL = S. 1. Suppose firms cannot observe worker's education. What wage will they offer to a high- ability worker? What is the optimal level of schooling for the high-ability worker? Why? 2. Suppose that firms can observe worker's educational attainment and believe that workers with the level of schooling above some benchmark S* are high-ability workers. For what values of S* high-and low-ability workers choose different levels of educational attainment (separating equilibrium)? 3. What will be the optimal level of schooling for high- and low-ability workers in a separating equilibrium? 4. Draw indifference curves of high- and low-ability workers and the values of S* that sustain the separating equilibrium. 5. For what levels of S* will all workers optimally choose to obtain positive schooling S* (pooling equilibrium). What will be the wage offered to high-ability workers? 6. Suppose that the government reforms the school system to promote education among low- ability workers and decreases the cost of education for low-ability workers to C1 = . For what range of educational requirements is the separating equilibrium sustained? Is it different from 2.2? Why?
Transcribed Image Text:Suppose that education does not affect worker's productivity, but it is more costly for low-ability workers to obtain the education. If firms cannot distinguish between different workers they must pay them all the wage equal to the expected productivity. If they can distinguish between workers with different abilities, they pay each worker their marginal product of labour and make zero profits. 70% of workers in the population have low ability. The productivity of low-ability workers is Y, = 20000, and the productivity of high-ability workers is Yµ = 50000. The cost of education to high-ability workers is CH(S) = . and the cost of education to low-ability workers is CL = S. 1. Suppose firms cannot observe worker's education. What wage will they offer to a high- ability worker? What is the optimal level of schooling for the high-ability worker? Why? 2. Suppose that firms can observe worker's educational attainment and believe that workers with the level of schooling above some benchmark S* are high-ability workers. For what values of S* high-and low-ability workers choose different levels of educational attainment (separating equilibrium)? 3. What will be the optimal level of schooling for high- and low-ability workers in a separating equilibrium? 4. Draw indifference curves of high- and low-ability workers and the values of S* that sustain the separating equilibrium. 5. For what levels of S* will all workers optimally choose to obtain positive schooling S* (pooling equilibrium). What will be the wage offered to high-ability workers? 6. Suppose that the government reforms the school system to promote education among low- ability workers and decreases the cost of education for low-ability workers to C1 = . For what range of educational requirements is the separating equilibrium sustained? Is it different from 2.2? Why?
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