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Difficulty: Very hardScales of Production and Economies of Scale

A pharmaceutical manufacturing company based in Aba expands its operation by increasing all factor inputs by 40%40\%. Consequently, its total daily output of antibiotics increases from 5,0005,000 boxes to 8,4008,400 boxes, while its long-run total cost rises from ₦25,000,000\text{₦}25,000,000 to ₦33,600,000\text{₦}33,600,000. Based on these production metrics, how are the firm's scale of production and long-run average cost (LRAC) affected?

  1. The firm exhibits increasing returns to scale, causing its long-run average cost to fall from ₦5,000\text{₦}5,000 to ₦4,000\text{₦}4,000 per unit.Answer
  2. B
    The firm exhibits decreasing returns to scale because its total cost increased from ₦25,000,000\text{₦}25,000,000 to ₦33,600,000\text{₦}33,600,000.
  3. C
    The firm experiences the short-run law of diminishing returns because production expanded rapidly.
  4. D
    The firm operates under constant returns to scale because both inputs and total expenditures increased simultaneously.

Answer

The firm exhibits increasing returns to scale, causing its long-run average cost to fall from ₦5,000\text{₦}5,000 to ₦4,000\text{₦}4,000 per unit.
The correct answer identifies that output increased by 68%68\% while factor inputs increased by only 40%40\%. Because the percentage increase in output exceeds the percentage increase in inputs, the firm experiences increasing returns to scale. Furthermore, long-run average cost drops from ₦5,000\text{₦}5,000 to ₦4,000\text{₦}4,000 per unit, demonstrating economies of scale.

Step-by-Step Solution

1
Calculate the percentage change in total output
Percentage change in output = 8,400−5,0005,000×100%=68%\frac{8,400 - 5,000}{5,000} \times 100\% = 68\%
Determining output growth rate is necessary to compare against input growth rate.
2
Compare output growth rate to input growth rate
Output increased by 68%68\% while all inputs increased by 40%40\%. Since 68%>40%68\% > 40\%, the firm experiences increasing returns to scale.
When output expands by a higher percentage than inputs, economies of scale / increasing returns to scale are present.
3
Calculate initial and new long-run average cost (LRAC)
Initial LRAC = ₦25,000,0005,000=₦5,000\frac{\text{₦}25,000,000}{5,000} = \text{₦}5,000 per unit. New LRAC = ₦33,600,0008,400=₦4,000\frac{\text{₦}33,600,000}{8,400} = \text{₦}4,000 per unit.
Evaluating average cost demonstrates the cost-saving effect of economies of scale.

Key Concept

Economies of Scale and Long-Run Average Cost
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Topics

Scales of Production and Economies of Scale

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