Which of the following is true for a monopoly firm?

Question

BlackTom AI · Accepted Answer

Monopolies face a downward-sloping market demand, so marginal revenue (MR) is below price and barriers to entry allow persistent profits. 1) Relevant knowledge points and concepts - Monopoly: single seller, faces market demand curve (P(Q)), has barriers to entry. - Profit maximization: choose Q where MR = MC, then set price P from demand at that Q. - Allocative efficiency: occurs when P = MC; productive efficiency often when output is at minimum average cost (AC). - In perfect competition, free entry drives economic profit to zero in the long run; with barriers, monopoly can sustain economic profit. 2) Step-by-step reasoning - Let demand be P = a − bQ (a, b > 0). Total revenue TR = P·Q = aQ − bQ^2. - MR = d(TR)/dQ = a − 2bQ. - For any positive Q, MR = a − 2bQ = (a − bQ) − bQ = P − bQ < P. So MR < P. - Profit-max rule: set MR = MC to find Q*. Then price P(Q*) > MR = MC, so P > MC. Thus monopoly charges P > MC and produces less than the allocatively efficient output. 3) Intermediate calculation shown above (TR, MR derivation) demonstrates MR < P. 4) Why the correct answer is correct - Because of barriers to entry, a monopoly that earns positive economic profit in the short run can prevent rivals from entering; therefore economic profit can persist into the long run. This is a defining feature of monopoly contrasted with perfect competition. 5) Why other options are incorrect - b. False: allocative efficiency requires P = MC, but monopoly sets P > MC. - c. False: as shown, MR < P for a downward-sloping demand (not more). - d. False: profit maximization occurs at MR = MC, not where AC is minimized; monopoly typically produces below the output that minimizes AC. 6) Conclusion All reasoning confirms option a ("Economic profit is possible in the long run.") is correct.

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