Question

Let the total cost (TC) = \( C = f(X) \) for a firm in the short run, which of the following expressions represents the correct relationship between marginal cost (MC) and average cost (AC)?

• A. Slope of AC = \( \frac{1}{X} \left[AC - MC \right] \)
• B. Slope of AC = \( \frac{1}{X} \left[AC - MC \right] \)
• C. \( MC = AC + X \left(\text{slope of AC} \right) \)
• D. \( X^2 \left(\text{slope of AC} \right) = X^2 MC - C \)

Hint:

The slope of the average cost curve depends on the difference between average cost and marginal cost.

Answer 1

The Correct Option is A

Step 1: Define the relationship.
The relationship between marginal cost (MC) and average cost (AC) is crucial for analyzing a firm's cost behavior. The slope of the AC curve and its interaction with MC dictate cost patterns at varying output levels.

Step 2: Evaluate options.
- (A) Slope of AC = \( \frac{1}{X} \left[AC - MC \right] \): This statement is accurate. The slope of the average cost curve is contingent on the disparity between average cost and marginal cost.
- (B) and (C) represent inaccurate interpretations.
- (D) is erroneous due to an incorrect formula for the relationship.

Step 3: Conclude.
The accurate formula for the slope of AC concerning MC is \( \frac{1}{X} \left[AC - MC \right] \).