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DSE Economics | Long-Run Cost and Economies of Scale Lesson-Prep Guide (Tutor Edition) | LRAC, Fixed-Cost Spreading and Minimum Efficient Scale
Students say that bigger is cheaper but cannot say by how much or when it stops. This lesson uses one cost table to split the long-run average cost curve into three segments.
Objectives — Students can: (1) turn average costs of $40 at 100 units and $28 at 400 units into total costs of 4,000 and 11,200, and explain the 30% fall; (2) spread a fixed cost of 2,000 to show fixed cost per unit falling from $20 to $5, a 75% drop, while average variable cost rises from $20 to $23; (3) place minimum efficient scale at 400 units and compute that two 200-unit plants cost 12,800 against 11,200 for one 400-unit plant, a gap of 1,600 or 12.5%.
01 Prerequisites (3-minute check)
If any of these fails, fix it before the lesson starts.
| Skill | Quick check | Pass mark |
|---|---|---|
| Short and long run | Fixed factors in the short run only | Say the difference is adding a plant |
| Average cost | Total cost divided by output | Compute 4,000 over 100 aloud |
| Marginal cost | The cost of one more unit | State that it cuts average cost at the minimum |
02 Lesson flow (45 minutes)
| Time | Stage | Tutor does | Student does |
|---|---|---|---|
| 0-8 min | Short and long run | Separate overtime from a new plant | State that no cost is fixed in the long run |
| 8-20 min | Fill the table | Work back from average to total cost | Compute 4,000, 11,200, 42,000 |
| 20-30 min | Spread the fixed cost | Spread 2,000 over 100 and 400 units | Compute 20 and 5 |
| 30-38 min | Three segments | Name a cause for falling, flat and rising | Mark minimum efficient scale |
| 38-43 min | Two plants against one | Compare 12,800 with 11,200 | Compute the 1,600 gap |
| 43-45 min | Exit check | Three questions answered aloud | All three right |
03 Teaching script (read it out)
Scene 1: Average cost hides the structure
Give the table: 100 units at $40, 200 at $32, 400 at $28, 800 at $28, 1,200 at $35.
First move: total cost is average cost times quantity, so 100 units cost 4,000, 400 units cost 11,200 and 1,200 units cost 42,000.
The fall from $40 to $28 is 12 over 40, which is 30%.
Why? Spread a fixed cost of 2,000: at 100 units it is $20 per unit, at 400 units $5, a fall of 75%. Variable cost goes from 2,000, which is $20 per unit, to 9,200, which is $23, up 15%.
That is the main line of the lesson: average cost falls because fixed cost is spread thinner, while variable cost per unit is quietly rising.
Make students convert to total cost before describing structure.
First move: total cost is average cost times quantity, so 100 units cost 4,000, 400 units cost 11,200 and 1,200 units cost 42,000.
The fall from $40 to $28 is 12 over 40, which is 30%.
Why? Spread a fixed cost of 2,000: at 100 units it is $20 per unit, at 400 units $5, a fall of 75%. Variable cost goes from 2,000, which is $20 per unit, to 9,200, which is $23, up 15%.
That is the main line of the lesson: average cost falls because fixed cost is spread thinner, while variable cost per unit is quietly rising.
Make students convert to total cost before describing structure.
Have students restate: average cost usually falls because fixed cost is spread, not because variable cost falls.
Scene 2: Falling, flat, rising
Plot the five points into a shallow U: falling from 100 to 400 units (economies of scale), flat from 400 to 800 (minimum efficient scale), rising at 1,200 (diseconomies, up 25%).
Three sources of economies: spreading fixed cost, which dominates here; division of labour and specialisation; and bulk buying discounts.
Three sources of diseconomies: too many management layers, rising coordination cost, and input or labour shortages pushing prices up.
Minimum efficient scale is the smallest output at which long-run average cost first reaches its minimum, here 400 units. Anything smaller is at a cost disadvantage.
Policy reading: if the market can only support one 400-unit plant, the shape is a natural monopoly; if demand is 4,000 units, ten plants fit and competition policy should let them coexist.
Warn that the flat segment is still the minimum, not unused capacity.
Three sources of economies: spreading fixed cost, which dominates here; division of labour and specialisation; and bulk buying discounts.
Three sources of diseconomies: too many management layers, rising coordination cost, and input or labour shortages pushing prices up.
Minimum efficient scale is the smallest output at which long-run average cost first reaches its minimum, here 400 units. Anything smaller is at a cost disadvantage.
