Question

You were recently promoted to a management position of a firm that produces a certain popular widget, replacing the previous manager.  The firm uses only two types of labor when producing the product: experienced workers and unskilled workers. The firm can hire as many workers as needed. Unskilled workers are paid a wage of $10 per hour and experienced workers $50 per hour.

In your initial analysis, you learn that at the current amounts of labor, the marginal product of unskilled labor is 50 and a marginal product of experienced labor is 100.

Why did the firm replaced the previous manager and promoted you? Explain in detail.

Answer 1

In the given situation,

Marginal product of labor per dollar spent in case of skilled labor=MPL_S/w_S=100/50=2

Marginal product of labor per dollar spent in case of unskilled labor=MPL_U/w_U=50/10=5

We find that MPL_S/w_SU/w_U

Cost minimizing combination of inputs requires that Marginal product per dollar spent should be equal for all inputs. It is not the case here. It means that firm is not utilizing the optimal input mix.

Since MPL_S/w_SU/w_U

We can say that firm is having more number of skilled labor than required. It has also employed lesser number of skilled labor than required for optimal mix. Non optimal input combination increases the cost and hence reduces the profitability of the firm.

Non optimal input factor mix is likely to be the reason for replacing the previous manager. Firm should increase the number of unskilled labor and decrease the number of skilled labor in order to minimize the cost.