The Long-Run Average Total Cost Curve

In the short run, a firm is stuck with whatever plant it built. In the long run, every input is variable, including the size of the factory itself. That freedom matters because different plant sizes have different short-run average cost curves, each with its own fixed costs and its own range of output where it runs most efficiently. A tiny plant is cheap per unit at low output but gets crowded and expensive as output grows. A huge plant has high fixed costs that only pay off at high output. The long-run curve is built from a whole family of these short-run curves, one for every possible plant size.

To draw it, imagine dozens of short-run curves, one per plant size, layered on a graph. At any output quantity, the firm picks whichever plant gives the lowest average cost at that exact quantity, not the plant that is lowest overall. For an output of 500 units, you would compare the short-run average cost of the small, medium, and large plant at Q = 500 specifically, and the cheapest one wins. The long-run curve is the lower envelope: it skims along the bottom of all those curves, switching from one short-run curve to the next as the cheapest option changes with quantity. It is not simply the single lowest short-run curve, because no one plant size stays cheapest across every output level.

This connects directly to economies and diseconomies of scale, which show up as the long-run curve first falling, then flattening, then rising. It also explains why a firm caught producing on the wrong short-run curve, one built for a different output, pays higher average costs than it would if it could rebuild its plant to the ideal size for that quantity.