Monopoly is different from a perfectly competitive firm in that a monopoly

Question

BlackTom AI · Accepted Answer

A monopoly faces the market demand curve and therefore must lower price to sell additional units; this makes marginal revenue (MR) less than price (demand) for each extra unit sold. 1) Relevant concepts: - Demand curve (price as a function of quantity) for a monopolist is downward sloping. - Total revenue TR = P(Q) · Q; marginal revenue MR = d(TR)/dQ. - Price takers (perfect competition) face horizontal demand; price equals marginal revenue. Price makers (monopoly) do not. 2) Step-by-step reasoning and derivation: Start with a linear demand: P = a − bQ. Total revenue: TR = P·Q = (a − bQ)Q = aQ − bQ^2. Differentiate TR with respect to Q to get MR: MR = d(TR)/dQ = a − 2bQ. Compare MR to price: P = a − bQ, so MR = P − bQ. Since bQ > 0 for Q > 0, MR < P for any positive output. Thus the MR curve lies below the demand curve at every positive quantity. 3) Intermediate steps shown: - TR = aQ − bQ^2 - MR = d/dQ (aQ − bQ^2) = a − 2bQ - MR = (a − bQ) − bQ = P − bQ < P for Q > 0 4) Why the correct answer is correct: Because selling an additional unit forces the monopolist to reduce price on all units sold (for a single-price monopoly), the additional revenue from the next unit (MR) is the price received minus the loss from lowering price on prior units; algebraically MR < P, so the MR curve lies below the demand curve. 5) Why the other choices are incorrect: - “does not have a U-shaped average total cost curve”: Both monopolies and competitive firms can have U-shaped ATC; the cost shape is independent of market structure. - “has an average fixed cost curve that is perfectly horizontal”: AFC = fixed cost/Q, which declines with Q, so it is downward sloping, not horizontal. - “always earns economic profits”: Monopolies can make profits, break even, or incur losses depending on costs and demand. - “operates in the inelastic segment of its demand curve”: Profit-maximizing monopolists produce where MR = MC; MR must be nonnegative, so they never choose the inelastic portion where MR < 0. 6) Conclusion: Therefore the correct choice is “has a marginal revenue curve that lies below its demand curve,” which matches the provided answer.

Monopoly is different from a perfectly competitive firm in that a monopoly单项选择题

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