When a firm is subject to constant returns to scale and decides to replicate its existing operation, which of the following remains the same?

Question

BlackTom AI · Accepted Answer

Under constant returns to scale (CRS), average cost remains unchanged because costs increase proportionally with output.

1. Relevant knowledge points and concepts
- Constant returns to scale: if all inputs are scaled by factor k, output scales by k as well.
- Total cost function C(q) under CRS satisfies C(kq) = k C(q).
- Average cost (AC) is defined as AC(q) = C(q)/q.
- Profit π = p·q − C(q) (where p is price); total cost and output scale with k under CRS.

2. Complete reasoning process step by step
- Start with original output q and total cost C(q).
- Replicate the operation by factor k (for example, k = 2 for doubling).
- Under CRS, new output = kq and new total cost = C(kq) = k C(q).

3. Calculations and intermediate steps
- Original average cost: AC(q) = C(q)/q.
- New average cost: AC(kq) = C(kq)/(kq) = [k C(q)]/(kq) = C(q)/q = AC(q).
- Original profit: π = p q − C(q).
- New profit: π' = p (kq) − C(kq) = p k q − k C(q) = k (p q − C(q)) = k π.
- Total cost changes from C(q) to k C(q).
- Output changes from q to k q.

4. Why the correct answer is correct
Because AC(kq) algebraically simplifies to AC(q) when C(kq)=kC(q). The cost per unit does not change under CRS since both numerator (total cost) and denominator (quantity) scale by the same factor.

5. Why the other options are incorrect
- The firm’s profit: scales by k (π' = k π), so it is not generally the same unless π = 0.
- Total costs: change proportionally (C' = k C(q)), so they are not the same.
- Output: changes to k q, so it is not the same.

6. Conclusion
Average cost remains the same under replication with constant returns to scale. This confirms the provided correct answer: Average cost.

When a firm is subject to constant returns to scale and decides to replicate its existing operation, which of the following remains the same?单项选择题

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