The condition for productive efficiency is

Question

BlackTom AI · Accepted Answer

Productive efficiency occurs when output is produced at the lowest possible average cost, so firms use the least-cost combination of inputs and operate at the “efficient scale.”

1. Relevant knowledge points and concepts
- Average cost (AC or ATC) = total cost divided by quantity (C/Q).  
- Marginal cost (MC) = derivative of total cost with respect to quantity (dC/dQ).  
- The minimum of the AC curve is the output level where AC is lowest (efficient scale). At that minimum, d(AC)/dQ = 0 and MC = AC. Productive efficiency refers to minimizing per-unit cost, not maximizing profit or equating price to marginal cost (those are different concepts).

2. Step-by-step reasoning
- Productive efficiency means producing at the point on the average cost curve where average cost is minimized.  
- Mathematically, set the derivative of AC with respect to Q equal to zero to find the minimum.

3. Calculations / intermediate steps
- AC(Q) = C(Q)/Q. Differentiate: d(AC)/dQ = [Q·C'(Q) - C(Q)] / Q^2.  
- Set derivative to zero: Q·C'(Q) - C(Q) = 0 → C'(Q) = C(Q)/Q → MC = AC.  
- Thus the minimum of AC occurs where MC = AC; the defining condition for productive efficiency is AC at its minimum.

4. Why the correct answer is correct
- Option d (“average costs are at a minimum”) exactly states the definition of productive efficiency: producing at the lowest average cost (efficient scale). The calculus above shows this is where MC = AC, but the defining statement is the AC minimum.

5. Why the other options are incorrect
- a. “MC = MR” is the profit-maximization rule, not a condition for productive efficiency.  
- b. “Price = MC” is allocative efficiency (socially optimal mix of goods), not productive efficiency.  
- c. “Price higher than AC” indicates positive economic profit, not cost minimization or efficiency.

6. Conclusion
- Therefore the correct condition for productive efficiency is that average costs are at a minimum (option d), which matches the provided answer.

The condition for productive efficiency is单项选择题

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