Chapter 7: Problem 14

How do we calculate marginal product?

Short Answer

Expert verified

To calculate the marginal product (MP), use the formula: \( MP = \frac{\Delta Q}{\Delta I} \), where \(\Delta Q\) denotes the change in total output and \(\Delta I\) denotes the change in input. For example, if a firm's total output rises from 100 to 130 units when the labor input increases by 1 unit, the marginal product of labor would be \(\frac{130-100}{5-4}=\frac{30}{1}=30\) units of output per additional unit of labor.

Step by step solution

1. Understanding Marginal Product

Marginal product is the additional output that a firm produces when it uses an additional unit of input, typically labor or capital. It helps in determining the most efficient production level for a firm.

2. Formula for Marginal Product

To calculate the marginal product (MP) of an input, use the following formula: \[ MP = \frac{\Delta Q}{\Delta I} \] Where: - \(MP\) represents the marginal product - \(\Delta Q\) denotes the change in total output (quantity produced) - \(\Delta I\) denotes the change in input (such as number of labor hours or units of capital)

3. Work with an Example

Suppose a firm produces 100 units of output using 4 units of labor. When it increases the labor input by 1 unit (to 5 units of labor), the total output rises to 130 units. Let's calculate the marginal product of labor.

4. Calculate Change in Output and Input

First, determine the change in output and input: - \(\Delta Q = 130 - 100 = 30\) units - \(\Delta I = 5 - 4 = 1\) unit of labor

5. Calculate the Marginal Product

Now, follow the formula for calculating the marginal product: \[ MP = \frac{\Delta Q}{\Delta I} = \frac{30}{1} = 30 \] The marginal product of labor for this firm is 30 units of output per additional unit of labor.