Why is MP less than AP when both fall?

Introduction:
In economics, the terms AP (Average Product) and MP (Marginal Product) are used to measure the productivity of inputs in the production process. When both AP and MP fall, it means that the productivity of each additional unit of input decreases. However, MP tends to be lower than AP in this scenario. In this explanation, we will explore the reasons behind this phenomenon.

Understanding Average Product (AP):
AP is calculated by dividing the total product (output) by the quantity of input used. It represents the average productivity of each unit of input. Initially, as more input is added, the total product increases at an increasing rate, resulting in a rising AP. However, at a certain point, the increase in input starts to have diminishing returns, causing AP to fall.

Understanding Marginal Product (MP):
MP, on the other hand, measures the change in total product resulting from adding one more unit of input. It calculates the productivity of the last unit of input. Like AP, MP also experiences diminishing returns as more input is added. Initially, MP is higher than AP, indicating an increase in productivity. However, as the law of diminishing returns sets in, MP decreases and eventually falls below AP.

Reasons for MP being less than AP when both fall:
1. Law of Diminishing Returns: The main reason for the decline in both AP and MP is the law of diminishing returns. As more units of input are added to the production process, the additional output (MP) derived from each additional unit starts to decrease. This decrease in MP contributes to the fall in AP.

2. Input Allocation: Another contributing factor is the allocation of inputs. When the production process is optimized, inputs are allocated in a way that maximizes efficiency and productivity. Initially, the allocation of inputs may be more effective, resulting in higher MP. However, as more units of input are added, the efficiency of input allocation may decline, leading to a decrease in MP.

3. Fixed Factors: In some cases, certain factors of production may be fixed, meaning they cannot be increased or changed easily. As more units of the variable factor (the input being measured) are added while the fixed factors remain the same, the productivity of each additional unit decreases. This decrease in productivity is reflected in the falling MP.

Conclusion:
In summary, when both AP and MP fall, it is primarily due to the law of diminishing returns and the declining productivity of each additional unit of input. Although both measures decrease, MP tends to be lower than AP because it represents the productivity of the last unit added, which experiences diminishing returns more prominently. Understanding these concepts helps economists and businesses analyze and optimize their production processes for maximum efficiency and output.