Question

Suppose the population consists of only high-ability workers (who make up

80% of the population) and low-ability workers (who make up 20% of the population).

The present value of a high-ability worker’s lifetime productivity is $600,000, while the

present value of a low-ability worker’s lifetime productivity is $400,000. Suppose the

costs of education for high-type workers are $20,000/year, while the costs of education

for low-type workers are $30,000/year. Firms would like to separate the two types

of workers, and will pay the high-type wage to anyone with at least a certain level of

education. Anyone without this certain level of education will receive the low-type wage.

(a) If firms cannot distinguish between the two types of workers, what wage

would the firm pay in a pooling equilibrium?

(b) If firms set the required education level at 12 years, which types of work-

ers will go to school?

(c) If firms set the required education level at 4 years, which types of workers

will go to school?

(d) What level of education can this firm set as a signal to separate types?

Answer 1

solution:

a] If the firms cannot distinguish between high skilled workers and low skilled workers, then the firm will be forced to pay wages that would be satisfactory to both the parties. The lifetime productivity of a high skilled worker is $600000 whereas the livetime productivity value of a low skilled worker is $400000. The economy is such that the major population of 80% is composed of high skilled workers and the remaining 20% is made up of the low skilled workers. When unable to distinguish between the two the pool in equilibrium would be $500000, as the majority being high skilled the firm will opt to have a mid of the lifetime productivity of the two.

b] If the firm set the required level of education upto 12 years, the high skilled workers would be going to school. The company setting the education level would be willing to pay high pay to thosse workers who attain that qualification. With the cost of education costing $ 20000 a year, high skilled workers would prefer going to school and getting education upto 12 years.

c] If the firm set the eduaction level at 4 years, then we would see that low skilled worker would prefer going to school with four years of going to school, the low skilled worker will have to pay $30,000 per year and will be receiving a lieftime productivity of high level which the cpmpany would be willing to give if they attain the required level of education.

d] The firm can set a level of education till 7 years for the low skilled workers and more than 7 years for the high skilled workers.

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