Lecture 8 · Week 10 · Besanko & Braeutigam ch. 8 · about 45 min

Cost Curves

Turning total cost into the per-unit curves that drive a firm's decisions: average fixed, average variable, average total and marginal cost, why marginal cost crosses each average curve at its minimum, and the shift from short-run to long-run cost curves.

By the end you can

Compute AFC, AVC, ATC and MC from a total cost function at a given output
Explain why MC crosses AVC and ATC exactly at each one's minimum
Explain why AFC always falls but MC and AVC are U-shaped
Distinguish short-run from long-run average cost, and connect long-run shape to returns to scale

From total cost to per-unit cost

The cost curve familyKey formulasFormula sheet →

AFC = \frac{FC}{Q} \qquad AVC = \frac{VC(Q)}{Q} \qquad ATC = \frac{TC(Q)}{Q} = AFC + AVC \qquad MC = \frac{dTC}{dQ}

$FC$: fixed cost, does not vary with Q
$VC(Q)$: variable cost, a function of output
$TC(Q)$: FC + VC(Q)

Use it when you are given a total cost function and need any of the per-unit cost measures at a specific output level.

Why MC crosses AVC and ATC at their minimums

This is exactly the same mathematical fact as “MP crosses AP at AP’s maximum” from Lesson 6, translated from output into cost. It is not a coincidence: marginal cost is, loosely, the cost-side mirror of marginal product.

MC and the average curvesKey relationshipFormula sheet →

MC \lt AVC \Rightarrow AVC \text{ falling} \qquad MC = AVC \Rightarrow AVC \text{ at its minimum} \qquad MC \gt AVC \Rightarrow AVC \text{ rising}

Use it when you need to explain, or read off a graph, why the MC curve passes through the minimum points of both the AVC and ATC curves — the same logic applies to ATC with AVC replaced by ATC throughout.

Try it: watch the four curves interact

Why the curves are shaped the way they are

Shape summaryKey shapesFormula sheet →

AFC: \text{always falling (spreading a fixed FC over more units)} \qquad MC, AVC, ATC: \text{U-shaped}

Use it when an exam asks you to explain — not just draw — why these particular shapes appear.

$AFC$ falls continuously because a fixed number (FC) is divided by an ever-larger $Q$ : it approaches, but never reaches, zero. $MC$ , $AVC$ and $ATC$ are U-shaped because of the short-run production story from Lesson 6: early units benefit from increasing marginal returns to the variable input (pulling MC down), but diminishing marginal returns eventually take over (pushing MC back up).

Short run versus long run

In the short run, at least one input (typically capital/plant size) is fixed, giving the U-shaped SRATC curves studied above. In the long run, a firm can also choose its plant size, so the long-run average total cost (LRATC) curve is the lower envelope of every possible short-run ATC curve — the cheapest way to produce each output level once plant size is also a choice variable.

Long-run average cost and returns to scaleConnectionFormula sheet →

\text{Economies of scale: LRATC falling} \qquad \text{Diseconomies of scale: LRATC rising} \qquad \text{Constant: LRATC flat}

Use it when you need to connect the shape of the long-run cost curve to the returns-to-scale concept from Lesson 6: increasing returns to scale produce economies of scale (falling LRATC), and so on.

Exam practice

Summary and review

$AFC = FC/Q$ , $AVC = VC(Q)/Q$ , $ATC = AFC+AVC$ , $MC = dTC/dQ$ .
MC crosses AVC and ATC exactly at each one’s minimum — the average/marginal relationship again.
AFC always falls; MC, AVC and ATC are typically U-shaped, reflecting increasing then diminishing marginal returns.
Fixed cost shifts ATC and AFC but leaves MC and AVC completely unaffected.
LRATC is the lower envelope of all short-run ATC curves; its shape mirrors returns to scale (economies, diseconomies, constant).