Questions: Production Function and Returns to Scale

Question 1

A firm doubles both its capital and labor inputs, and output exactly doubles. What does this describe?

• A. Diminishing marginal returns to labor
• B. Increasing returns to scale
• C. Constant returns to scale
• D. Decreasing returns to scale

Answer: (C)

Returns to scale describe the effect of scaling all inputs proportionally. If doubling all inputs exactly doubles output (output scales by the same factor), the technology exhibits constant returns to scale. Increasing returns would mean output more than doubles; decreasing returns means it less than doubles. Diminishing marginal returns is a separate concept that applies to adding one input while the other is held fixed.

Question 2

Diminishing marginal returns to labor means that each additional worker hired reduces the firm's total output.

• T. True
• F. False

Answer: False

Diminishing marginal returns means each additional worker adds less to output than the previous one — but they still add a positive amount. Total output is still increasing, just at a decreasing rate. Marginal product becomes negative only when the workforce is so crowded that adding another worker actually gets in the way, which is a distinct and more extreme situation.

Question 3

Explain why diminishing marginal returns and decreasing returns to scale are different concepts, not the same thing.

Model answer: Diminishing marginal returns is a short-run phenomenon: it describes what happens when only one input (e.g., labor) increases while others (e.g., capital) are held fixed. Decreasing returns to scale is a long-run concept: it describes what happens when all inputs are scaled up proportionally. A technology can exhibit constant returns to scale in the long run while still showing diminishing marginal returns to any single input in the short run.

The distinction is about what is varying. In the short run, some inputs are fixed, so adding more of one input runs into the constraint imposed by the fixed factor (crowding effects). Returns to scale exist in a hypothetical long run where the firm can adjust every input simultaneously — a completely different question about the technology's inherent scalability.