AP MicroeconomicsProduction & Costs
Envelope Curve (Long-Run ATC)
The envelope curve is the long-run average total cost curve, which 'wraps around' and is tangent to every short-run ATC curve, lying on or below all of them.
In the long run a firm can choose any plant size, so each plant size has its own short-run ATC curve. The LRATC is the lower boundary (the 'envelope') formed by the lowest achievable cost at each output, tangent to each short-run curve at the output where that plant is optimal. Importantly, the tangency point is usually NOT the minimum of the short-run ATC, except at the single output where LRATC is itself at its minimum. The downward part reflects economies of scale and the upward part diseconomies of scale.