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9609 · 9.1.2

Scale of operations — practice questions

Practice and worked examples for 9609 Scale of operations. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

National retailer merges with rival, doubling stores to 1,200. Unit costs fall 8% year one but rise 3% year three. Explain using economies and diseconomies.

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Year 1 economies: Bulk purchasing from suppliers (technical), single IT/ad campaign (marketing/financial), central warehousing.

Year 3 diseconomies: Integration chaos — duplicate HQs, conflicting cultures (7.2.4), slow decisions (7.1.2 tall hierarchy), demotivated staff fearing redundancy (2.2).

Evaluation: Merger theoretically sound for scale but management failed to capture synergies — need delayering and culture programme before further expansion.

Worked example 2

A furniture manufacturer, 'ComfyChairs Ltd', is considering expanding its production facility. Currently, it produces 50,000 chairs per year. Its annual fixed costs are $200,000 and the variable cost per chair is $10. The proposed expansion would increase output to 150,000 chairs per year. The new, larger factory would have annual fixed costs of $450,000. Due to bulk-buying raw materials, the variable cost per chair is expected to fall by 10%. Calculate the average cost per chair before and after the expansion and explain the result.

Show solution outline

The solution involves calculating the long-run average cost (LRAC) at two different scales of operation.

Step 1: Calculate the current average cost per chair.

  • Current Output = 50,000 chairs
  • Fixed Costs (FC) = 200,000200,000
  • Variable Cost per unit (VC) = 1010
  • Total Variable Cost (TVC) = Output × VC = 50,000 × 10=10 = 500,000
  • Total Cost (TC) = FC + TVC = 200,000+200,000 + 500,000 = 700,000700,000
  • Current Average Cost (AC) = TC / Output = 700,000/50,000=700,000 / 50,000 = 14.00 per chair

Step 2: Calculate the average cost per chair after expansion.

  • New Output = 150,000 chairs
  • New Fixed Costs (FC) = 450,000450,000
  • New Variable Cost per unit (VC) = 10×(1−0.10)=10 \times (1 - 0.10) = 9
  • New Total Variable Cost (TVC) = 150,000 × 9=9 = 1,350,000
  • New Total Cost (TC) = 450,000+450,000 + 1,350,000 = 1,800,0001,800,000
  • New Average Cost (AC) = TC / Output = 1,800,000/150,000=1,800,000 / 150,000 = 12.00 per chair

Step 3: Conclusion and Explanation.

  • The average cost per chair falls from 14.00to14.00 to 12.00, a saving of $2.00 per unit.
  • This demonstrates economies of scale. The cost reduction is due to:
    • Purchasing economies: The firm secured a 10% discount on raw materials from buying in bulk, reducing the variable cost per unit.
    • Technical economies: Although total fixed costs increased, they did not triple with the tripled output. The more efficient, larger-scale machinery and facility spread these fixed costs over a much larger number of units, reducing the fixed cost per unit from 4(4 (200k/50k) to 3(3 (450k/150k).
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