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Difficulty: HardScales of Production and Economies of Scale

A commercial cassava processing firm located in Ibadan expands its scale of operation by increasing all of its production inputs (labor, machinery, and land) simultaneously by 60%60\%. Following this expansion, the firm's total output of cassava flour increases from 500500 metric tonnes to 900900 metric tonnes per month. Based on this outcome, which of the following best describes the economic law demonstrated by the firm and its effect on long-run unit cost?

  1. The firm exhibits increasing returns to scale, resulting in economies of scale and falling long-run average total cost.Answer
  2. B
    The firm exhibits diminishing marginal returns, causing its short-run average variable cost to decline.
  3. C
    The firm exhibits decreasing returns to scale, leading to internal diseconomies of scale and rising average cost.
  4. D
    The firm exhibits constant returns to scale, keeping long-run average cost entirely unchanged.

Answer

The firm exhibits increasing returns to scale, resulting in economies of scale and falling long-run average total cost.
The percentage change in output is 900−500500×100%=80%\frac{900 - 500}{500} \times 100\% = 80\%. Because the percentage expansion in output (80%80\%) exceeds the percentage expansion in all inputs (60%60\%), the firm experiences increasing returns to scale. In long-run production theory, increasing returns to scale imply that average costs decrease as output expands, generating economies of scale.

Step-by-Step Solution

1
Calculate the percentage change in total output.
Percentage Change in Output=900−500500×100%=400500×100%=80%\text{Percentage Change in Output} = \frac{900 - 500}{500} \times 100\% = \frac{400}{500} \times 100\% = 80\%.
Determining the proportionate growth in output is required to evaluate returns to scale.
2
Compare the percentage change in output with the percentage change in inputs.
Output increased by 80%80\%, which is greater than the 60%60\% increase in all production inputs.
Returns to scale measures how output responds when all inputs are scaled proportionately in the long run.
3
Identify the long-run production condition and cost implication.
Since %ΔOutput>%ΔInputs\% \Delta \text{Output} > \% \Delta \text{Inputs}, the firm experiences increasing returns to scale, which corresponds to economies of scale (decreasing long-run average total cost).
When output expands faster than input factors, cost per unit of output declines.

Key Concept

Increasing Returns to Scale and Economies of Scale
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Topics

Scales of Production and Economies of Scale

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