A firm faces the following relationship between the real wage it pays and the effort exerted by its workers. The marginal product of labor for this firm is given by MPN = E (100 - N)/9.The firm will choose to pay a wage such that the effort level is

Question

A firm faces the following relationship between the real wage it pays and the effort exerted by its workers.  The marginal product of labor for this firm is given by MPN = E (100 - N)/9.The firm will choose to pay a wage such that the effort level is

Quizplus · Accepted Answer

To maximize its profits, the firm will choose to pay the wage that equates the marginal product of labor to the wage rate, which is also known as the value of the marginal product of labor (VMPL) and is given by VMPL = MPN x P.
Since the wage rate is not given in the problem, we can assume it to be equal to 1 for simplicity. Therefore, the VMPL simplifies to VMPL = (100 - N)/9.
To maximize profits, the firm will choose the effort level that maximizes the VMPL. 
To find the optimal effort level, we can take the derivative of the VMPL with respect to N and set it equal to zero:
dVMPL/dN = -1/9 = 0
Solving for N, we get N = 27.
Therefore, the firm will choose to pay a wage such that the effort level is 27 to maximize its profits.

A Firm Faces the Following Relationship Between the Real Wage