Why does the SMC curve cut the AVC curve at the minimum point of the AVC curve?

Exercises · Q18

SMC

Telangana TsbieTextbookSubjective· 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 SMC curve cuts the AVC curve at its minimum because when marginal cost is below average variable cost, it pulls the average down; when it is above, it pulls the average up — the only point where the average stops falling and starts rising is where marginal cost equals average variable cost.

This is one of the most elegant relationships in microeconomics, and it follows from a simple logical principle: the behaviour of an average depends on the value of the next (marginal) unit.

Think of your own test scores. If your average score so far is 70, and you score 90 on the next test (marginal score > average), your average rises. If you score 50 (marginal < average), your average falls. The average stays unchanged only when the next score equals the current average. Exactly the same logic applies to costs.

The Short-Run Marginal Cost (SMC) is the cost of producing one additional unit of output. The Average Variable Cost (AVC) is the total variable cost divided by the total output. Now, as long as the cost of producing the next unit (SMC) is less than the current AVC, that next unit pulls the average down. So AVC is falling. Conversely, when SMC is greater than AVC, each additional unit pushes the average up, so AVC is rising.

The only point where AVC stops falling and hasn't yet started rising is its minimum. At that exact point, the marginal unit neither raises nor lowers the average — SMC must equal AVC. That is why the SMC curve cuts the AVC curve from below at the AVC curve's minimum point.

\text{When } SMC < AVC \implies AVC \text{ is falling}

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Q.Why does the $SMC$ curve cut the $AVC$ curve at the minimum point of the $AVC$ curve?

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