At which point does the SMC curve cut the SAC curve? Give reason in support of your answer.

Exercises · Q19

SMC

Sikkim CbseNCERTSubjective· 3mImportance★★★★★

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Concept understanding — Marginal Cost Average Variable Cost Relationship

Let’s start with something you already know from everyday life.

Imagine you run a small stall selling samosas. You already have the stove, oil, and spices — those are your fixed costs. Every extra samosa you make needs more dough and more oil — those are your variable costs. Now, suppose making 10 samosas costs you ₹100 in variable costs (₹10 per samosa on average). If you make 11 samosas, the extra (marginal) cost might be only ₹8 — maybe because you’re using the hot oil more efficiently. That ₹8 is your marginal cost. Notice something: the average variable cost (AVC) was ₹10, but the marginal cost (MC) is ₹8 — lower. What happens to the average? It gets pulled down. The new AVC for 11 samosas becomes ₹108 ÷ 11 ≈ ₹9.82. So when MC is below AVC, AVC falls. If the 12th samosa costs ₹12 (MC > AVC), the average will rise.

That’s the whole relationship in a nutshell: MC pulls AVC along with it.

The precise meaning

Marginal Cost (MC) is the addition to total variable cost when one more unit is produced. In symbols:

MC_n = TVC_n - TVC_{n-1}

where $TVC$ is total variable cost and $n$ is the number of units.

Average Variable Cost (AVC) is total variable cost divided by output:

AVC = \frac{TVC}{Q}

where $Q$ is the quantity produced.

The relationship between them is a mathematical property of averages and marginals, not just an economic guess. Whenever the marginal (the extra) is less than the average, the average falls. Whenever the marginal is greater than the average, the average rises. The marginal equals the average only at the point where the average stops falling and starts rising — that is, at the minimum point of the AVC curve.

Important

The MC curve intersects the AVC curve at the minimum point of the AVC curve. This is a universal result — it holds for any U-shaped cost curves.

Why it matters

In the NCERT Class 12 Microeconomics textbook (Chapter 3: Production and Costs), this relationship is used to explain the shape of the firm’s supply curve and the shutdown decision. A firm will continue producing in the short run as long as price covers average variable cost. The MC curve above the minimum AVC is the firm’s short-run supply curve.

If you draw the diagram: AVC is U-shaped (falls then rises). MC is also U-shaped but crosses AVC at its lowest point. Before the crossing, MC lies below AVC; after, MC lies above AVC. This is not a coincidence — it’s the same logic as your samosa stall. …

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The Short-run Marginal Cost (SMC) curve cuts the Short-run Average Cost (SAC) curve at the minimum point of the SAC curve. This occurs because when marginal cost is below average cost, average cost falls; when marginal cost is above average cost, average cost rises; thus, marginal cost must equal average cost at its minimum.

To understand where the Short-run Marginal Cost ( $SMC$ ) curve intersects the Short-run Average Cost ( $SAC$ ) curve, it is crucial to grasp the fundamental relationship between any marginal value and its corresponding average value. This relationship is a mathematical necessity, not just an economic observation.

Consider any average value, such as your average marks in a series of exams. If your score on the next exam (the marginal score) is lower than your current average, your overall average will decrease. If your marginal score is higher than your current average, your overall average will increase. The only way your average can remain unchanged, or transition from falling to rising, is if your marginal score is exactly equal to your average score.

Applying this principle to costs:

When the cost of producing an additional unit of output (the Short-run Marginal Cost, $SMC$ ) is less than the average cost of all units produced so far (the Short-run Average Cost, $SAC$ ), the $SAC$ must be falling. The cheaper additional unit pulls the average down.
When the cost of producing an additional unit of output ( $SMC$ ) is greater than the average cost ( $SAC$ ), the $SAC$ must be rising. The more expensive additional unit pulls the average up. …

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Q.At which point does the SMCSMCSMC curve cut the SACSACSAC curve? Give reason in support of your answer.

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Q.At which point does the $SMC$ curve cut the $SAC$ curve? Give reason in support of your answer.

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