Question

You were recently hired to replace the manager of the Roller Division at a major conveyor-manufacturing firm, despite the manager’s strong external sales record. Roller manufacturing is relatively simple, requiring only labor and a machine that cuts and crimps rollers. As you begin reviewing the company’s production information, you learn that labor is paid \(12 per hour and the last worker hired produced 80 rollers per hour. The company rents roller cutters and crimping machines for \)15 per hour, and the marginal product of capital is 110 rollers per hour. What do you think the previous manager could have done to keep his job?

Short answer

The manager might grow capital while reducing labor.

Step-by-step solution

Introduction

The following equation helps finding the capital$\left(\mathrm{K}\right)$and labor$\left(\mathrm{L}\right)$input combination that minimizes costs.

$\frac{{\mathrm{MP}}_{\mathrm{L}}}{\mathrm{w}}=\frac{{\mathrm{MP}}_{\mathrm{K}}}{\mathrm{r}}$

Where ${\mathrm{MP}}_{\mathrm{L}}$stands for Marginal Product of Labor; $\mathrm{w}$stands for wage; and ${\mathrm{MP}}_{\mathrm{k}}$stands for Marginal Product of Capital.

Explanation

Given that the previous person employed was paid $12 per hour and produced 80 rollers per hour. The company used to lease roller cutters and crimping equipment for $15 per hour, based on the marginal product of capital of 110 rollers per hour. Using this information-:

$$\begin{gathered} \frac{M{P}_L}{w}=\frac{80}{12} \\ \text{= 6.67} \\ \frac{M{P}_K}{r}=\frac{110}{15} \\ \text{= 7.33} \end{gathered}$$

By substituting the values, we can see that:

$$\begin{gathered} \frac{M{P}_L}{w}<\frac{M{P}_K}{r} \\ =\frac{80}{12}<\frac{110}{15} \end{gathered}$$

We can conclude that, the manager could have grown capital while reducing labor.