Question

The following table shows total output (in tax returns completed per day) of the accounting firm of Hoodwink and Finagle: $$\begin{array}{cc}\text { Number of } & \text { Number of Returns } \\\\\text { Accountants } & \text { per Day } \\\\\hline 0 & 0 \\\1 & 5 \\\2 & 12 \\\3 & 17 \\\4 & 20 \\\5 & 22\end{array}$$ Assuming the quantity of capital (computers, adding machines, desks, etc.) remains constant at all output levels: a. Calculate the marginal product of each accountant. b. Over what range of employment do you see increasing returns to labor? Diminishing returns? c. Explain why \(M P L\) might behave this way in the context of an accounting firm.

Short answer

a. The MPL for each accountant is: 1st accountant = 5, 2nd accountant = 7, 3rd accountant = 5, 4th accountant = 3, 5th accountant = 2.\nb. The range of employment with increasing returns to labor is from 0 to 2 accountants, and the range with diminishing returns to labor is from 2 to 5 accountants. \nc. The MPL behaves this way due to the law of diminishing returns. As more accountants are added to a fixed amount of capital, each accountant has less capital to work with, leading to smaller increases in output.

Step-by-step solution

Calculate MPL

The MPL can be calculated using the formula: MPL = Change in Total Output / Change in Labor. Based on the data in the table, the MPL for each additional accountant can be calculated as follows: for the 1st accountant, MPL = (5-0)/(1-0) = 5; for the 2nd accountant, MPL = (12-5)/(2-1) = 7; for the 3rd accountant, MPL = (17-12)/(3-2) = 5; for the 4th accountant, MPL = (20-17)/(4-3) = 3; for the 5th accountant, MPL = (22-20)/(5-4) = 2.

Identify the Range of Employment with Increasing and Diminishing Returns to Labor

The range of employment with increasing returns to labor is the range where the MPL is increasing, which is from 0 to 2 accountants. The range with diminishing returns to labor is the range where the MPL is decreasing, which is from 2 to 5 accountants.

Explain the Behavior of MPL

The MPL is behaving this way because of the law of diminishing returns, a principle stating that at some point, adding an additional unit of a variable input, holding all other inputs constant, will result in smaller increases in output. In an accounting firm, as more accountants are added to a fixed amount of capital, each accountant has less capital to work with, so the additional output produced by each accountant declines.

Key concepts

Marginal Product of Labor

The Marginal Product of Labor (\(MPL\)) is a critical concept in production theory. It measures the change in output resulting from employing an additional worker, holding all costs constant. In simpler terms, it tells us how much more is produced when we add another worker to the mix. This is easily calculated using the formula:

• \(MPL = \frac{\text{Change in Total Output}}{\text{Change in Labor}}\)

For example, in the accounting firm scenario, the change in total output when moving from 0 to 1 accountant is from 0 to 5 returns per day. Thus, the \(MPL\) is \(5\) for the first accountant. Understanding\(MPL\) helps firms decide the optimal number of workers to employ to maximize productivity without overextending their resources.
Overall, the \(MPL\) can vary depending on the number of workers. Initially, it may increase, but eventually, it will decrease due to other factors like fixed physical capital.

Law of Diminishing Returns

The Law of Diminishing Returns is an economic principle that describes what happens when more and more units of a variable input, like labor, are added to a fixed input, like capital. Initially, additional workers can lead to higher increases in total output, leveraging the equipment and space better. This is evident when the \(MPL\) is increasing.
However, after a certain point, adding more workers leads to smaller increases in output. This occurs because the variable input has become saturated relative to the fixed input, leading to less efficient production. In the context of the accounting firm, once they hired the second accountant, the firm initially experienced increasing returns with an \(MPL\) that grows.
Yet, after the second accountant, diminishing returns took over, as evidenced by the decreasing \(MPL\) for the additional accountants employed. This sees the \(MPL\) fall progressively as you reach 5 accountants, as shared resources become overstretched.

Increasing Returns to Labor

Increasing Returns to Labor occurs during the initial stages of labor employment, particularly when adding more workers results in higher marginal gains in output. In an accounting firm, this can happen because the initial addition of workers can help share the workload and improve the speed of processing returns.
With 1 to 2 accountants, each additional accountant significantly improves the efficiency and output, showing an \(MPL\) that increases from 5 to 7. This might be because one accountant can help the other, utilizing technology and tools more efficiently, and even facilitate better division of labor.
In this range, the firm benefits from better coordination and specialization, meaning each accountant can focus on different tasks that complement each other's work, allowing the team to work together more effectively and improve overall productivity.