Question

Question 2. Consider a simple economy with two types of workers. There are capable workers (type A), constituting 70% of the population, with remaining workers (type B) being of average ability. There are two types of job opportunities as well, labeled Good and Bad. In a Bad job, either type of worker produces 20 units of output. In a Good job, Type A worker produces 80 units, and the Type B worker produces 0. The economy is doing well so there is enough demand for workers. This means that for each type of job companies must pay what they expect the employee to produce. Companies must hire each worker without observing his type and pay him before knowing his actual output. But Type A workers can signal their qualification by getting educated. For a Type A worker, the cost of getting educated to level n is 0.4n2, whereas for a Type B worker, it is n2. These costs are measured in the same units as output, and n must be an integer. (a) What is the minimum level of n that will achieve separation? (b) Now suppose the signal is made unavailable. Which kind of jobs will be filled by which kinds of workers and at what wages? Who will gain and who will lose from this change?

Answer 1

Answer a :-

Now let us assume total number of workers =100

Number of capable workers =70

Number of average workers = 30

If we assume that a standard mix of workers is hired by the company

Then for every additional 10 workers company hires a proportion of 7:3.

That means 7 capable workers and 3 average workers

The output produced by 10 workers will be (7*80)+(3*0)

560 units .

Thus labour productivity =560/10=56 unit / labour

Now the marginal cost for each labour would be their education expenditure

So if we consider n =6

Then for good labour the cost would be 0.4(8)²=25.6

For bad labour =(8)²=64

Average marginal cost =(64+25.6)/2= 45.8

Thus n =6

Answer b :-

Now signal is unavailable

Both produces 20 units each

Marginal revenue per labour =20 units

Now the n here cannot exceed 4

So the cost of education for capable people =0.4(4)²⁼6.4

Cost of education for average people =(4)²⁼16

Thus average MC or wage =( 16+6.4)/2=11.2/per labour