18. An economy is producing at the least-cost rate of production when:
A. price and the minimum average total cost are equal.
B. marginal cost is greater than average total cost.
C. marginal revenue is greater than price.
D. price and marginal revenue are equal.

Question

BlackTom AI · Accepted Answer

Productive efficiency (the least-cost rate of production) occurs at the output level where average total cost (ATC) is minimized.

1. Relevant knowledge points and concepts
- Average total cost (ATC) = total cost divided by output; its minimum is the point of least-cost production (productive efficiency).
- Marginal cost (MC) is the change in total cost from producing one more unit. The MC curve intersects the ATC curve at ATC’s minimum.
- For a price-taking (perfectly competitive) firm, price (P) equals marginal revenue (MR). In long-run equilibrium, P = MC = minimum ATC.

2. Step-by-step reasoning
- The least-cost rate is defined by the output q* that minimizes ATC(q). At a minimum, the derivative of ATC with respect to q is zero.
- Differentiate ATC(q) = C(q)/q and set d(ATC)/dq = 0, which yields the condition MC(q*) = ATC(q*). Thus the MC curve crosses ATC at its minimum.
- In long-run competitive equilibrium, price equals marginal cost (P = MC) and firms earn zero economic profit so P equals the minimum ATC. Therefore P = min ATC at the least-cost rate.

3. Calculational detail (intermediate steps)
- ATC(q) = C(q)/q. d(ATC)/dq = [q·C'(q) - C(q)]/q^2.
- Setting d(ATC)/dq = 0 gives q·C'(q) - C(q) = 0 → C'(q) = C(q)/q → MC(q) = ATC(q).
- So the minimizing q satisfies MC = ATC; for a competitive firm in long run, P = MC = ATC(min).

4. Why the correct answer is correct
- Choice A states price and the minimum average total cost are equal. That matches the long-run least-cost condition where firms produce at the output minimizing ATC and price equals that minimum ATC.

5. Why the other options are incorrect
- B: “MC > ATC” describes a region where ATC is rising, not minimized; it is not the least-cost rate.
- C: “MR > price” cannot hold for a price-taking firm because MR = price.
- D: “price and marginal revenue are equal” is true in perfect competition but is a general property, not the defining condition for least-cost output (it doesn’t ensure ATC is minimized).

6. Conclusion
Therefore the correct choice is A: price and the minimum average total cost are equal, which matches the provided answer.

18. An economy is producing at the least-cost rate of production when: A. price and the minimum average total cost are equal. B. marginal cost is greater than average total cost. C. marginal revenue is greater than price. D. price and marginal revenue are equal. Single choice

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