Long-run average cost and economies of scale

A teaching model — costs are notional; not figures for the power industry.

Output Q
100
Scale measure S = marginal ÷ average cost1 LAC 20 · LMC 20

The boundary — bottom of long-run average cost

Each plant size has a short-run average cost curve (SAC); the long-run average cost (LAC) wraps them from below. At small output, growing lowers unit cost (economies of scale); past some point it raises it (diseconomies). Where a plant’s curve touches the long-run curve is not that plant’s own lowest point.

010203040Cost per unitplant 50plant 100plant 150★ 012050100150200Output QS = LMC/LAC

Plant SAC LAC LMC ● tangency ◆ SAC minimum ★ LAC minimum (LMC = LAC)

PlantTangency QSAC minimum QLowest SAC
505066.6721.67
10010010020
150150133.3321.67

Model assumption: LAC = 30 − 0.2Q + 0.001Q², plant s’s SAC = LAC + 0.002(Q − s)². The envelope and the meaning of economies of scale are in the study guide; the formulas are learning supplements. Moving along the curve is economies of scale; the whole curve shifting down is learning.

Not in this calculation

  • Economies of scope (several goods together)
  • The expansion path and cost-minimising conditions
  • Learning that lowers costs over time — mentioned only
  • Minimum efficient scale of real plant and any power-industry figures
  • Power-market rules such as capacity payments or SMP

Using the example values

Tool: Renuary (CC BY 4.0) · Numbers are examples. Method and limits on the original page.