Average Total Cost vs Envelope Curve (Long-Run ATC)
Average Total Cost and Envelope Curve (Long-Run ATC) are two Production & Costs concepts in AP Economics that students often mix up. Average Total Cost is the total cost per unit of output produced. 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. Here is how they compare side by side.
It is found by dividing total cost by the quantity of output. Average total cost includes both average fixed and average variable costs and typically forms a U-shaped curve due to spreading fixed costs and diminishing returns.
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.
Short-Run ATC vs the Long-Run Envelope Curve: One Plant or Any Plant
| Short-Run Average Total Cost (ATC) | Long-Run ATC (Envelope Curve) | |
|---|---|---|
| What is held fixed | Plant size and any other fixed input | Nothing at all; every input can be changed |
| How many curves are drawn | One for each possible plant size | A single curve for the whole firm |
| What creates the U shape | Diminishing marginal returns to the variable input | Economies of scale, then diseconomies of scale |
| Position relative to the other | Sits on or above the long run curve at every output | Sits on or below every short run curve |
| Where the two touch | At the one output the plant was chosen for | Tangent to each short run curve at exactly one output |
| Are fixed costs present | Yes, the plant is a commitment for the period | No, every cost is avoidable when nothing is fixed |
| Time frame implied | Too little time to change the plant | Enough time to build, expand, shrink or exit |
The long run curve is assembled by picking the cheapest plant at each output
Give a firm three possible plants and read their short run average total cost at three output levels. The small plant costs 8 dollars a unit at 100 units, 10 dollars at 200 and 14 dollars at 300. The medium plant costs 11, 7 and 9 dollars at the same outputs. The large plant costs 16, 10 and 6 dollars. Now ask what a firm with enough time to build anything would pay. At 100 units it picks the small plant and pays 8 dollars. At 200 units it picks the medium plant and pays 7 dollars. At 300 units it picks the large plant and pays 6 dollars. Those three lowest figures, 8 then 7 then 6, are the long run average total cost curve for this firm across that range. Every short run figure that is not chosen sits above the long run figure at the same output, which is the whole content of the claim that the envelope lies on or below each short run curve. A firm stuck with the small plant while demand grows to 300 units pays 14 dollars rather than 6, and that 8 dollar penalty per unit is the cost of being in the short run. The numbers are illustrative.
Tangency is what the envelope guarantees, not a meeting of minimums
The most common error here is drawing the long run curve so it passes through the lowest point of every short run curve. It does not. Each short run curve touches the envelope at the single output for which that plant is the cheapest choice, and everywhere else it lies above. Only one plant has its own minimum sitting on the envelope: the plant used at the lowest point of the long run curve, which is the minimum efficient scale. Along the falling stretch of the long run curve, each plant is deliberately run at an output below its own short run minimum, because moving up to a slightly bigger plant beats squeezing the current one. Along the rising stretch, each plant is run past its own minimum. The intuition is that the firm cares about the cost of the output it wants, not about flattering any single plant. A second point worth holding onto: the two curves are U shaped for unrelated reasons, diminishing returns in the short run and scale effects in the long run. See /glossary/economies-of-scale and /micro/production-costs.
Frequently asked questions
What is the difference between short run and long run average total cost?
Short run average total cost is measured with the plant size held fixed, while long run average total cost is the lowest cost per unit available once the firm can change every input including the plant. There is one short run curve per plant and only one long run curve.
Why is long run ATC called an envelope curve?
Because it wraps around the family of short run curves, touching each one at a single output and never rising above any of them. It is built from the lowest cost per unit available at each quantity once plant size is free to change.
Does the long run curve touch the minimum of every short run curve?
No, it touches each short run curve at the output where that plant is the cheapest option, which is usually not that plant's own lowest point. The two minimums coincide for only one plant, the one operating at the lowest point of the long run curve.
Live Production Costs graph. Drag the curves, or open the full version.
Get AP Econ exam tips in your inbox
Occasional emails with study tips, new interactive graphs, and exam-season reminders. Free, no spam.
No spam. Unsubscribe anytime. Read our privacy policy.
Keep track of what you have studied
A free EconLearn account adds progress tracking, your quiz history, and achievements. Studying here is free either way, and there is nothing to pay for as a student.
Create a free accountAlready have one? Sign in
Last updated