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 YL = 20000, and the productivity of high-ability workers is YH = 50000. The cost of education to high-ability workers is CH(S) = S 4 , 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 highability 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 YL = 20000, and the productivity of high-ability workers is YH = 50000. The cost of education to high-ability workers is CH(S) = S 4 , 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 highability 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
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 lowability workers and decreases the cost of education for low-ability workers to CL = S 2 . For what range of educational requirements the separating equilibrium is sustained? Is it different from 2.2? Why?
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