Suppose there are two types of workers. Type 1 workers have a marginal product o

Question

Suppose there are two types of workers. Type 1 workers have a marginal product of labor (MPL) = 1. That is, if a firm hires an extra Type I worker, that worker will produce 1 extra unit of output. Type II workers have a MPL = 2. The firm can sell each extra unit of output for P = $10,000.

Firms are unable to identify whether or not a worker is Type I or Type II unless the worker sends a signal of what type they are. The signal that workers can send is a level of education, e. The firm adopts the following hiring strategy:

If e > e* then offer the worker a wage rate equal to $20,000.

If e < e* then offer the worker a wage rate equal to $10,000.

The cost to Type I workers of getting education level e is $4000*e. The cost to Type II workers of getting education level e is $2000*e. Assuming the workers choose e in an optimal manner, characterize the values of e* that will lead to a separating equilibrium.

Explanation / Answer

For, aseparating equilibrium , Type 1 workers should choose to receive a wage of 10,000 and Type 2 worker choose to receive a wage of 20,000.

Now lets look at for what values of e woill this happen.

Type 2 player will choose High Wage of 20,000 when the cost of cost of eduction to reaceive 20,000 wage is less than wage of 20,000

20,000 > 2000*e

e < 20,000/2,000

e < 10

Worker of Type 1 will choose , Low Wage of 10,000 when the cost of cost of eduction to reacieve 20,000 wage is greater 20,000

20,000 < 4000*e

5 < e

e > 5

the values of e* that will lead to a separating equilibrium will be

   5 < e < 10

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