What Is The Relationship Between Average Product And Marginal Product

What is the Relationship Between Average Product and Marginal Product?

Understanding the relationship between average product (AP) and marginal product (MP) is crucial for businesses aiming to optimize their production processes and maximize profits. These two concepts, central to economics and management, describe the productivity of variable inputs, usually labor, in relation to output. This article will delve deep into defining both AP and MP, illustrating their relationship graphically and mathematically, and exploring the implications for production decisions.

Defining Average Product (AP) and Marginal Product (MP)

Before examining their relationship, let's clearly define each term:

Average Product (AP)

The average product represents the average output produced per unit of input. In simpler terms, if you're considering labor as your variable input, the average product of labor (APL) is the total output (TP) divided by the number of labor units (L) employed. Mathematically:

AP = TP / L

For instance, if 10 workers produce 100 units of output, the average product of labor is 10 units per worker (100/10 = 10). The average product is a useful metric for assessing the overall productivity of a firm's resources. A high average product indicates efficient use of resources, while a low average product suggests areas for improvement.

Marginal Product (MP)

The marginal product measures the additional output generated by employing one more unit of input. Focusing again on labor, the marginal product of labor (MPL) is the change in total output (ΔTP) resulting from a one-unit increase in labor (ΔL). The formula is:

MP = ΔTP / ΔL

Continuing the previous example, if adding an 11th worker increases total output to 115 units, the marginal product of the 11th worker is 15 units (115-100 = 15). The marginal product is vital for understanding the contribution of each additional unit of input. A high marginal product suggests that adding more units of input will significantly increase output, while a diminishing marginal product indicates that the incremental gains from additional input are decreasing.

The Relationship Between AP and MP: A Graphical Representation

The relationship between average product and marginal product can be best understood through a graph. Typically, both AP and MP curves are plotted against the quantity of the variable input (e.g., labor). The curves usually exhibit the following characteristics:

• Initially, both AP and MP rise: As you add the first few units of labor, both the average and marginal products increase. This is often due to specialization and division of labor. Workers can focus on specific tasks, increasing efficiency and overall output.

• MP intersects AP at AP's maximum: This is a crucial point. The marginal product curve always intersects the average product curve at the average product's maximum point. When MP is above AP, AP is rising; when MP is below AP, AP is falling. This is because if the additional output (MP) is higher than the average output (AP), it pulls the average up. Conversely, if the additional output is lower than the average, it pulls the average down.

• MP eventually declines (Law of Diminishing Returns): Beyond a certain point, the marginal product starts to decrease. This is a manifestation of the law of diminishing returns, which states that as you add more units of a variable input while holding other inputs constant, the additional output from each additional unit will eventually decrease. This is because of factors like limited space, equipment, or managerial capacity.

• AP follows MP's trend but lags: The average product curve follows a similar trend to the marginal product curve, rising initially and then declining. However, it always lags behind the marginal product curve. This lag reflects the averaging effect. The average product is influenced by all previous marginal products, while the marginal product reflects only the last unit added.

(Insert a graph here illustrating the typical relationship between AP and MP curves. The X-axis should represent the quantity of input (e.g., labor), and the Y-axis should represent output (AP and MP). The MP curve should intersect the AP curve at the maximum point of the AP curve. Both curves should initially rise, then MP should decline and intersect AP, and finally AP will decline.)

The Mathematical Relationship Between AP and MP

The relationship between AP and MP can also be expressed mathematically. Consider a small change in the number of labor units (ΔL). The change in total output (ΔTP) is equal to the marginal product (MP) multiplied by the change in labor units:

ΔTP = MP * ΔL

We can also express the average product as:

AP = TP / L

If we consider a small increase in labor units, we can analyze how the average product changes:

ΔAP = [(TP + ΔTP) / (L + ΔL)] – (TP / L)

Substituting ΔTP = MP * ΔL, we get a complex expression showing that the change in average product is influenced by both the average product and the difference between the marginal product and the average product. This confirms the graphical observation that when MP > AP, AP increases, and when MP < AP, AP decreases.

Implications for Production Decisions

Understanding the relationship between AP and MP has significant implications for businesses making production decisions:

• Optimal Input Level: Firms aim to operate where the marginal product is positive, maximizing output. However, they should also consider the cost of inputs. The point where the marginal product starts to decline is often an indicator that adding more inputs will become increasingly less cost-effective.

• Cost Minimization: By analyzing AP and MP, firms can identify the most efficient combination of inputs to minimize production costs for a given output level.

• Profit Maximization: Profit maximization involves finding the optimal output level where marginal revenue equals marginal cost. Understanding marginal product helps in determining the optimal level of variable inputs required to achieve that output level.

• Resource Allocation: Analyzing AP and MP for different inputs can assist businesses in efficiently allocating their resources among various production activities.

Beyond the Basic Model: Factors Influencing AP and MP

The basic model of AP and MP assumes a simplified environment. Several factors can influence the shapes and positions of these curves in the real world:

• Technological advancements: Improvements in technology can shift both AP and MP curves upwards, leading to higher productivity.

• Changes in other inputs: Variations in the quantities of fixed inputs (e.g., capital) can also affect the shape and position of AP and MP curves. Increasing fixed inputs might initially increase the marginal and average product but will ultimately still lead to diminishing returns.

• Quality of inputs: The quality of the variable inputs also plays a significant role. Higher-skilled workers, for example, might exhibit higher MP and AP compared to less-skilled workers.

• Management efficiency: Efficient management can optimize resource allocation and improve both AP and MP.

Conclusion: A Powerful Tool for Production Analysis

The relationship between average product and marginal product provides a powerful framework for understanding and analyzing production processes. By carefully examining these curves, businesses can make informed decisions about resource allocation, cost minimization, and ultimately, profit maximization. While the basic model provides a fundamental understanding, it's essential to consider the various real-world factors that can influence these curves and to adapt analytical approaches to specific contexts. The interplay between AP and MP remains a cornerstone concept in economics and a crucial element of effective business management.