Long-run cost, economies of scale and minimum efficient scale

Overview

Long-run average cost curve and how is it derived, long-run average cost curve sometimes called an envelope curve and internal economies of scale.

What you need to know

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Questions from this subtopic

Each one with the model answer underneath.

1. 1

   What is the long-run average cost curve and how is it derived?

   Model answer

   The long-run average cost curve shows the lowest average cost of producing each level of output when every factor of production can be varied, so the firm is free to choose its plant size. It is derived as the envelope of all the short-run average cost curves, each corresponding to one possible scale of plant. For every output the long-run curve takes the lowest short-run average cost available from any plant size.

2. 2

   Why is the long-run average cost curve sometimes called an envelope curve?

   Model answer

   Each short-run average cost curve represents the costs achievable with one fixed plant size, and there is a different curve for every possible plant. The long-run curve wraps around the whole family of short-run curves from below, touching each one at the single output for which that plant is the cheapest choice. It therefore never lies above any short-run curve and touches each at only one point.

3. 3

   Why can the long-run average cost curve never lie above a short-run average cost curve?

   Model answer

   In the long run the firm can choose any plant size, including the one it currently has, so every short-run option remains available to it. Having more options can only lower or leave unchanged the minimum achievable cost, never raise it. The long-run curve is therefore always at or below every short-run curve.

4. 4

   What would a diagram showing a firm's short-run cost curves alongside its long-run average cost curve look like?

   Model answer

   Put output per period on the horizontal axis and cost per unit on the vertical axis. Draw several U-shaped short-run average cost curves, one for each plant size, positioned progressively to the right, and draw the long-run average cost curve as a flatter, saucer-shaped curve tangential to each of them from below. On the falling section of the long-run curve, tangency occurs to the left of the short-run curve's own minimum, at the minimum of the long-run curve the two minima coincide, and on the rising section tangency occurs to the right of the short-run minimum.

5. 5

   Why is the point of tangency between a short-run and the long-run average cost curve not usually at the minimum of the short-run curve?

   Model answer

   On the falling part of the long-run curve, a firm expecting to expand will find it cheaper to build a slightly larger plant and under-use it than to run a smaller plant at full efficiency, so tangency occurs to the left of the short-run minimum. On the rising part, the reverse applies and the plant is worked beyond its own least-cost output. Only at the minimum of the long-run curve, which is the minimum efficient scale, do the two minima coincide.

6. 6

   What is the difference between economies of scale and the law of diminishing returns?

   Model answer

   Economies of scale are a long-run phenomenon in which increasing all factors together lowers average cost, because output rises more than proportionately to inputs. Diminishing returns is a short-run phenomenon in which adding a variable factor to a fixed factor causes marginal product to fall and marginal cost to rise. The first requires every factor to change, the second requires at least one to stay fixed, so the two cannot operate at the same time.

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