If a firm has zero variable costs or only fixed cost, under which market structure will the equilibrium quantity supplied be determined at the point where marginal revenue is zero?

Introduction / Context:
This question tests understanding of profit maximisation under different market structures when a firm faces zero variable cost or only fixed cost. In such a situation, total cost does not change with output, so the firm essentially maximises total revenue. The key is to recall which market structure allows a single firm to influence price through its output decisions and therefore leads to a condition where marginal revenue equals zero at the revenue maximising output.

Given Data / Assumptions:

• The firm has zero variable cost or only fixed cost, so total cost is constant with respect to output.
• Profit equals total revenue minus total cost, and since cost is constant, profit maximisation coincides with revenue maximisation.
• We are asked which market structure yields equilibrium where marginal revenue is zero.
• Standard assumptions for monopoly and perfect competition apply.

Concept / Approach:
In perfect competition, an individual firm is a price taker and faces a perfectly elastic demand curve. Its marginal revenue equals the given market price for all levels of output and never becomes zero within the relevant range. In contrast, a monopolist faces a downward sloping market demand curve. As the monopolist expands output, price falls, and marginal revenue decreases and can eventually become zero. When cost is zero, profit is maximised where total revenue is maximised, which occurs where marginal revenue is zero. This condition is characteristic of a revenue maximising monopoly.

Step-by-Step Solution:
1. With zero variable cost, total cost is either zero or only fixed, so it does not depend on output.2. Profit equals total revenue minus total cost. With constant total cost, profit is maximised when total revenue is maximised.3. Total revenue is maximised at the output level where marginal revenue equals zero, because at that point any further increase in output would reduce total revenue.4. Only a firm that has control over price through its output choices will face a downward sloping demand curve and a marginal revenue curve that can fall to zero.5. This description matches a monopoly rather than a perfectly competitive firm, which always sells at a fixed market price with marginal revenue equal to price.6. Therefore, under monopoly, a zero cost firm will choose an equilibrium output at the point where marginal revenue becomes zero.

Verification / Alternative check:
Consider a simple linear demand curve for a monopolist such as P = a - bQ, where P is price and Q is quantity. Total revenue is TR = P * Q = aQ - bQ^2. Marginal revenue is d(TR)/dQ = a - 2bQ. Setting marginal revenue equal to zero gives a - 2bQ = 0, so Q = a/(2b). This is the revenue maximising output. With zero cost, profit is highest at this quantity. In perfect competition, however, TR = P * Q with P constant, and marginal revenue is always equal to P, never zero for positive prices. This confirms that the scenario in the question is associated with monopoly.

Why Other Options Are Wrong:
Option A: In perfect competition, a single firm is a price taker. Marginal revenue equals price and does not fall to zero within the relevant range, so equilibrium is not given by marginal revenue equal to zero.
Option C: Oligopoly involves a few firms with interdependent decisions. The simple marginal revenue equals zero rule for a single firm with full market control does not usually describe its equilibrium in such basic questions.
Option D: Monopolistic competition involves many firms selling differentiated products. While each has some market power, basic exam questions about a single firm with full control over the market are typically referring to monopoly, not monopolistic competition.
Option E: Duopoly is a special case of oligopoly with two firms and strategic interaction, which again is not what is implied in this question.

Common Pitfalls:
A common confusion is between profit maximisation and revenue maximisation. Usually, profit maximisation occurs where marginal revenue equals marginal cost. In this special case of zero cost, marginal cost is zero, and profit maximisation could occur where marginal revenue equals zero if the entire relevant range has marginal cost of zero. Students also sometimes forget that a perfectly competitive firm has marginal revenue equal to price and does not have a downward sloping demand curve. Keeping these distinctions clear helps avoid mistakes.

Final Answer:
For a firm with zero variable costs or only fixed cost, the equilibrium quantity supplied at the point where marginal revenue is zero is characteristic of a monopoly.