Question

Say there are two types of workers, low productivity types (60% of the population) and high productivity types (40% of the population). They have lifetime productivity of 200 and 400 respectively. The employer knows the proportion of each type and their relative productivity but cannot distinguish between individuals’ future productivity at the point of hiring.

What wage would a competitive employer pay? [10]
Say the cost of education for a low productivity worker is 30. A high productivity worker enjoys a lower cost of education: 15. Education has no effect on productivity. The employer now introduces contracts so as to attract high productivity workers (only). What minimum level of education will an employer require to ensure that only high productivity workers apply for these jobs? What surplus does each type of worker earn? [30]
Suppose that the employer now introduces jobs with no educational requirement so as to attract low productivity types also. How should this change the requirements for the high productivity jobs? [30]
Who loses and gains from the introduction of these jobs? [30]

Answer 1

1. Ratio of low productivity worker and high productivity worker (L_L /L_H)= 60%/40%= 3/2

Also relative productivity of low productivity and high productivity workers (R_p ) = 200/400= 1/2

Therefore, wage paid to each worker category by a competitive employer = (L_L /L_H)/R_p = 3/2/1/2= 3

2. Cost of education of high productivity worker = 15

Also (L_L /L_H) = 3/2

Therefore, minimum education level to be set by employer must cost = cost of education of high productivity worker/ (L_L /L_H)

                                                                                               = 15/3/2= 10

Therefore, the employer should set a minimum education level that cost 10 to each type of worker so that only high productivity workers can apply for the job and low productivity workers cannot immediately apply for the job due to their high cost of education.

Surplus of high productivity worker = Actual cost of education- cost of minimum education fixed by the employer = 15-10=5

Surplus of low productivity worker = 30-10=20

3. If employer introduces job with no education requirement, it will set minimum education level that cost = cost of education of low productivity worker/ (L_L /L_H)= 30/3/2= 20

At education level costing 20, only low productivity workers can apply for the jobs as high productivity workers cannot apply for the job due to high cost of education fixed by employer.

Surplus of low productivity worker = 30-20=10

Surplus of high productivity worker = 15-20=-5

From both categories of jobs, low productivity workers gain the most and high productivity workers loses.