Question

Given below are two statements:
Statement (I): Linear programming and budgeting have certain features in common, however, the former is a much more refined tool.
Statement (II): AVC per unit of output reaches a maximum at that level of output where APP is also at its maximum.
In light of the above statements, choose the most appropriate answer from the options given below.

• A. Both Statement (I) and Statement (II) are true.
• B. Both Statement (I) and Statement (II) are false.
• C. Statement (I) is true but Statement (II) is false.
• D. Statement (I) is false but Statement (II) is true.

Hint:

Remember the inverse relationship between cost and productivity:
- Maximum \(\text{APP}\) corresponds to Minimum \(\text{AVC}\).
- Maximum \(\text{MPP}\) corresponds to Minimum \(\text{MC}\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question requires an understanding of farm planning tools (budgeting vs. linear programming) and production economics cost relationships.
Specifically, we look at the mathematical relationship between physical product curves and variable cost curves.

Step 2: Key Formula or Approach:
The mathematical link between Average Variable Cost (\(\text{AVC}\)) and Average Physical Product (\(\text{APP}\)) of a variable input is given by:
\[ \text{AVC} = \frac{\text{TVC}}{Y} = \frac{P_x \cdot X}{Y} = \frac{P_x}{\left(\frac{Y}{X}\right)} = \frac{P_x}{\text{APP}_x} \]
where \( P_x \) is the unit price of the input \( X \), and \( Y \) is the total output.

Step 3: Detailed Explanation:
Let us evaluate Statement (I) first.
Both linear programming (LP) and farm budgeting are planning techniques used for resource allocation.
Budgeting is a trial-and-error method to estimate costs and returns, whereas LP is a refined, mathematically precise optimization technique that determines the absolute best allocation under linear constraints.
Hence, Statement (I) is true.
Now let us evaluate Statement (II).
Using our formula:
\[ \text{AVC} = \frac{P_x}{\text{APP}_x} \]
Because the input price \( P_x \) is constant, \( \text{AVC} \) is inversely proportional to \( \text{APP}_x \).
Consequently, when the Average Physical Product (\(\text{APP}_x\)) is at its maximum, the Average Variable Cost (\(\text{AVC}\)) must reach its minimum, not its maximum.
Thus, Statement (II) is false.

Step 4: Final Answer:
Statement (I) is true but Statement (II) is false.