The condition for allocative efficiency is

Question

BlackTom AI · Accepted Answer

Allocative efficiency occurs where price (the marginal benefit to consumers) equals marginal cost (the marginal cost of producing an extra unit).

1) Relevant concepts:
- Marginal benefit (MB) is the extra value consumers place on one more unit; in competitive markets MB = price (P).
- Marginal cost (MC) is the extra cost of producing one more unit.
- Total surplus (TS) = consumer surplus + producer surplus; TS is maximized when MB = MC.

2) Step‑by‑step reasoning:
- Represent total surplus as TS(Q) = ∫0^Q MB(q) dq − ∫0^Q MC(q) dq.
- To find the Q that maximizes TS, take the derivative dTS/dQ = MB(Q) − MC(Q).
- Set first order condition to zero: MB(Q) − MC(Q) = 0 → MB(Q) = MC(Q).
- In a competitive market MB = P, so the condition becomes P = MC.

3) Intermediate calculation shown:
- d/dQ [∫0^Q MB(q) dq] = MB(Q); d/dQ [∫0^Q MC(q) dq] = MC(Q).
- Thus maximize TS ⇒ MB(Q) − MC(Q) = 0 ⇒ MB(Q) = MC(Q) ⇒ P = MC.

4) Why this is correct:
- When P = MC, the last unit’s value to consumers equals the cost to society of producing it, so no net welfare gain or loss from producing one more or one fewer unit — social welfare is maximized.

5) Why the other options are incorrect:
- a. MC = MR is the firm’s profit‑maximizing condition (or loss‑minimizing) in any market structure, not the social welfare condition. For monopolies MR < P, so MC = MR typically gives P > MC and reduces welfare.
- c. Average costs at a minimum is productive efficiency (lowest average cost), not allocative efficiency (which concerns marginal values).
- d. Price higher than average cost indicates positive economic profit, not that allocation maximizes welfare.

Conclusion: The condition for allocative efficiency is price equals marginal cost, so answer b is correct.

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