Correct Option: B. MC is equal to ATC Detailed Explanation: To understand the relationship between Marginal Cost (MC) and Average Total Cost (ATC) when ATC is at its minimum point, we need to delve into the definitions and the behavior of these cost curves.

1. Definitions:
2. Marginal Cost (MC): This is the additional cost incurred by producing one more unit of a good or service. It is calculated as the change in total cost divided by the change in quantity produced.
3. Average Total Cost (ATC): This is the total cost of production divided by the number of units produced. It reflects the average cost per unit.
4. Cost Curves:
5. The ATC curve typically has a U-shape. Initially, as production increases, ATC decreases due to spreading fixed costs over more units and increasing efficiency. However, after a certain point, ATC starts to increase due to diminishing returns.
6. The MC curve also has a U-shape and intersects the ATC curve at its lowest point.
7. Minimum Point of ATC:
8. The minimum point of the ATC curve is significant because it represents the most efficient scale of production. At this point, the cost per unit is minimized.
9. The relationship between MC and ATC at this minimum point is crucial: when MC is less than ATC, producing additional units will lower the average cost, and when MC is greater than ATC, producing additional units will increase the average cost.
10. Key Relationship:
11. At the minimum point of the ATC curve, the MC curve intersects the ATC curve. This means that:
    • When MC = ATC, the average total cost is at its minimum.
    • If MC < ATC, ATC is decreasing.
    • If MC > ATC, ATC is increasing.

Thus, when ATC is at its minimum, the correct relationship is that MC is equal to ATC. Why Other Options Are Incorrect:

• Option A: MC is less than ATC:
• This statement is true when ATC is decreasing. However, it cannot be true at the minimum point of ATC, as we established that at the minimum point, MC must equal ATC.
• Option C: MC is greater than ATC:
• This statement is true when ATC is increasing. Again, this cannot be the case at the minimum point of ATC, where MC must equal ATC.
• Option D: MC is unrelated to ATC:
• This statement is incorrect because MC and ATC are fundamentally related in the context of production costs. Their relationship is critical for understanding cost behavior in the short run.

Summary of Key Points:

• At the minimum point of the Average Total Cost (ATC) curve, Marginal Cost (MC) is equal to ATC.
• The relationship between MC and ATC determines whether ATC is increasing or decreasing.
• Understanding this relationship is crucial for making production decisions and achieving cost efficiency.
• The U-shape of both the MC and ATC curves illustrates the principles of economies and diseconomies of scale.

This understanding is essential for any economics student preparing for professional exams, as it forms the basis for analyzing cost structures in various market conditions.