Long-Run Average Cost (LAC) — The Envelope Curve

The long run is the period long enough for a firm to change EVERY factor of production, including the size of its plant or scale of operation — nothing remains fixed. In the long run, a firm is not stuck with the single plant size it happened to build; it can choose to build any one of a whole range of possible plant sizes, and each possible plant size has its own separate short-run average cost (SAC) curve, U-shaped exactly as described above.

The Long-Run Average Cost (LAC) curve, also called the planning curve, is built from this entire family of SAC curves: for each level of output, the firm selects whichever plant size gives the LOWEST average cost of producing that output, and the LAC curve traces out this lowest-cost point across every output level. Geometrically, the LAC curve is drawn tangent to every one of the many SAC curves, touching each one at a single point without ever cutting through any of them — which is exactly why it is called the "envelope curve": it envelops the whole family of short-run SAC curves from below. …