Policy reading: if the market can only support one 400-unit plant, the shape is a natural monopoly; if demand is 4,000 units, ten plants fit and competition policy should let them coexist.
Warn that the flat segment is still the minimum, not unused capacity.
Have students restate: minimum efficient scale is the smallest output at the lowest average cost.
Scene 3: Comparing plant sizes with numbers
Two plants of 200 units cost 6,400 each, so 12,800 together. One plant of 400 units costs 11,200. The gap is 1,600, or 12.5%.
Convert to per unit: 1,600 over 400 is $4 a unit, a figure far more useful than saying much cheaper, because it can enter a price discussion directly.
Then ask what happens if the large plant pays $5 a unit extra in transport. Merging is then $1 a unit worse, so the scale advantage is eaten by freight.
This is the standard evaluation move: economies exist, but other costs can offset them.
Close with a sentence students can reuse: compare cost per unit first, then ask what offsets it.
Convert to per unit: 1,600 over 400 is $4 a unit, a figure far more useful than saying much cheaper, because it can enter a price discussion directly.
Then ask what happens if the large plant pays $5 a unit extra in transport. Merging is then $1 a unit worse, so the scale advantage is eaten by freight.
This is the standard evaluation move: economies exist, but other costs can offset them.
Close with a sentence students can reuse: compare cost per unit first, then ask what offsets it.
Have students restate: a merger pays only if unit savings beat the offsetting costs.
04 Question types and worked steps
| Type | Example | Steps | Answer |
|---|---|---|---|
| Calculation | Total cost from average cost | Multiply by output | 4,000 and 11,200 |
| Explanation | Why average cost falls | Fixed cost spreading plus division of labour | Two causes, one line each |
| Diagram | Mark minimum efficient scale | First minimum of the LRAC curve | 400 units |
| Evaluation | Whether a merger pays | Unit gap against offsetting costs | $4 gap, $5 freight, so no |
Sanity check (teach this): Multiply before subtracting: total cost first, then remove fixed cost.
Use the original value as the denominator: 12 over 40 is 30%, not 12 over 28.
The 25% rise is 7 over 28, measured from 400 units.
Minimum efficient scale is the first minimum, so take 400, not 800.
The unit gap divides by the large plant output, not by the combined output.
Use the original value as the denominator: 12 over 40 is 30%, not 12 over 28.
The 25% rise is 7 over 28, measured from 400 units.
Minimum efficient scale is the first minimum, so take 400, not 800.
The unit gap divides by the large plant output, not by the combined output.
05 Independent practice (3 questions)
| Question | Answer | What to watch |
|---|---|---|
| Total cost at 400 units | 11,200 | Check multiplication by output |
| Fixed cost per unit at 100 and 400 | $20 and $5 | Check fixed cost is removed before dividing |
| Extra cost of two small plants | 1,600, or 12.5% | Check the denominator is 12,800 |
06 Common mistakes and what to say
| Mistake | Student writes | Say this |
|---|---|---|
| Treating average as total | Writes that 400 units cost $28 | Total cost is 400 times 28, which is 11,200. |
| Assuming variable cost falls | Writes that labour gets cheaper as output grows | Variable cost rises from $20 to $23 here; the fall is in spread fixed cost. |
| Taking the largest output | Answers that minimum efficient scale is 1,200 units | It is the smallest output at the lowest cost, which is 400. |
| Ignoring offsets | Writes that merging always saves 12.5% | Freight and coordination must be compared: $4 against $5 reverses the answer. |
07 Homework (paper, section and question numbers)
- Secondary Economics chapter index — Firms and production unit, questions 1 to 4
- Production cost and diminishing returns — Redo the short-run cost table first
- Lesson-prep hub — Compare other subjects
08 Exit check (last 5 minutes)
| Question | Answer | Decision |
|---|---|---|
| Total cost at 400 units | 11,200 | All three right means policy reading is safe |
| Minimum efficient scale | 400 units | One wrong means re-teach act two |
| Gap between two small plants and one large | 1,600, or 12.5% | Two wrong means repeat act three |
09 Tutor FAQ
Are economies of scale the same as returns to scale?
Not quite. Returns to scale compare inputs with output; economies of scale describe average cost falling, including purchasing and management effects.
Can minimum efficient scale be a range?
Yes. Here 400 and 800 units both cost $28, so the efficient scale is a segment.
Must small plants fail?
No. They survive on differentiation, location or niche demand, but not on price against a large plant.
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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.
