Cost Curves

The family of cost curves

From a firm’s total cost \(C(q) = F + VC(q)\) we build four per-unit curves:

• AFC = \(F/q\) — average fixed cost, always falling (fixed cost spread over more units).
• AVC = \(VC(q)/q\) — average variable cost, U-shaped.
• ATC = \(C(q)/q\) = AVC + AFC — U-shaped, lies above AVC, gap = AFC.
• MC = \(\dfrac{dC}{dq}\) — marginal cost.

The key geometry: MC cuts AVC and ATC at their minimum points — because an average falls while the marginal is below it and rises once the marginal is above it.

Try it. Raise fixed cost F — AFC and ATC shift up (MC and AVC don’t move), and the ATC minimum slides right. Watch MC slice through both U’s at their lowest points.

Fixed cost F: 20

▬ MC ▬ AVC ▬ ATC ▬ AFC

What to notice

• MC cuts AVC and ATC at their minimums — the dots. Left of a minimum, MC is below the average (pulling it down); right of it, MC is above (pulling it up).
• Raise F: AFC and ATC shift up, the ATC minimum moves right, but MC and AVC don’t move (fixed cost isn’t marginal or variable).
• The vertical gap between ATC and AVC is AFC — and it shrinks as q grows.