The question asks to identify the statement that is NOT true regarding the relationship between Average Cost (AC) and Marginal Cost (MC).

Analyzing Cost Relationships

Statement 1: MC Falling Rate vs. AC Falling Rate

When Marginal Cost (MC) is falling, it is generally falling at a faster rate than Average Cost (AC). This is because MC represents the cost of the last unit, while AC is the average of all units. As MC falls below AC, it pulls the AC curve down, and typically does so more steeply than AC itself is falling.

Conclusion: This statement is generally true.

Statement 2: MC Increasing While AC Decreases

It is a fundamental concept that MC can increase while AC is still decreasing. This occurs when MC is below AC. MC rises eventually, and when it crosses AC from below, it starts pulling AC upwards. However, before MC rises above AC, there's a phase where MC is rising but still less than AC, causing AC to fall.

Conclusion: This statement accurately describes the relationship.

Statement 3: AC Constant Condition

Average Cost (AC) is constant only at its minimum point. At the minimum point of the AC curve, Marginal Cost (MC) equals Average Cost (AC). The statement claims that when AC is constant, AC < MC. This contradicts the principle that AC = MC at the minimum point of AC.

Mathematical representation:

• When AC is at its minimum, $AC = MC$.
• The statement implies $AC < MC$ when AC is constant.

Conclusion: This statement is NOT true.

Statement 4: MC Intersects AC at Minimum

A key principle in cost theory is that the MC curve intersects the AC curve at the lowest point of the AC curve. Before this point, MC is below AC; after this point, MC is above AC.

Conclusion: This statement is true.

Final Determination

Based on the analysis, statement 3 is the only one that incorrectly describes the relationship between AC and MC. Specifically, when AC is constant (at its minimum), AC is equal to MC, not less than MC.