Long-Run Average Cost | Econ Academy

In the long run, the firm can choose its plant size — how many factories, how big each one is, how much capital to install. Each plant size has its own short-run $A T C$ ( $S R A C$ ) curve. The long-run average cost ( $L R A C$ ) curve is the “envelope” that wraps around all possible $S R A C$ curves, showing the lowest possible average cost at each output level.

Key Term

Long-Run Average Cost ($LRAC$)

The $L R A C$ curve is the envelope of all short-run average cost curves. For each output level, it shows the minimum average cost achievable when the firm can choose any plant size.

At each point on the $L R A C$ , the firm is using the optimal plant size for that output level.

Think of it this way: a small coffee shop (plant size 1) has a low $A T C$ for 100 cups/day but high $A T C$ for 1,000 cups. A large cafe (plant size 2) has a low $A T C$ for 1,000 cups but high $A T C$ for 100 cups (too much idle capital). The $L R A C$ traces the bottom of whichever $S R A C$ is cheapest at each output level — the firm picks the best plant size for its target output.

Interactive —

L R A C

as Envelope of

S R A C

Curves

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Several short-run ATC curves and the long-run envelope below them.

LRAC is the minimum of all SRACs — the firm picks the optimal K for each q

Key Term

Minimum Efficient Scale ($MES$)

The minimum efficient scale is the smallest output at which $L R A C$ reaches its minimum. Below $M E S$ , the firm hasn’t yet exploited all economies of scale. At $M E S$ , it’s producing at the lowest possible long-run average cost.

Worked Example

A firm has three possible plant sizes with the following minimum $A T C$ s:

Plant Size	Min $A T C$	Best output
Small	12 dollars	500 units
Medium	8 dollars	1,500 units
Large	10 dollars	3,000 units

What is the $M E S$ ? Which plant size should the firm choose if it expects demand of 2,000 units?

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Why doesn’t $L R A C$ just connect the minimums of each $S R A C$ curve?

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Practice · 1 / 4

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Test your understanding of long-run average cost:

The $L R A C$ curve is the envelope of:

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