Question

Average product is equal to marginal product when:

• A. Marginal Product is unity
• B. Marginal Product is zero
• C. Average Product is minimum
• D. Average Product is maximum

Hint:

Remember the rules of the AP and MP relationship:
- When \( \text{MP} > \text{AP} \), AP is rising.
- When \( \text{MP} < \text{AP} \), AP is falling.
- When \( \text{MP} = \text{AP} \), AP is at its maximum.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In microeconomics and production economics, the law of variable proportions describes the relationships between Total Product (TP), Average Product (AP), and Marginal Product (MP) as a variable input is added to a fixed input.

Step 2: Detailed Explanation:
Let us examine the mathematical and graphical relationships between Average Product (AP) and Marginal Product (MP):
- The Average Product is defined as \( \text{AP} = \frac{\text{TP}}{x} \), where \( x \) is the variable input.
- The Marginal Product is the rate of change of Total Product with respect to the input: \( \text{MP} = \frac{d(\text{TP})}{dx} \).
- To find the point where Average Product is maximized, we take the derivative of AP with respect to \( x \) and set it equal to zero:
\[ \frac{d(\text{AP})}{dx} = \frac{d}{dx} \left( \frac{\text{TP}}{x} \right) = 0 \]
Using the quotient rule:
\[ \frac{x \cdot \frac{d(\text{TP})}{dx} - \text{TP} \cdot 1}{x^2} = 0 \]
\[ x \cdot \text{MP} - \text{TP} = 0 \implies \text{MP} = \frac{\text{TP}}{x} \]
Since \( \frac{\text{TP}}{x} = \text{AP} \), we have:
\[ \text{MP} = \text{AP} \]
- This mathematical proof shows that the Marginal Product curve intersects the Average Product curve at the exact point where the Average Product is at its maximum.

Step 3: Final Answer:
Average product is equal to marginal product when Average Product is maximum.