When the average total cost curve is at its minimum, we know that the

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Question restatement: When the average total cost curve is at its minimum, we know that the

Option a: average variable cost curve intersects the average total cost curve. This is a common misconception; the ATC minimum is not defined by an intersection with AVC. In fact, AVC and ATC are separate curves, and ATC is the sum of average fixed cost (AFC) and AVC. The point where ATC is minimized does not hinge on AVC crossing ATC.

Option b: average variable cost curve is above the average total cost curve. By definition, ATC = AFC + AVC, and since AFC is nonnegative, AVC cannot be above ATC at all points where ATC is defined. This statement misrepresents the relationship between AVC and ATC.

Option c: marginal cost curve intersects the average total cost curve. This is a standard result in cost theory: ATC is minimized at the output level where MC = ATC, meaning MC intersects ATC at its minimum point. The intuition is that MC reflects the cost of producing one more unit; when MC is below ATC, ATC is falling, and when MC is above ATC, ATC is rising, with the crossover at the minimum.

Option d: marginal cost curve is above the average total cost curve. If MC were consistently above ATC, ATC would be rising for all output levels, which would not place ATC at a minimum. This contradicts the existence of a minimum point for ATC.

In summary, the only statement that aligns with the standard cost-minimization condition is that the marginal cost curve intersects the average total cost curve at the minimum point of ATC. The other options rely on incorrect interpretations of the relationships among MC, AVC, and ATC.

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