Question

Which of the following options correctly defines the geometric relationship between the Short-run Marginal Cost (SMC) curve and the Average Variable Cost (AVC) curve?

• A. \( \text{The SMC curve intersects the AVC curve from below at its lowest (minimum) point.} \)
• B. \( \text{The SMC curve remains completely parallel and sits strictly above the AVC curve at all output levels.} \)
• C. \( \text{The SMC curve cuts the AVC curve at its highest maximum point during early production phases.} \)
• D. \( \text{The SMC curve always intersects the AVC curve at the exact same output level where Average Fixed Cost reaches zero.} \)

Hint:

The marginal cost curve always passes through the lowest points of both the Average Variable Cost (AVC) and the total Average Cost (AC) curves.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In microeconomics, there is a strict mathematical relationship between marginal values and average values.
If the marginal (the cost of the next unit) is less than the average, the average must fall.
If the marginal is more than the average, the average must rise.
If the marginal is equal to the average, the average is constant (at its minimum).
Step 2: Detailed Explanation:
Let's analyze the movement of \(SMC\) and \(AVC\):
1. Initial Stage: As production increases, both \(SMC\) and \(AVC\) fall due to increasing returns. During this stage, \(SMC\) falls faster and stays below the \(AVC\) curve. Since \(SMC<AVC\), it pulls the average down.
2. Turning Point: Eventually, diminishing returns set in. \(SMC\) starts to rise while \(AVC\) is still falling.
3. Intersection: As \(SMC\) continues to rise, it eventually catches up to the \(AVC\). At the point where \(SMC = AVC\), the \(AVC\) curve reaches its lowest point (minimum).
4. Post-Intersection: Once \(SMC\) rises above the \(AVC\), it starts pulling the average up. Now, \(SMC>AVC\), and the \(AVC\) curve begins its upward slope.
Geometric Result:
Because \(SMC\) was below \(AVC\) and then moves above it, it must pass through the bottom-most point of the \(AVC\) curve.
Step 3: Final Answer:
The \(SMC\) curve cuts the \(AVC\) curve from below at its minimum point.
Thus, Option (A) is correct.