Answer :
The question pertains to the graphical representation of the relationship between Average Product (AP) and Marginal Product (MP) in the context of production analysis in economics.
To understand the graphical relationship between AP and MP, it's important to first define the concepts:
Average Product (AP): This is the output per unit of input, usually labor. It is calculated as the total output produced divided by the number of units of input used. Mathematically, it can be expressed as:
[tex]AP = \frac{Total\ Output}{Quantity\ of\ Input}[/tex]Marginal Product (MP): This refers to the additional output produced when one more unit of input is added, keeping all other inputs constant. It is the derivative of the total product function with respect to the input:
[tex]MP = \frac{\Delta Total\ Output}{\Delta Quantity\ of\ Input}[/tex]
Graphical Relationship Explanation:
- As more units of input are added, the MP initially increases due to increasing returns to scale. However, as inputs continue to increase, the returns diminish, causing MP to eventually decrease.
- The AP curve also increases as long as the MP is greater than the AP because adding an input increases the average output per unit.
- The key point to note is that the MP curve crosses the AP curve at the maximum point of the AP curve. This is because, at this point, the AP is at its highest value, and any additional input will start reducing the AP as the MP drops below it.
Based on this understanding, the correct multiple-choice option that describes the relationship is:
(C) MP cuts AP from above, at the maximum point of AP.
