Chapter 7: Problem 14

How do we calculate marginal product?

Short Answer

Expert verified

To calculate marginal product, follow these steps: 1) Gather data on the total product for each level of input, 2) Calculate the change in total product between each level, 3) Calculate the change in variable input, 4) Divide the change in total product by the change in variable input. For example: | Number of Workers | Change in Total Product | Change in Variable Input | Marginal Product | |-------------------|-------------------------|--------------------------|------------------| | 1 | 6 | 1 | 6 | | 2 | 9 | 1 | 9 | | 3 | 6 | 1 | 6 |

Step by step solution

Understand the concept of marginal product

Marginal product is the additional quantity of output that is produced by employing one more unit of a variable input, like labor, while keeping all other inputs, like capital and resources, constant. It helps to determine the effectiveness of adding additional inputs and can be used to determine optimal production levels for a firm.

Identify the total product for each level of input

First, gather data on the total product produced for each level of the variable input (labor, in this case). This information can usually be obtained from production data or potentially from a production function. For example, let's consider the following data: | Number of Workers | Total Product (units) | |-------------------|-----------------------| | 0 | 0 | | 1 | 6 | | 2 | 12 | | 3 | 21 | | 4 | 27 |

Calculate the change in total product

To find the marginal product, we need to calculate the change in total product between each level of variable input. To do this, subtract the total product produced at the previous level of input from the total product produced at the current level of input. For example: - Change when going from 0 to 1 worker: \(12 - 6 = 6\) - Change when going from 1 to 2 workers: \(21 - 12 = 9\) - Change when going from 2 to 3 workers: \(27 - 21 = 6\)

Calculate the change in variable input (labor)

Now, calculate the change in the variable input (number of workers) between each level. In this case, the change in the number of workers is just 1 as we are employing one additional worker at each level.

Calculate the marginal product

Finally, divide the change in total product by the change in variable input to obtain the marginal product for each level of input. For example: | Number of Workers | Change in Total Product | Change in Variable Input | Marginal Product | |-------------------|-------------------------|--------------------------|------------------| | 1 | 6 | 1 | 6 | | 2 | 9 | 1 | 9 | | 3 | 6 | 1 | 6 | The marginal product for each additional worker is, respectively, 6, 9, and 6 units.