What do the long run marginal cost and the average cost curves look like?

Exercises · Q21

Q. What do the long run marginal cost and the average cost curves look like?

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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In the long run, all inputs are variable, so the LRMC and LRAC curves are U-shaped, with LRMC intersecting LRAC at its minimum point — exactly the same relationship as in the short run, but driven by returns to scale rather than by diminishing returns to a fixed factor.

The key to understanding long-run cost curves is to remember that in the long run, there are no fixed factors. A firm can choose any plant size, any technology, any scale of operation. This changes the reason the curves are U-shaped, but not their shape.

In the short run, the U-shape of the average variable cost (AVC) and marginal cost (MC) curves comes from the law of diminishing marginal returns — as you add more variable input to a fixed plant, output per extra worker eventually falls. In the long run, there is no fixed plant. The U-shape comes from returns to scale: first increasing returns (cost per unit falls as scale rises), then constant returns, then decreasing returns (cost per unit rises as scale rises).

The Long Run Average Cost (LRAC) Curve

The LRAC curve is the envelope of all possible short-run average cost (SRAC) curves. Each SRAC curve corresponds to a particular plant size. In the long run, the firm can choose the plant size that gives the lowest average cost for its chosen output level.

For low output levels, a small plant (SRAC₁) gives the lowest cost.
For medium output, a medium plant (SRAC₂) is best.
For high output, a large plant (SRAC₃) is best.

The LRAC curve touches each SRAC curve at exactly one point — the point where that plant size is optimal. It is U-shaped:

Downward-sloping portion: Economies of scale — specialisation, bulk buying, technological indivisibilities. Average cost falls as output rises.
Flat portion (if any): Constant returns to scale — doubling all inputs exactly doubles output, so average cost is constant.
Upward-sloping portion: Diseconomies of scale — coordination problems, management inefficiencies, communication breakdowns. Average cost rises as output rises.

Watch out

A common mistake is to think the LRAC curve passes through the minimum of each SRAC curve. It does not. The LRAC touches each SRAC at the point where that plant size is optimal for that output — which is not necessarily the SRAC's minimum. Only the SRAC of the optimal plant size (the one whose minimum equals the LRAC minimum) is tangent at its own minimum.

The Long Run Marginal Cost (LRMC) Curve

The LRMC curve shows the change in total long-run cost when output increases by one unit, with the firm free to adjust all inputs (including plant size). It is derived from the LRAC curve in exactly the same way that short-run MC is derived from short-run AVC:

LRMC = \frac{\Delta LRTC}{\Delta Q}

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Q.What do the long run marginal cost and the average cost curves look like?

The Long Run Average Cost (LRAC) Curve

The Long Run Marginal Cost (LRMC) Curve

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